Method for determining the installation position of a vibration absorber, vibration absorber, and design method for a vibration absorber

Abstract

To more effectively reduce heavy floor impact noise.SOLUTION: An installation position determination method of a vibration absorber includes: a floor condition identifying process S11 for identifying a condition of a floor; a resonance frequency calculation process S12 for calculating a resonance frequency of the floor on the basis of the condition of the floor; a resonance range calculation process S13 for calculating a resonance range which is a range in which an index value indicating ease of resonance of the floor becomes larger than a threshold by using the resonance frequency and a mode function expressing a vibration mode of the floor; a vibration absorber characteristic determination process S14 for determining a characteristic of the vibration absorber on the basis of the resonance frequency; and a vibration absorber installation position determination process S15 for determining an installation position of the vibration absorber on the basis of a resonance range Ak.SELECTED DRAWING: Figure 10

Description

[Technical Field]

[0001] The present invention relates to a method for determining the installation position of a vibration absorber, a vibration absorber, and a method for designing a vibration absorber. [Background technology]

[0002] In apartment buildings and other multi-unit dwellings, impact noise is transmitted to the floor below when objects fall on the floor above or when people jump. Impact noise can be classified into light impact noise and heavy impact noise. Light impact noise includes, for example, the sound of dropping a light object such as a spoon, or the sound of footsteps in slippers. Heavy impact noise includes, for example, the sound produced when people jump or run around, or when heavy objects are dropped. Light impact noise can be easily reduced by laying carpet on the floor, but reducing heavy impact noise basically requires making the floor thicker. For this reason, countermeasures against heavy impact noise are not easy. In contrast, for example, Patent Document 1 discloses a configuration for reducing structure-borne sound by placing vibration absorbers on the floor when the floor is a concrete slab. In this configuration, multiple vibration absorbers are evenly distributed on the floor. It is desirable to reduce heavy impact noise more effectively. [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] Patent No. 6478516 [Overview of the project] [Problems that the invention aims to solve]

[0004] The problem that this invention aims to solve is to provide a method for determining the installation position of a vibration absorber, a vibration absorber, and a method for designing a vibration absorber that can more effectively reduce heavy floor impact noise. [Means for solving the problem]

[0005] To solve the above problems, the present invention employs the following means. In other words, the present invention provides a method for determining the installation position of a vibration absorber, which, when installing a plurality of vibration absorbers on a floor, each comprising a mass and a spring body provided beneath the mass, in order to reduce heavy floor impact noise, determines the installation position of each of the vibration absorbers, and is characterized by comprising: a floor condition identification step of identifying the conditions of the floor; a resonance frequency calculation step of calculating the resonance frequency of the floor based on the floor conditions; a resonance range calculation step of calculating a resonance range in which an index value indicating the ease of resonance of the floor is greater than a threshold value, using the resonance frequency and a mode function that expresses the vibration mode of the floor; a vibration absorber characteristic determination step of determining the characteristics of the vibration absorber based on the resonance frequency; and a vibration absorber installation position determination step of determining the installation position of the vibration absorber based on the resonance range. In this configuration, the resonance frequency calculation step calculates the floor's resonance frequency based on the floor conditions identified in the floor condition identification step. The resonance range calculation step calculates the resonance range, which is the range where an index value indicating the floor's susceptibility to resonance exceeds a threshold, using the floor's resonance frequency and a mode function representing the floor's vibration modes. The vibration absorber characteristic determination step determines the characteristics of the vibration absorber based on the calculated resonance frequency. Furthermore, the vibration absorber installation position determination step determines the installation position of the vibration absorber with the determined characteristics based on the resonance range. In this way, vibration absorbers with characteristics corresponding to the floor's resonance frequency are installed at the installation positions determined based on the resonance range where the degree of resonance exceeds the threshold. This allows for efficient placement of vibration absorbers, effectively reducing heavy floor impact noise.

[0006] In one embodiment of the present invention, the variable of the mode function includes an order which is a value relating to the number of resonance ranges, and in the resonance frequency calculation step, the resonance frequency is calculated corresponding to each of a plurality of values ​​of the order, and in the resonance range calculation step, a value is selected from the plurality of values ​​in which the corresponding resonance frequency falls within the range of frequencies to be reduced, and this value is substituted into the order which is the variable of the mode function, and the resonance range is calculated by comparing this with the threshold. Floors vibrate in various ways. For example, when a floor consists of beams or joists and planks placed on top of those beams or joists, the number of resonance ranges—that is, areas prone to vibration—which are the ranges in which the index value indicating susceptibility to resonance exceeds a threshold, varies depending on the conditions under which the vibration occurs, such as the excitation point. Similarly, even when the floor is plank-shaped with a uniform cross-section, the number of resonance ranges in both the long and short directions of the floor varies depending on the conditions under which the vibration occurs. Thus, the order, which is a value related to the number of resonance ranges, can take on multiple values. Therefore, the mode function that represents the vibration modes of a floor includes the order as a variable. As the order can take on multiple values, in the configuration described above, the resonance frequency calculation step calculates the resonance frequency for each of the multiple values ​​of the order. Then, in the resonance range calculation step, a value is selected from the multiple values ​​of the order that includes the range of frequencies to be reduced. Here, in the mode function, the value selected as described above is substituted for the variable order, which is considered to represent the vibration mode of the vibration when the resonance frequency is included in the range of frequencies to be reduced. In the resonance range calculation step, the resonance range is calculated using the mode function expressed in this way. In this way, the resonance range when the floor vibrates at a resonance frequency included in the range of frequencies to be reduced is appropriately calculated, and the installation position of the vibration absorber is determined based on this resonance range, so that the vibration absorber can be installed in a more appropriate location and heavy floor impact sound can be reduced more effectively.

[0007] In one aspect of the present invention, when the floor includes a beam or joist and a board material provided on the beam or joist, in the resonance frequency calculation step, the length l of the beam or joist, the Young's modulus E in the axial direction in which the beam or joist extends, the second moment of area I in the axial direction, the total cross-sectional area S of one of the beam or joist and the board material supported by the beam or joist corresponding to the beam or joist when the floor is viewed in cross-section in a direction orthogonal to the axial direction, the density ρ of the floor, the order n, and the coefficient α determined according to the length l of the beam or joist, the following resonance frequency formula (1) [Number] is used to calculate the resonance frequency f fix (n) corresponding to each of the plurality of values of the order n. According to such a configuration, when the floor includes a beam or joist and a board material provided on the beam or joist, in the resonance frequency calculation step, the resonance frequency of the floor based on the conditions of the floor can be appropriately calculated. Therefore, it becomes possible to more appropriately determine and calculate the characteristics of the vibration absorber and the resonance range, and to appropriately determine the installation position of the vibration absorber. Accordingly, the impact sound of the heavy floor can be reduced more effectively.

[0008] In one aspect of the present invention, in the resonance range calculation step, based on the selected value of the order n, as the mode function, the following formula (2) [Number] is used to calculate an index value indicating the ease of resonance at each position x with the end of the beam or joist as the origin when viewed in plan, and a range in which the index value is greater than the threshold value is determined as the resonance range. According to such a configuration, when the floor includes a beam or joist and a board material provided on the beam or joist, the resonance range can be appropriately determined.

[0009] In one embodiment of the present invention, when the floor is plate-shaped and has a uniform cross-section, the resonance frequency calculation step is performed using the following resonance frequency formula (3), which is expressed by the length a in the long side direction of the floor, the length b in the short side direction of the floor, Poisson's ratio ν, Young's modulus E, second moment of area I, the order m in the long side direction, and the order n in the short side direction.

number

[0010] In one embodiment of the present invention, in the resonance range calculation step, from among a plurality of combinations of the order m in the long side direction and the order n in the short side direction, a combination is selected in which the corresponding resonance frequency falls within the range of frequencies to be reduced, and based on the selected combination, the mode function is given by the following equation (4):

number

[0011] In one embodiment of the present invention, the mass body is a granular body enclosed in a bag, the spring body comprises one or more laminated bodies formed by stacking and connecting multiple sheet materials vertically, and the vibration absorber further comprises an outer sheet material that integrally encloses the mass body and the spring body. In this configuration, the mass is supported from below by a spring, and the vibration absorber functions as a dynamic vibration absorber that dampens vibrations input from the outside. By installing such a vibration absorber at a location determined based on the resonance range where the degree of resonance exceeds a threshold, heavy floor impact noise can be effectively reduced. Furthermore, since the mass and spring are integrally encased in the outer sheet material, there is no need to transport the mass and spring separately during installation, making it easy to handle the vibration absorber. Furthermore, because the laminate is modularized, it is easy to handle, and the process of changing the spring constant of the vibration absorber by changing or adjusting the number of laminates is also easy.

[0012] Furthermore, the vibration absorber of the present invention comprises a mass body, a spring body provided below the mass body, and an outer sheet material that integrally encloses the mass body and the spring body, wherein the mass body is a granular body enclosed in a bag, and the spring body comprises one or more laminated bodies formed by stacking and connecting multiple sheet materials vertically. In this configuration, the mass is supported from below by a spring, allowing the vibration absorber to function as a dynamic vibration absorber that dampens vibrations input from the outside. By installing such a vibration absorber on the floor, heavy floor impact noise can be effectively reduced. Furthermore, since the mass and spring are integrally encased in the outer sheet material, there is no need to transport the mass and spring separately during installation, making it easy to handle the vibration absorber. Furthermore, because the laminate is modularized, it is easy to handle, and the process of changing the spring constant of the vibration absorber by changing or adjusting the number of laminates is also easy.

[0013] Furthermore, the vibration absorber design method of the present invention is a vibration absorber design method as described above, characterized by comprising the steps of: identifying the resonant frequency of the floor on which the vibration absorber is installed; and determining the number of laminates to be installed on the floor based on the resonant frequency of the floor. With this configuration, the number of layers to be installed on the floor can be determined based on the resonant frequency of the floor on which the vibration absorber is installed, thereby allowing for the design of a vibration absorber tailored to the floor conditions. By installing such a vibration absorber on the floor, heavy floor impact noise can be effectively reduced. [Effects of the Invention]

[0014] According to the present invention, it is possible to reduce heavy floor impact noise more effectively. [Brief explanation of the drawing]

[0015] [Figure 1] This is a cross-sectional view showing the configuration of a vibration absorber according to an embodiment of the present invention. [Figure 2] This is a cross-sectional view showing an example of a vibration absorber comprising multiple laminated bodies that constitute a spring. [Figure 3] This diagram shows a container for storing and transporting vibration absorbers. [Figure 4] This is a cross-sectional view showing an example of a floor configuration for installing vibration absorbers. [Figure 5] This figure shows an example of the distribution of vibration levels occurring in a floor with a uniform cross-section under multiple vibration modes. [Figure 6] This figure shows another example of the distribution of vibration levels occurring in a floor with a uniform cross-section under multiple vibration modes. [Figure 7] This figure shows another example of the distribution of vibration levels occurring in a floor with a uniform cross-section under multiple vibration modes. [Figure 8] This figure shows yet another example of the distribution of vibration levels occurring in a floor with a uniform cross-section under multiple vibration modes. [Figure 9] This block diagram shows the functional configuration of a computing device that executes the method for determining the installation position of a vibration absorber and the method for designing a vibration absorber according to this embodiment. [Figure 10] This flowchart shows the flow of the method for determining the installation position of the vibration absorber according to this embodiment. [Figure 11] This figure shows the distribution of vibration levels on the floor when the vibration modes are of order m=2 and n=2. [Figure 12] This figure shows an example of the arrangement of vibration absorbers on a floor with a uniform cross-section, determined based on the method for determining the installation position of vibration absorbers according to this embodiment. [Figure 13] This is a cross-sectional view showing an example of a floor configuration in which a vibration absorber is installed, in the case of a floor equipped with beams or joists, according to an embodiment of the present invention. [Figure 14] This figure shows the distribution of vibration levels in a floor with the structure shown in Figure 13, assuming a vibration mode of order n=2. [Figure 15] This figure shows an example of the resonance range when the frequency range targeted for vibration reduction in a floor includes resonance frequencies with multiple combinations of order values. [Figure 16A] This figure shows the arrangement of vibration absorbers in a comparative example, in a verification example for a floor with a uniform cross-section. [Figure 16B] This figure shows the arrangement of vibration absorbers in an example of a verification case for a floor with a uniform cross-section. [Figure 17] This figure shows the verification results of the amount of vibration reduction by the vibration absorber in the example and comparative example. [Figure 18] This is a diagram of a floor used for verification regarding floors with beams or joists. [Figure 19A] This figure shows the vibration distribution at the resonant frequency when the excitation point on the joist is excited. [Figure 19B] This figure shows the vibration distribution at the resonant frequency when the excitation point between the joists is excited. [Figure 20A] This figure shows the vibration distribution at frequencies different from the resonant frequency, which are included in the target frequency range, when an excitation point on a joist is excited. [Figure 20B]This figure shows the vibration distribution at frequencies different from the resonant frequency, which are included in the target frequency range, when the excitation point between the joists is excited. [Modes for carrying out the invention]

[0016] Hereinafter, with reference to the attached drawings, embodiments for implementing the method for determining the installation position of a vibration absorber, the vibration absorber, and the design method for the vibration absorber according to the present invention will be described. In the method for determining the installation position of vibration absorbers according to an embodiment of the present invention, when installing multiple vibration absorbers on the floor in order to reduce heavy floor impact noise, the installation position of each vibration absorber is determined. In the method for determining the installation position of vibration absorbers according to this embodiment, the vibration absorbers used are as shown below. (Vibration absorber) Figure 1 shows a cross-sectional view illustrating the configuration of a vibration absorber according to an embodiment of the present invention. As shown in Figure 1, the vibration absorber 100 comprises a mass body 110, a spring body 120, and an outer sheet material 130. In this embodiment, the vibration absorber 100 functions as a so-called dynamic vibration absorber (tuned mass damper) through the combination of a mass body 110 and a spring body 120 that supports the mass body 110. The mass 110 is a granular material 112 enclosed in a bag 111. The mass 110 has a predetermined mass because the granular material 112 is sealed in the bag 111. For example, dry silica sand (particle size 0.3 to 1.2 mm, unit volume weight 1.6 kg / L) is used as the granular material 112. However, the granular material 112 is not limited to the above, and may be composed of an aggregate of inorganic materials such as sand, gravel, stone, and pebbles. The particle size of the granular material 112 is also not limited to the above. The bag 111 can be made of polyethylene, for example, but is not limited to this, and may be made of other vinyl-based materials as appropriate. The bag 111 may also be made of a nonwoven fabric that allows air to pass through. Furthermore, the size of the bag 111 and the amount of granular material 112 sealed in the bag 111 are not limited and may be set as appropriate. The spring body 120 is provided below the mass body 110. The spring body 120 is configured to be elastically deformable in the vertical direction. The spring body 120 elastically supports the mass body 110. The spring body 120 consists of a laminated body 122 formed by stacking and connecting multiple sheet materials 121 vertically. As the sheet material 121, for example, polyethylene woven fabric used for sandbags can be used. In addition to this, as the sheet material 121, materials that are non-combustible and fire-resistant, such as glass cloth, may also be used. There are no limitations on the thickness of the sheet material 121 or the number of sheets 121 stacked, but it is preferable to select the thickness of the sheet material 121 and the number of stacked sheets so that it functions as a spring body 120. Multiple sheet materials 121 stacked as the laminated body 122 can be connected and unitized by means of a stapler, sewing machine, welding, etc. As shown in Figure 2, the laminated body 122, which is formed by stacking multiple sheet materials 121 vertically, may be provided by stacking multiple sets of these laminated bodies.

[0017] The outer sheet material 130 encloses the mass body 110 and the spring body 120 as a single unit. The outer sheet material 130 may be made of the same material as the sheet material 121, or it may be made of a different material. Furthermore, it is preferable that the outer sheet material 130 is made of a breathable material. As will be explained below, the number of laminates 122 in the spring body 120 is adjusted and determined to efficiently absorb and suppress floor vibrations in accordance with the resonant frequency of the floor to which it is installed. Here, if a non-breathable material is used for the outer sheet material 130, the outer sheet material 130 that encloses the mass body 110 and the spring body 120 is sealed, and in addition to the spring body 120, the air inside the outer sheet material 130 acts as a spring. As a result, the spring constant of the vibration absorber 100 as a whole changes from the adjustment made to match the resonant frequency of the floor, causing the resonant frequency of the vibration absorber 100 to deviate from the resonant frequency of the floor, and as a result, it becomes impossible to efficiently absorb and suppress floor vibrations. Although it is possible to use a non-breathable material for the outer sheet material 130, in this case, it is preferable to ensure breathability by forming multiple through holes.

[0018] The vibration absorber 100 is manufactured in advance by adjusting the mass of the mass body 110, the spring constant of the spring body 120 (i.e., the number of laminated bodies 122), etc., according to the conditions of the target area such as the floor on which the vibration absorber 100 is installed, so that the resonant frequency of the vibration absorber 100 matches or is close to the resonant frequency of the floor on which it is installed, thereby efficiently absorbing and suppressing floor vibrations. While the vibration absorber 100 may be manufactured at the construction site, it is preferable that it be manufactured in a factory with a suitable environment by workers familiar with the process. This makes it possible to efficiently manufacture the vibration absorber 100 while minimizing variations in its performance as a dynamic vibration absorber. Furthermore, when transporting the vibration absorbers 100 from the factory to the construction site, or when temporarily storing the vibration absorbers 100, stacking multiple vibration absorbers 100 between the time the vibration absorbers 100 are manufactured and when they are actually installed at the construction site can cause excessive load, which can alter the spring properties of the spring body 120. Therefore, it is preferable to limit the number of vibration absorbers 100 stacked to two or fewer, for example, so that the load does not affect the spring properties. For this reason, it is preferable to use a box-shaped container 200 having compartments 205 that can accommodate a predetermined number or fewer vibration absorbers 100 stacked together, as shown in Figure 3. The container 200 has one or more compartments 205, provided by having multiple compartment walls 203 spaced laterally between the bottom plate 201 and the top plate 202. In this embodiment, the container 200 has two compartments 205 in the lateral direction, but the number of compartments 205 in the lateral direction is not limited to two; it may be one or three or more. Furthermore, in this embodiment, the container 200 has one compartment 205 in the vertical direction, but it may have two or more compartments 205 in the vertical direction. Multiple such containers 200 can be stacked vertically.

[0019] As described above, it is preferable to pre-adjust (tune) the resonant frequency of the vibration absorber 100 to match the conditions of the floor on which it will be installed. For example, when installing the vibration absorber 100 to reduce heavy floor impact noise, it is preferable to adjust the frequency of the vibration absorber 100 to the 63Hz band, which is a frequency band of approximately 45Hz to approximately 90Hz that has a significant impact on heavy floor impact noise. In addition, depending on the conditions of the floor 1, a sharp resonance may occur at a frequency slightly lower than the lower limit of the 63Hz band, which may affect the 63Hz band. For this reason, depending on the conditions, it may be necessary to adjust the frequency of the vibration absorber 100 to a frequency lower than approximately 45Hz. Here, the frequency adjustment of the vibration absorber 100 can be easily and efficiently performed by adjusting the number of stacked sets of laminated bodies 122, which constitute the spring body 120, for example, by fixing the mass of the mass body 110 and stacking multiple sheets of sheet material 121. If the frequency of the vibration absorber 100, which integrates the mass body 110 and one set of laminated bodies 122, is f (Hz), then the vibration absorber 100 with two sets of laminated bodies 122 stacked on top of each other will have a frequency half an octave lower (0.7 times f). The vibration absorber 100 with four sets of laminated bodies 122 stacked on top of each other will have a frequency one octave lower (0.5 times f). Therefore, for example, if the resonant frequency with one laminate 122 is 63Hz, to adjust the resonant frequency to 63Hz × 0.7 = 45Hz, you would need to stack two sets of laminate 122. Similarly, to adjust the resonant frequency to 63Hz × 0.5 = 31Hz, you would need to stack four sets of laminate 122.

[0020] The vibration absorber 100's resonant frequency can also be adjusted by adjusting the mass of the mass body 110. For example, increasing the mass of the mass body 110 will lower the vibration absorber 100's resonant frequency. However, adjusting the amount of granular material 112 filled into the bag 111 to adjust the mass of the mass body 110 is time-consuming, so adjusting the number of stacked sets of the laminate 122 as described above is a simpler operation. Furthermore, as shown in Figure 4, if the floor 1 on which the vibration absorber 100 is installed is a dry double floor having a structural floor 2 that constitutes the building's frame and flooring material 4 installed on the structural floor 2 via support columns 3, the vibration absorber 100 is installed on the structural floor 2 below the flooring material 4, which is the so-called underfloor section. In the case of a house, the distance between the structural floor 2 and the flooring material 4 is often about 100 to 200 mm. For this reason, the height of the vibration absorber 100 needs to be set so that it fits within the underfloor space. Also, if the mass of the mass body 110 is excessively reduced, the resonance frequency of the vibration absorber 100 may become higher than the frequency band (63 Hz band) that is important for heavy floor impact sound. Furthermore, the load on the worker when installing the vibration absorber 100 must also be considered. For these reasons, it is preferable that the mass of the mass body 110 be, for example, about 3 kg to 15 kg. In this embodiment, the mass body 110 is, for example, about 3.75 kg. Furthermore, it is desirable to adjust the spring constant of one set of laminates 122 such that the resonant frequency of the vibration absorber 100 falls within the 63 Hz band when one to four sets of laminates 122 are assembled. If the number of sets of laminates 122 exceeds five, the momentum of the laminates 122 in directions other than the vertical increases when absorbing vibrations from the floor 1, causing the laminates 122 to no longer act stably as springs. In this embodiment, the spring constant of one set of laminates 122 is set to, for example, approximately 8.5 × 10⁵ N / m.

[0021] In practice, it is desirable that the factory has multiple types of mass bodies 110 having different masses and laminates 122 having different spring constants prepared in advance. By doing so, regardless of the resonant frequency of the floor 1, the resonant frequency of the vibration absorber 100 can be adjusted to match the resonant frequency of the floor 1 by combining a mass body 110 with an appropriate mass and a laminate 122 with an appropriate spring constant, and by appropriately determining the number of sets of laminates 122.

[0022] If the total mass of the multiple vibration absorbers 100 installed on the floor 1 is 3 to 15% of the mass of the floor 1, it is possible to effectively reduce solid-borne sound such as floor impact sound without increasing the structural load on the building. In particular, when the aim is to reduce the sound by 5 dB or more, it is preferable that the total mass of the multiple vibration absorbers 100 installed on the floor 1 be 10% or more of the mass of the floor 1. Multiple vibration absorbers 100 are installed on the floor 1 so that their total mass falls within the above range.

[0023] In this embodiment, the subject is either a floor 1A that is plate-shaped, has a uniform cross-section, and is formed from, for example, a concrete slab or CLT (Cross Laminated Timber), or a floor 1B (see Figure 13) that has a non-uniform cross-section and is equipped with a plate material and beams or joists that support the plate material. When the floor 1 (1A, 1B) vibrates, the distribution of which parts of the floor 1 are prone to vibration and which parts are not, and the ease with which they vibrate, will differ depending on the configuration of the floor 1. Here, we will first describe the case where floor 1(1A) is in the form of a plate and has a uniform cross-section. The case where floor 1(1B) has a non-uniform cross-section and consists of a plate and beams or joists that support the plate will be described later.

[0024] Rather than distributing the multiple vibration absorbers 100 evenly on the floor 1, it is preferable to place them in areas where the floor 1 is prone to vibration due to resonance. Generally, the distribution of susceptibility to vibration differs not only from the characteristics of the floor 1 but also from the vibration mode, which is the nature of the vibration. For example, Figures 5 to 8 show examples of the distribution of vibration intensity in a plate-shaped floor 1A with a uniform cross-section, across multiple vibration modes. In Figures 5 to 8, the white areas indicate the highest vibration intensity, and the denser the hatching, the lower the vibration intensity. As shown in Figure 5, when a rectangular floor 1A in plan view has the x-direction as the longer side and the y-direction as the shorter side, the number of regions in each direction where the vibration intensity is high and vibration is likely is called the order. For example, in Figure 5, the region A with the highest vibration intensity is formed in the center of floor 1A, resulting in a vibration mode with an order of 1 (1st order) in both the long-side direction (x-direction) and the short-side direction (y-direction). In Figure 6, the area A with the greatest degree of vibration is formed at two locations along the long side of floor 1A. Therefore, the vibration mode is of order 2 (second order) in the long side direction (x direction) and order 1 (first order) in the short side direction (y direction). In Figure 7, the area A with the greatest degree of vibration is formed at three locations along the long side of floor 1A. Therefore, the vibration mode is of order 3 (third order) in the long side direction (x direction) and order 1 (first order) in the short side direction (y direction). In Figure 8, the area A with the greatest degree of vibration is formed in four locations on floor 1A: two in the long side direction and two in the short side direction. Therefore, the vibration modes are of order 2 (second order) in both the long side direction (x direction) and the short side direction (y direction). In this embodiment, the resonance range is defined as the range in the floor 1A that includes at least a portion of the range A where the degree of vibration is greatest, and where the degree of resonance is greater than a preset threshold, and the vibration absorber 100 is installed within this range. The order is a value related to the number of resonance ranges. For example, the product of the order in the long-side direction and the order in the short-side direction may be the number of resonance ranges. The resonance range may be set to include the entire range A where the degree of vibration is greatest.

[0025] (Method for determining the installation position of vibration absorbers, method for designing vibration absorbers) The following describes the method for determining the installation position of a vibration absorber and the method for designing a vibration absorber in this embodiment, where the floor 1A is plate-shaped and has a uniform cross-section. Figure 9 is a block diagram showing the functional configuration of the computing device that executes the method for determining the installation position of a vibration absorber and the method for designing a vibration absorber according to this embodiment. The method for determining the installation position of a vibration absorber and the method for designing a vibration absorber according to this embodiment are executed by the computing device 10. The computing device 10 is a computer device equipped with a CPU, memory, storage device, etc. The computing device 10 realizes the method for determining the installation position of a vibration absorber and the method for designing a vibration absorber according to this embodiment by executing processing based on a pre-installed program. As shown in Figure 9, the calculation unit 10 functionally includes a floor condition identification unit 11, a resonance frequency calculation unit 12, a resonance range calculation unit 13, a vibration absorber characteristic determination unit 14, and a vibration absorber installation position determination unit 15. The floor condition identification unit 11 identifies the conditions of the floor 1A. The conditions of the floor 1A identified by the floor condition identification unit 11 include the dimensions of each part of the floor 1A used to calculate the resonant frequency of the floor 1A, various parameter values ​​of the materials constituting the floor 1A, coefficients, etc. The conditions of the floor 1A may be obtained, for example, from the design information (CAD information) of the floor 1A, or they may be input externally by the operator of the calculation unit 10. The resonance frequency calculation unit 12 calculates the resonance frequency of floor 1A based on the conditions of floor 1A identified by floor condition identification unit 11. As will be described in detail later, the resonance frequency calculation unit 12 calculates the resonance frequency for floor 1A for each of multiple values ​​of order corresponding to various multiple vibration modes. The resonance range calculation unit 13 selects and identifies an order value such that the corresponding resonance frequency is included in the frequency band targeted for vibration reduction in the floor 1A, based on the resonance frequencies corresponding to each of the multiple order values ​​calculated by the resonance frequency calculation unit 12. The resonance range calculation unit 13 uses the resonance frequencies corresponding to the identified order value and a mode function that represents the vibration mode of the floor 1A to calculate an index value indicating the ease of resonance at each position of the floor 1A. The resonance range calculation unit 13 calculates the range of the floor 1A in which the calculated index value indicating the ease of resonance is greater than a preset threshold as the resonance range. The vibration absorber characteristic determination unit 14 determines the characteristics of the vibration absorber 100 based on the resonance frequency of the floor 1A calculated by the resonance frequency calculation unit 12. The vibration absorber characteristic determination unit 14 determines the number of laminated units 122 that make up the spring body 120, according to the resonance frequency of the floor 1A, as a characteristic of the vibration absorber 100. The vibration absorber installation position determination unit 15 determines the installation position of the vibration absorber 100 based on the resonance range calculated by the resonance range calculation unit 13.

[0026] Figure 10 is a flowchart showing the flow of the method for determining the installation position of the vibration absorber according to this embodiment. As shown in Figure 10, the method for determining the installation position of the vibration absorber according to this embodiment includes a floor condition determination step S11, a resonance frequency calculation step S12, a resonance range calculation step S13, a vibration absorber characteristic determination step S14, and a vibration absorber installation position determination step S15. When the floor 1A on which the vibration absorber 100 is installed is formed in a plate-like shape with a uniform cross-section, for example, using reinforced concrete or CLT, as shown in Figure 4, in the floor condition identification step S11, the floor condition identification unit 11 obtains the Young's modulus E of the floor 1A, the second moment of area i, the length a in the long side direction of the floor 1A, the length b in the short side direction of the floor 1A, Poisson's ratio ν, etc., as conditions for the floor 1A.

[0027] In the resonance frequency calculation step S12, the resonance frequency calculation unit 12 calculates the resonance frequency of the floor 1A. The plate-shaped floor 1A, having a uniform cross-section, can be assumed to be a rectangular plate in plan view with its outer periphery completely fixed. As already explained using Figures 5 to 8, the floor 1A, having a uniform cross-section, has independent values ​​as orders in the long-side direction and short-side direction, depending on the vibration mode. Therefore, the resonance frequency f fix (m, n) is calculated as a function of the degree m in the direction of the longer side and the degree n in the direction of the shorter side, using the following equation (11).

number

[0028] <关于公式编号等内容,保留原文 However, since the outer peripheral part of the actual building floor 1A is not always completely fixed, it may be slightly lower than each resonance frequency of the floor 1A calculated by the above formula (11). Therefore, in practice, the resonance frequency calculation unit 12 multiplies the resonance frequency f fix (m, n) calculated by the above formula (11) by a preset coefficient w, and uses the value f(m, n) as f fix (m, n). <关于公式编号等内容,保留原文

Equation

[0029] <关于公式编号等内容,保留原文 In the resonance range calculation step S13, the resonance range calculation unit 13 specifies the value of the order corresponding to the frequency band targeted for vibration reduction on the floor 1A based on the resonance frequency f fix (m, n) calculated by the resonance frequency calculation unit 12. In particular, when the floor 1A is in the shape of a plate and has a uniform cross-section, in the resonance range calculation step S13, in the resonance frequency calculation step S12, the resonance frequency f fixFrom among the multiple combinations (m, n) of the order m in the long-side direction and the order n in the short-side direction calculated for (m, n), a combination (m, n) is selected in which the corresponding resonant frequency falls within the range of frequencies to be reduced. Specifically, the resonant frequency f calculated in the resonant frequency calculation step S12 is selected within the frequency range of the target floor 1A, which is intended to have its vibrations reduced by the vibration absorber 100. fix Identify combinations of degree values ​​(m, n) that include (m, n). For example, in the resonant frequency calculation step S12, the resonant frequency f fix (m, n) f fix (1, 1) = 15 f fix (1, 2) = 28 f fix (2, 1) = 35 f fix (2, 2) = 60 f fix (3, 1) = 95 If calculated as such, and the frequency range of the target floor 1A is 45-90Hz, then the resonant frequency f calculated in the resonant frequency calculation step S12 is selected from among multiple order values ​​(m, n) (=(1,1), (1,2), (2,1), (2,2), (3,1)). fix Select and identify (2, 2), where (m, n) is an order value that falls within the above frequency range.

[0030] In the resonance range calculation step S13, the resonance range calculation unit 13 uses the selected order value (in the above example, (m, n) = (2, 2)) to formulate the mode function. As shown in Figure 11, the mode function is expressed as a two-dimensional coordinate system with the origin (0, 0) at the lower left corner, with the longer side of the floor 1A positioned along the x-axis and the shorter side along the y-axis, and the coordinates corresponding to each position on the floor 1A being (x, y). Using these coordinate values ​​x, y and the orders m, n, the mode function is expressed by the following equation (13).

number

[0031] In the above example, the order value (m, n) selected in the resonance frequency calculation step S12 is (2, 2). Therefore, in equation (13) above, the values ​​are substituted for m=2 and n=2 respectively, and the mode function is formulated as G(x, y, 2, 2). The resonance range calculation unit 13 then calculates G(x, y, 2, 2) at each position (x, y) on the floor 1A, converts the obtained values ​​to decibels, and calculates an index value indicating the ease of resonance. Specifically, for each value obtained by substituting the coordinate (x, y) into G(x, y, 2, 2), the value is 20 times the common logarithm, i.e., 20 × log 10 Calculate (G(x, y, 2, 2)). Figure 11 plots the decibel values ​​of G(x, y, 2, 2). In the resonance range calculation step S13, the resonance range calculation unit 13 calculates the range in which the index value indicating the susceptibility of the floor 1A to resonance, as shown in Figure 11, is greater than a preset threshold, as the resonance range Ak, which is the range in which the floor 1A is prone to vibration. For example, in the example in Figure 11, the index value of the degree of vibration in the floor 1A is converted to decibels from a value obtained by a mode function so that it is, for example, between -60 and 10 dB. In this case, it is desirable to set the threshold to a value that is 15 dB to 30 dB smaller than the maximum value of the range in which the index value can take, which is 10 dB. More specifically, if the threshold is set to -5 dB, which is the value obtained by subtracting 15 from 10, the resonance range Ak will be in the range of -5 dB to 10 dB. Also, if the threshold is set to -20 dB, which is the value obtained by subtracting 30 from 10, the resonance range Ak will be in the range of -20 dB to 10 dB. The threshold may be set such that, for example, when the index values ​​are plotted as shown in Figure 11, the area where the index value exceeds the threshold is approximately 40% to 60% of the total area of ​​floor 1A. In this embodiment, the resonance range Ak is set to be a rectangle that includes the portion where the index value exceeds the threshold, but it is not limited to this. The resonance range Ak may have a shape that coincides with the portion where the index value exceeds the threshold when the index value is plotted as shown in Figure 11.

[0032] In the vibration absorber characteristic determination step S14, the vibration absorber characteristic determination unit 14 determines the characteristics of the vibration absorber 100 based on the resonant frequency of the floor 1A. Based on the resonant frequency of the target floor 1A from which vibrations are to be reduced by the vibration absorber 100, the vibration absorber characteristic determination unit 14 determines the number of laminated units 122 constituting the spring body 120 as a characteristic of the vibration absorber 100, according to the resonant frequency of the floor 1A. For example, in the above example, the resonant frequency of the target floor 1A is around 63 Hz, and in this case, a set of laminated bodies 122 is used as the vibration absorber 100. In the vibration absorber installation position determination step S15, the vibration absorber installation position determination unit 15 determines the installation position of the vibration absorber 100 based on the resonance range Ak calculated by the resonance range calculation unit 13 in the resonance range calculation step S13. That is, as shown in Figure 12, multiple vibration absorbers 100 whose characteristics were determined in the vibration absorber characteristic determination step S14 are installed inside the four resonance ranges Ak set on the floor 1A corresponding to Figure 11. In Figure 12, the vibration absorber 100 is partially provided inside the resonance range Ak, but it is also possible to provide the vibration absorber 100 over the entire area inside the resonance range Ak.

[0033] Next, we will describe the case where the floor 1(1B) has a non-uniform cross-section and comprises planks and beams or joists that support the planks. For example, as shown in Figure 13, in the case of a wooden floor 1B constructed using conventional post-and-beam or two-by-four construction methods, the floor 1B comprises planks 5 and beams or joists 6 that support the planks 5. In this case, the floor 1B is greatly affected by the beams or joists 6. In such cases, in the width direction W perpendicular to the axial direction in which the beams or joists 6 extend, i.e., in the direction in which the beams or joists 6 are spaced apart, the floor 1B is provided with beams or joists 6 at appropriate intervals, so the susceptibility to vibration does not change significantly at any position. Therefore, especially in such cases, the floor 1B vibrates at the resonant frequency of bending vibration in the axial direction of the beams or joists 6. When the board material 5 is thin and has low rigidity, its influence on the bending vibration of the beam or joist 6 is small. However, in apartment buildings, for example, the board material 5 tends to be thicker due to lamination in order to improve the performance of blocking heavy floor impact sound and fire resistance, and in such cases, the influence of the board material 5 on the bending vibration of the beam or joist 6 becomes significant. For this reason, the floor 1B must be considered as having bending rigidity as a whole, with the beam or joist 6 and board material 5 combined. Therefore, in the case where the floor 1B has a non-uniform cross-section and comprises planks and beams or joists supporting the planks, the area D formed by the planks 5 extending on both sides of the beam or joist 6, when viewed from the axial direction of the beam or joist 6, is considered as a beam with a T-shaped cross-section.

[0034] In the case where the floor 1B has a T-shaped cross-section, the floor condition identification step S11 shown in Figure 10 obtains the following conditions for the floor 1B: the length l of the beam or joist 6, the Young's modulus E in the axial direction in which the beam or joist 6 extends, the second moment of area I in the axial direction, the total cross-sectional area S of one beam or joist 6 and the plate material 5 supported by the beam or joist 6 corresponding to the beam or joist 6 when the floor 1B is viewed in cross-section in a direction perpendicular to the axial direction, the density ρ of the floor 1B, etc.

[0035] Next, in the resonant frequency calculation step S12, the resonant frequency calculation unit 12 formulates an equation for calculating the resonant frequency of the floor 1B. As described above, floor 1B vibrates due to resonance of bending vibration in the axial direction, not in the width direction W. Therefore, the vibration modes are considered to remain unchanged in the width direction W and change only in the axial direction. For this reason, the number of axial directions in which the degree of vibration is high and vibration is likely to occur is defined as the order. For example, Figure 14 shows the vibration modes when the order is 2, where there are two resonance ranges Ak in the axial direction that are prone to vibration. Therefore, the resonant frequency f fix (n) is calculated as a function of the degree n in the axial direction, by the following equation (14).

number

[0036] In the resonant frequency calculation step S12, the resonant frequency is calculated according to equation (14) above, corresponding to each of the multiple values ​​of the order. Specifically, for each of the multiple values ​​of the axial order n, for example 1, 2, and 3, the resonant frequency f is calculated according to equation (14) above. fix Find (n).

[0037] In the resonance range calculation step S13, the resonance range calculation unit 13 calculates the resonance frequency f corresponding to each of the multiple order values ​​calculated by the resonance frequency calculation unit 12. fix Based on (n), the order value corresponding to the frequency band targeted for vibration reduction in floor 1B is determined. In particular, when floor 1B has a T-shaped cross section, in the resonance range calculation step S13, the resonance frequency f is determined in the resonance frequency calculation step S12.fix From among the multiple values ​​of the axial order n calculated for (n), a value is selected in which the corresponding resonant frequency falls within the range of frequencies to be reduced. Specifically, the resonant frequency f calculated in the resonant frequency calculation step S12 is selected within the frequency range of the target floor 1B, which is intended to have its vibrations reduced by the vibration absorber 100. fix Identify the degree value n that contains (n). For example, in the resonant frequency calculation step S12, the resonant frequency f fix (n) is, f fix (1) = 15 f fix (2) = 60 f fix (3) = 95 If calculated as such, and the frequency range of the target floor 1B is 45-90Hz, then the resonant frequency f calculated in the resonant frequency calculation step S12 is selected from among multiple values ​​n (=1, 2, 3) of the order. fix Select and identify 2, which is the order value of (n) that falls within the above frequency range.

[0038] In the resonance range calculation step S13, the resonance range calculation unit 13 uses the vibration mode of the selected order value (2 in the above example) to formulate a mode function. As shown in Figure 14, the mode function is expressed as a one-dimensional coordinate system with the floor 1B viewed from above, with the axis direction aligned along the x-axis direction and the left end as the origin (0,0). When the coordinate corresponding to each position on the axial direction of the floor 1B is denoted as x, the mode function is expressed by the following equation (15) using this coordinate value x and the order n.

number

[0039] In the above example, since the value n of the order selected in the resonant frequency calculation step S12 is 2, in equation (15) above, the value is substituted for the variable n as n=2, and the mode function is formulated as G(x,2). Then, in this embodiment, G(x,2) is calculated at each position x on the floor 1B, and the obtained values ​​are converted to decibels to calculate an index value indicating the ease of resonance. Specifically, for each value obtained by substituting the coordinate x into G(x,2), the value is 20 times the common logarithm, i.e., 20 × log 10 Calculate (G(x, 2)). Figure 14, which has already been explained, plots the decibel values ​​of G(x, 2). In the resonance range calculation step S13, the resonance range calculation unit 13 calculates the range in which the index value indicating the ease of resonance of the floor 1B becomes greater than a preset threshold value as the resonance range Ak. The threshold value may be determined in the same manner as in the above embodiment. In this case as well, the order is a value related to the number of resonance ranges. For example, the order in the axial direction can be the number of resonance ranges.

[0040] In the vibration absorber characteristic determination step S14, the vibration absorber characteristic determination unit 14 determines the characteristics of the vibration absorber 100 based on the resonant frequency of the floor 1B. Based on the resonant frequency of the target floor 1B from which vibrations are to be reduced by the vibration absorber 100, the vibration absorber characteristic determination unit 14 determines the number of laminated units 122 constituting the spring body 120 as a characteristic of the vibration absorber 100, according to the resonant frequency of the floor 1B. In the vibration absorber installation position determination step S15, the vibration absorber installation position determination unit 15 determines the installation position of the vibration absorber 100 based on the resonance range Ak calculated by the resonance range calculation unit 13 in the resonance range calculation step S13. That is, as shown in Figure 14, multiple vibration absorbers 100 whose characteristics were determined in the vibration absorber characteristic determination step S14 are installed in the two resonance ranges Ak set on the floor 1B.

[0041] The above-described method for determining the installation position of vibration absorbers 100 is a method for determining the installation position of vibration absorbers 100 when multiple vibration absorbers 100, each comprising a mass body 110 and a spring body 120 provided below the mass body 110, are installed on a floor 1 in order to reduce heavy floor impact noise, and the method comprises: a floor condition identification step S11 for identifying the conditions of the floor 1; a resonance frequency calculation step S12 for calculating the resonance frequency of the floor 1 based on the conditions of the floor 1; a resonance range calculation step S13 for calculating the resonance range Ak of ​​the floor 1, which is the range in which an index value indicating the ease of resonance of the floor 1 is greater than a threshold, using the resonance frequency and a mode function that expresses the vibration mode of the floor 1; a vibration absorber characteristic determination step S14 for determining the characteristics of the vibration absorber 100 based on the resonance frequency; and a vibration absorber installation position determination step S15 for determining the installation position of the vibration absorber 100 based on the resonance range Ak. With this configuration, in the resonance frequency calculation step S12, the resonance frequency of the floor 1 is calculated based on the conditions of the floor 1 identified in the floor condition identification step S11. In the resonance range calculation step S13, the resonance range Ak, which is the range in which the index value indicating the ease of resonance of the floor 1 is greater than a threshold, is calculated using the resonance frequency of the floor 1 and a mode function that represents the vibration mode of the floor 1. In the vibration absorber characteristic determination step S14, the characteristics of the vibration absorber 100 are determined based on the calculated resonance frequency. Furthermore, in the vibration absorber installation position determination step S15, the installation position of the vibration absorber 100 having the determined characteristics is determined based on the resonance range Ak. In this way, the vibration absorber 100 having characteristics corresponding to the resonance frequency of the floor 1 is installed at the installation position determined based on the resonance range Ak in which the degree of resonance is greater than a threshold. This allows the vibration absorber 100 to be efficiently positioned and heavy floor impact noise to be effectively reduced.

[0042] Furthermore, the mode function's variables include an order, which is a value related to the number of resonance ranges Ak. In the resonance frequency calculation step S12, the resonance frequency is calculated for each of the multiple values ​​of the order. In the resonance range calculation step S13, a value is selected from the multiple values ​​such that the corresponding resonance frequency falls within the range of frequencies to be reduced. This value is substituted into the order variable of the mode function, and this is compared with a threshold value to calculate the resonance range Ak. Floor 1 vibrates in various ways. For example, when floor 1B comprises beams or joists 6 and a plate 5 placed on the beams or joists 6, the number of resonance ranges Ak, i.e., the areas prone to vibration, which are the range in which the index value indicating susceptibility to resonance exceeds a threshold, in the axial direction along which the beams or joists 6 extend, changes depending on the conditions under which the vibration occurs, such as the excitation point. Similarly, when floor 1A is plate-shaped with a uniform cross-section, the number of resonance ranges Ak in the long and short directions of floor 1A also changes depending on the conditions under which the vibration occurs. Thus, the order, which is a value related to the number of resonance ranges Ak, can take on multiple values. Therefore, the mode function that expresses the vibration modes of the floor includes the order as a variable. As the order can take on multiple values, in the configuration described above, the resonance frequency is calculated in the resonance frequency calculation step S12 for each of the multiple values ​​of the order. Then, in the resonance range calculation step S13, a value is selected from the multiple values ​​of the order in which the corresponding resonance frequency falls within the range of frequencies to be reduced. Here, in the mode function, the value selected as described above is substituted for the variable order, which is considered to represent the vibration mode of the vibration when the resonance frequency falls within the range of frequencies to be reduced. In the resonance range calculation step S13, the resonance range Ak is calculated using the mode function expressed in this way. In this way, the resonance range Ak when the floor 1 vibrates at a resonance frequency that falls within the range of frequencies to be reduced is appropriately calculated, and the installation position of the vibration absorber 100 is determined based on this resonance range Ak. As a result, the vibration absorber 100 can be installed in a more appropriate location, and heavy floor impact sound can be reduced more effectively.

[0043] Furthermore, when the floor 1A is plate-shaped and has a uniform cross-section, in the resonance frequency calculation step S12, the resonance frequency f corresponding to each of the multiple combinations of the order m in the long-side direction and the order n in the short-side direction is calculated using the above resonance frequency formula (11). fix Calculate (m, n). With this configuration, when the floor 1A is plate-shaped and has a uniform cross-section, the resonance frequency of the floor 1A can be appropriately calculated in the resonance frequency calculation step S12 based on the conditions of the floor 1A. Therefore, it becomes possible to more appropriately determine and calculate the characteristics of the vibration absorber and the resonance range Ak, and to appropriately determine the installation position of the vibration absorber 100. Consequently, heavy floor impact noise can be reduced more effectively.

[0044] Furthermore, if the floor 1A is plate-shaped and has a uniform cross-section, in the resonance range calculation step S13, a combination (m, n) is selected from among multiple combinations (m, n) of the order m in the long-side direction and the order n in the short-side direction in which the corresponding resonance frequency falls within the range of frequencies to be reduced. Based on the selected combination, an index value indicating the ease of resonance at each position (x, y) with the corner of the floor 1A as the origin when viewed from above is calculated using the above equation (13) as the mode function, and the range in which the index value is greater than the threshold is determined as the resonance range Ak. With this configuration, the resonance range Ak can be appropriately determined when the floor 1A is plate-shaped and has a uniform cross-section.

[0045] Furthermore, if the floor 1B comprises beams or joists 6 and boards 5 placed on top of the beams or joists 6, in the resonance frequency calculation step S12, the resonance frequency f corresponding to each of the multiple values ​​of order n is calculated using the above resonance frequency formula (14). fix Calculate (n). With this configuration, when the floor 1B comprises beams or joists 6 and boards 5 installed on top of the beams or joists 6, the resonant frequency of the floor 1B can be appropriately calculated in the resonant frequency calculation step S12 based on the conditions of the floor 1B. This makes it possible to more appropriately determine and calculate the characteristics of the vibration absorber and the resonance range Ak, and to determine the installation position of the vibration absorber 100. Consequently, heavy floor impact noise can be reduced more effectively.

[0046] Furthermore, if the floor 1B includes beams or joists 6 and boards 5 placed on top of the beams or joists 6, in the resonance range calculation step S13, based on the selected value of order n, an index value indicating the ease of resonance at each position x with the end of the beam or joist 6 as the origin when viewed from above is calculated using the above equation (15) as the mode function, and the range in which the index value is greater than the threshold is determined as the resonance range Ak. With this configuration, when the floor 1B comprises beams or joists 6 and boards 5 placed on top of the beams or joists 6, the resonance range Ak can be appropriately determined.

[0047] Furthermore, the vibration absorber 100 described above comprises a mass body 110, a spring body 120 provided below the mass body 110, and an outer sheet material 130 that integrally encloses the mass body 110 and the spring body 120. The mass body 110 is a granular body 112 enclosed in a bag 111, and the spring body 120 comprises one or more laminated bodies 122 formed by stacking and connecting multiple sheet materials 121 vertically. With this configuration, the mass body 110 is supported from below by the spring body 120, and the vibration absorber 100 functions as a dynamic vibration absorber that dampens vibrations input from the outside. By installing such a vibration absorber 100 at an installation position determined based on, for example, the resonance range Ak where the degree of resonance is greater than a threshold, heavy floor impact noise can be effectively reduced. Furthermore, since the mass body 110 and the spring body 120 are integrally encased in the outer sheet material 130, there is no need to transport the mass body 110 and the spring body 120 separately during installation, making it easy to handle the vibration absorber 100. Furthermore, since the laminate 122 is unitized, it is easy to handle, and the process of changing the spring constant of the vibration absorber by changing or adjusting the number of laminates 122 is also easy.

[0048] The vibration absorber 100 design method of the present invention is a vibration absorber 100 design method as described above, comprising the steps of: identifying the resonant frequency of the floor 1 on which the vibration absorber 100 is installed (resonant frequency calculation step S12); and determining the number of laminated bodies 122 to be installed on the floor 1 based on the resonant frequency of the floor 1 (vibration absorber characteristic determination step S14). With this configuration, the number of laminated units 122 to be installed on the floor 1 is determined based on the resonant frequency of the floor 1 on which the vibration absorber 100 is installed, thereby allowing the vibration absorber 100 to be designed according to the conditions of the floor 1. By installing such a vibration absorber 100 on the floor 1, heavy floor impact noise can be effectively reduced.

[0049] (Modified version of the embodiment) The method for determining the installation position of a vibration absorber, the vibration absorber, and the method for designing a vibration absorber according to the present invention are not limited to the embodiments described above with reference to the drawings, and various modifications are possible within the technical scope. For example, in the resonance range calculation step S13 of the above embodiment, if there are multiple values ​​among the order such that the corresponding resonance frequency falls within the range of frequencies to be reduced, the resonance range Ak may be set based on each of these multiple values. For example, as shown in Figure 15, when the floor 1A is plate-shaped and has a uniform cross-section, there are two types of vibration modes: one where the order m in the long-side direction is 2 and the order n in the short-side direction is 1, with a combination of (2, 1); and another where the order m in the long-side direction is 1 and the order n in the short-side direction is 2, with a combination of (1, 2). In these cases, the corresponding resonant frequencies f fix (2, 1), resonant frequency f fix If (1, 2) falls within the range of frequencies to be reduced, the vibration absorber 100 may be installed in a range that includes at least one of the resonance range Ak1 for the combination (2, 1) and the resonance range Ak2 for the combination (1, 2) (the range colored in Figure 15). The same consideration is possible even when the floor consists of beams or joists 6 and boards 5 placed on top of the beams or joists 6. In this way, impact noise from heavy floors can be effectively reduced regardless of which of the multiple vibration modes the floor 1 vibrates in. In addition to the above, it is possible to select or replace the configurations listed in the above embodiments, or to change them to other configurations as appropriate, as long as it does not deviate from the spirit of the present invention.

[0050] (Examples) The installation position of the vibration absorber 100, determined by the method for determining the installation position of the vibration absorber 100 shown in the above embodiment, was verified. Finite element analysis was used as the verification method. As an example of floor 1, a reinforced concrete slab was used. In one example, as shown in Figure 16B, multiple vibration absorbers 100 were placed near the resonance range of floor 1A. In a comparative example, as shown in Figure 16A, vibration absorbers 100 were installed evenly across the entire slab. The slab dimensions were 6m x 6m in plan and 200mm in thickness. With these dimensions, a second resonance occurs at 56Hz in the 63Hz band, which is important for heavy floor impact sound. In both the example and comparative example, 484 vibration absorbers 100 were installed, each equipped with a mass 110 weighing 3.75kg, so that the total mass of the slab was approximately 10%. For each of the examples and comparative examples, the amount of vibration reduction (the vibration reduction effect due to the installation of the vibration absorber 100) was calculated by calculating the difference in vibration compared to when the vibration absorber 100 is not installed, using finite element analysis. As a result, as shown in Figure 17, in the 63 Hz band where reduction was targeted, the vibration reduction amount was 8.1 dB in the comparative example, while the vibration reduction amount in the embodiment was 11.6 dB, indicating that the embodiment had a 3.5 dB greater reduction effect. Incidentally, a common measure to reduce heavy floor impact noise is to increase the thickness of floor 1A. However, if we simply convert these effects to slab thickness, 8.1 dB is equivalent to increasing a 200 mm slab to 320 mm, and 11.6 dB is equivalent to increasing it to 390 mm. Therefore, the difference in effect between the two corresponds to a difference of 70 mm in slab thickness.

[0051] Furthermore, verification using finite element analysis was also performed on floor 1B, which is equipped with plank material 5 and beams or joists 6. Assuming an actual wooden floor structure 1, the floor 1 with the dimensions shown in Figure 18 was used. The joists 6 are 38mm x 235mm, and the boards 5 are composite boards consisting of 9mm wooden boards, 42mm gypsum boards, and 24mm wooden boards. The Young's modulus of wood used in the calculation is 6E+09N / m 2 , density 600kg / m 3 The Young's modulus of gypsum board is 1.8E+09N / m 2 , density 750kg / m 3 I used it. The excitation points P1 and P2 in Figure 18 were excited, and the vibration velocity levels along line LA and line LB were determined. Excitation point P1 and line LA are located on joist 6, while excitation point P2 and line LB are located between joists 6. In floor 1B, resonance occurs at a frequency of 65 Hz. Figure 19A shows the vibration distribution at the positions of lines LA and LB at the resonant frequency of 65 Hz when the excitation point P1 on the joist 6 is excited. Figure 19B shows the vibration distribution at the positions of lines LA and LB at the resonant frequency when the excitation point P2 between the joists 6 is excited. As shown in Figure 19, regardless of whether the excitation point is on or between the joists 6, the vibration is based on the second-order vibration mode of bending of the joist 6. Figure 20A shows the vibration distribution at a frequency of 50Hz, which is different from the resonant frequency of 65Hz, when the excitation point on the joist is excited. Figure 20B shows the vibration distribution at the same frequency of 50Hz when the excitation point between the joists is excited. From Figures 20A and 20B, it can be observed that even at a frequency of 50Hz, the vibration is based on a vibration mode close to the second order of bending of joist 6. In particular, even when a location other than joist 6 (excitation point P2) is excited, joist 6 vibrates more significantly, and since the vibration is based on a vibration mode close to the second order of bending of joist 6, it can be seen that in such a floor structure, if we focus on the area around 63Hz, the bending vibration of joist 6 is dominant. Therefore, when installing vibration absorbers 100 on a wooden floor 1B, as described above, by considering the bending vibration in a T-shaped beam formed by the plate material 5 and the beam or joist 6, and installing vibration absorbers 100 at locations corresponding to the resonance range of that vibration mode, vibrations can be suppressed efficiently and heavy floor impact noise can be reduced. [Explanation of Symbols]

[0052] 1, 1A, 1B Floor 122 Laminate 5. Board material 130. Outer sheet material. 6. Beam or joist Ak, Ak1, Ak2 Resonance range 100 Vibration absorber S11 Floor condition identification process 110 Mass body S12 Resonant frequency calculation process 111 Bag S13 Resonance Range Calculation Process 112 Granular material S14 Vibration absorber characteristics determination process 120 Spring body S15 Vibration absorber installation position determination process 121 Sheet material

Claims

1. A method for determining the installation position of vibration absorbers, in which multiple vibration absorbers, each comprising a mass and a spring body provided beneath the mass, are installed on the structural floor constituting the building's frame in order to reduce heavy floor impact noise, wherein the installation position of each vibration absorber is determined. The spring body comprises one or more laminated units formed by stacking and connecting multiple sheet materials vertically. The number of the aforementioned laminates is determined in accordance with the resonant frequency of the structural floor. A floor condition identification step to identify the conditions of the aforementioned structural floor, A resonant frequency calculation step for calculating the resonant frequency of the structural floor based on the conditions of the structural floor, A resonance range calculation step, which calculates the resonance range of the structural floor, in which an index value indicating the ease of resonance of the structural floor becomes greater than a threshold value, using the aforementioned resonance frequency and a mode function that represents the vibration mode of the structural floor. A process for determining the characteristics of the vibration absorber based on the aforementioned resonance frequency, A vibration absorber installation position determination step, which determines the installation position of the vibration absorber based on the resonance range, A method for determining the installation position of a vibration absorber, characterized by having the following features.

2. The variables of the mode function include an order which is a value relating to the number of resonance ranges, In the resonance frequency calculation step, the resonance frequency is calculated corresponding to each of the multiple values ​​of the order, In the resonance range calculation step, a value is selected from among the multiple values ​​in which the corresponding resonance frequency falls within the range of frequencies to be reduced. This value is substituted into the order variable of the mode function, and the resonance range is calculated by comparing it with the threshold value. The method for determining the installation position of a vibration absorber according to feature 1.

3. When the structural floor comprises beams or joists and planks placed on the beams or joists, In the resonant frequency calculation step, the following resonant frequency formula (1) is used, which is expressed by the length l of the beam or joist, the Young's modulus E in the axial direction in which the beam or joist extends, the second moment of area I in the axial direction, the total cross-sectional area S of one beam or joist and the plate material supported by the beam or joist corresponding to the beam or joist when the structural floor is viewed in cross-section in a direction perpendicular to the axial direction, the density ρ of the structural floor, the order n, and a coefficient α determined according to the length l of the beam or joist. [Math 1] As a result, the resonant frequency f corresponding to each of the multiple values ​​of the order n ｆｉｘ Calculate (n) The method for determining the installation position of a vibration absorber according to feature 2.

4. In the resonance range calculation step, based on the selected value of the order n, the mode function is given by the following equation (2): [Math 2] Using this method, an index value indicating the ease of resonance at each position x, with the end of the beam or joist as the origin when viewed from above, is calculated, and the range in which the index value is greater than the threshold is determined as the resonance range. The method for determining the installation position of a vibration absorber according to feature 3.

5. When the aforementioned structural floor is plate-shaped and has a uniform cross-section, In the resonance frequency calculation step, the following resonance frequency formula (3) is used, which is expressed by the length a in the long side direction of the structural floor, the length b in the short side direction of the structural floor, Poisson's ratio ν, Young's modulus E, second moment of area I, the order m in the long side direction, and the order n in the short side direction. [Math 3] As a result, the resonant frequency f corresponds to each of the multiple combinations of the order m in the long side direction and the order n in the short side direction. ｆｉｘ Calculate (m, n) The method for determining the installation position of a vibration absorber according to feature 2.

6. In the resonance range calculation step, from among a plurality of combinations of the order m in the long side direction and the order n in the short side direction, a combination is selected in which the corresponding resonance frequency falls within the range of frequencies to be reduced, and based on the selected combination, the mode function is given by the following equation (4): [Math 4] Using this method, an index value indicating the ease of resonance at each position (x, y) with the corner of the structural floor as the origin when viewed from above is calculated, and the range in which the index value is greater than the threshold is determined as the resonance range. The method for determining the installation position of a vibration absorber according to feature 5.

7. The mass is a granular body enclosed in a bag, The vibration absorber is The mass body and the spring body are further enclosed by an outer sheet material, Multiple through holes are formed in the outer sheet material. A method for determining the installation position of a vibration absorber according to any one of claims 1 to 6.

8. A mass body and, A spring body provided below the mass body, The device comprises the aforementioned mass body and an outer sheet material that integrally encloses the aforementioned spring body, The mass is a granular body enclosed in a bag, The spring body comprises one or more laminated units formed by stacking and connecting multiple sheet materials vertically. The number of the aforementioned stacks is determined to match the resonant frequency of the structural floor that constitutes the building's frame where it will be installed. A vibration absorber characterized by the following features.

9. A method for designing a vibration absorber according to claim 8, A step of identifying the resonant frequency of the structural floor on which the vibration absorber is installed, The process includes determining the number of laminates to be installed on the structural floor based on the resonant frequency of the structural floor. A method for designing a vibration absorber characterized by the following features.

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