Method for estimating the maximum excitation force of a vibration-isolating floor structure

Abstract

The maximum excitation force can be easily estimated based on the measured acceleration. [Solution] The method includes an acceleration measurement step for measuring the acceleration of a vibration-isolating floor 3 provided on a support structure 2 via a support spring 4 with its spring axis oriented vertically; a maximum acceleration calculation step for determining the maximum acceleration from the time series of accelerations; a primary natural frequency calculation step for determining the primary natural frequency from the Fourier spectrum of accelerations; a transfer function calculation step for determining the transfer function from the input excitation force of the vibration-isolating floor to the response acceleration; and a maximum excitation force calculation step for calculating the maximum excitation force from the maximum acceleration, primary natural frequency, and transfer function.

Description

[Technical Field]

[0001] This invention relates to a method for estimating the maximum excitation force of a vibration-isolating floor structure. [Background technology]

[0002] A vibration-damping floor is a system that makes it difficult for vibrations from machinery placed on it, as well as vertical vibrations from people moving around during live concerts, to be transmitted, thereby reducing vibrations transmitted to the floor, building foundation, and surrounding ground (see, for example, Patent Document 1). [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] Japanese Patent Publication No. 2022-30067 [Overview of the Initiative] [Problems that the invention aims to solve]

[0004] When verifying the effectiveness of vibration-isolating floors or confirming whether the actual applied excitation force matches prior assumptions, it is important to determine the maximum excitation force (maximum excitation force) applied by machinery or vertical vibrations. It is conceivable to directly measure the excitation force using sensors such as load cells; however, due to spatial or cost constraints, it is difficult to install sensors such as load cells in vibration-isolating floors. On the other hand, small and inexpensive acceleration sensors are easy to install even on vibration-damping floors. However, since they do not directly measure the excitation force, it is necessary to estimate the excitation force based on the measured acceleration. One possible method for estimating the maximum excitation force based on measured acceleration is to construct an inverse system of the vibration-isolating floor, use this system and the acceleration time series to obtain the time series of excitation force through time history response analysis, and use the maximum value of this analysis as the estimated maximum excitation force. However, time history response analysis is time-consuming, making it difficult to adopt when dealing with a large amount of measured data.

[0005] Therefore, the present invention aims to provide a method for estimating the maximum excitation force of a vibration-damping floor structure that can easily estimate the maximum excitation force based on the measured acceleration. [Means for solving the problem]

[0006] To achieve the above objective, the method for estimating the maximum excitation force of a vibration-isolating floor structure according to the present invention comprises: an acceleration measurement step of measuring the acceleration of a vibration-isolating floor provided via support springs with spring axes oriented vertically on a support structure; a maximum acceleration calculation step of determining the maximum acceleration from the time series of the acceleration; a primary natural frequency calculation step of determining the primary natural frequency from the Fourier spectrum of the acceleration; a transfer function calculation step of determining the transfer function from the input excitation force of the vibration-isolating floor to the response acceleration; and a maximum excitation force calculation step of calculating the maximum excitation force from the maximum acceleration, the primary natural frequency, and the transfer function.

[0007] In this invention, the maximum excitation force can be easily estimated based on the measured acceleration. Sensors such as load cells that directly measure the excitation force of vibration-isolating floors are difficult to incorporate into vibration-isolating floors due to spatial and cost constraints, and are also difficult to install after the vibration-isolating floor is completed. On the other hand, acceleration sensors that measure the acceleration of vibration-isolating floors are easy to install on vibration-isolating floors and can be installed even after the vibration-isolating floor is completed or during operation. In this invention, the maximum excitation force can be easily estimated based on the acceleration measured by acceleration sensors. Furthermore, by measuring the acceleration of a vibration-isolating floor during live performances or other events where vertical vibrations actually occur, the maximum vertical excitation force can be estimated based on the measured acceleration, making it easy to examine the effectiveness of the vibration-isolating floor and whether the actual excitation force matches the design assumptions.

[0008] In the method for estimating the maximum excitation force of a vibration-isolating floor structure according to the present invention, in the transfer function calculation step, the equation of motion of the vibration-isolating floor is expressed by the following equation (1), and from the following equation (2) obtained by Laplace transform of equation (1), the transfer function is calculated by the following equation (3), and in the maximum excitation force calculation step, when the acceleration is a sine wave, in equation (3), the maximum acceleration amax Using the angular frequency ω and the imaginary unit j, set s = jω to obtain the maximum excitation force using the following formula (4). When the acceleration is represented by the sum of a primary sine wave, a secondary sine wave, and a tertiary sine wave, the maximum excitation force may be calculated from the formula (4) by approximating any one of the primary sine wave, the secondary sine wave, and the tertiary sine wave.

[0009]

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[0010] In the method for estimating the maximum excitation force of the vibration isolation floor structure according to the present invention, in the transfer function calculation step, the equation of motion of the vibration isolation floor is represented by the following formula (5), and the transfer function is calculated by the following formula (7) from the following formula (6) obtained by Laplace-transforming the formula (5). In the maximum excitation force calculation step, when the acceleration is a sine wave, in the formula (7), the maximum acceleration a max , using the angular frequency ω and the imaginary unit j, set s = jω to obtain the maximum excitation force F max using the following formula (8). When the acceleration is represented by the sum of a primary sine wave, a secondary sine wave, and a tertiary sine wave, the maximum acceleration a max is decomposed into three components of a primary sine wave, a secondary sine wave, and a tertiary sine wave, and the maximum excitation force for each component is calculated from the formula (8) for each component, and the maximum excitation force F max may be calculated by adding the maximum excitation forces for each component.

[0011]

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[0012] This configuration allows for easy estimation of the maximum excitation force regardless of the acceleration waveform.

[0013] In the method for estimating the maximum excitation force of a vibration-isolating floor structure according to the present invention, the acceleration measurement step may involve measuring the displacement and velocity of the vibration-isolating floor to calculate the acceleration.

[0014] Even with this configuration, it is easy to install displacement sensors and speedometers on the vibration-isolating floor to calculate acceleration, and the displacement sensors and speedometers can be installed even after the vibration-isolating floor is completed or while it is in operation. [Effects of the Invention]

[0015] According to the present invention, the maximum excitation force can be easily estimated based on the measured acceleration. [Brief explanation of the drawing]

[0016] [Figure 1] This is a model diagram of a vibration-isolating floor structure according to an embodiment of the present invention. [Figure 2] (a), (b), and (c) are model diagrams illustrating the arrangement of the support spring, damping element, and rotational inertia mass element, respectively. [Figure 3] This graph shows a typical waveform of vertical excitation force. [Figure 4] This graph shows an example of an acceleration time series and its Fourier spectrum. [Figure 5] This is a graph showing the analysis results. [Figure 6]It is the board diagram of G-1(s).

Embodiment for Carrying out the Invention

[0017] Hereinafter, a method for estimating the maximum excitation force of the vibration isolation floor structure according to an embodiment of the present invention will be described based on FIGS. 1-6. As shown in FIG. 1, the vibration isolation floor structure 1 according to this embodiment has a structure in which a vibration isolation floor 3 (floating floor) is installed on a support structure 2 via support springs 4. The support structure 2 is, for example, the foundation of a building or the like. The vibration isolation floor 3 may be installed in a recess that opens upward provided in the building body. The support spring 4 is a rigid element. The spring axis of the support spring 4 is in the vertical direction. In the vibration isolation floor structure 1 according to this embodiment, a damping element 5 and a rotational inertia mass element 6 are provided between the support structure 2 and the vibration isolation floor 3. The damping element 5 is, for example, a viscous damper, an oil damper, or the like. The rotational inertia mass element 6 is, for example, an inerter, a rotational inertia mass damper, or the like. Hereinafter, the mass of the vibration isolation floor 3 is m, the damping constant of the damping element 5 is c, the rigidity of the support spring 4 is k, the inertial mass of the rotational inertia mass element 6 is b, the relative displacement between the support structure 2 and the vibration isolation floor 3 is x, and the maximum excitation force acting on the vibration isolation floor 3 is F max are shown. It is assumed that the values of these m, c, k, and b are obtained from design values and the like. The acceleration of the vibration isolation floor 3 is measured by an acceleration sensor.

[0018] The vibration-isolating floor structure 1 may not be provided with either or both of the damping element 5 and the rotational inertia mass element 6. The arrangement of the support spring 4, damping element 5, and rotational inertia mass element 6 may be set as appropriate. For example, as shown in Figure 1, the support spring 4, damping element 5, and rotational inertia mass element 6 may be provided in parallel between the support structure 2 and the vibration-isolating floor 3. As shown in Figure 2(a), the support spring 4 and damping element 5 may be provided in parallel, and these may be provided in series with the rotational inertia mass element 6. As shown in Figure 2(b), the support spring 4 and rotational inertia mass element 6 may be provided in parallel, and these may be provided in series with the damping element 5. As shown in Figure 2(c), the damping element 5 and rotational inertia mass element 6 may be provided in parallel, and these may be provided in series with the support spring 4. The combination and arrangement of the support spring, damper, rotational inertia mass element, and mass body (vibration-isolating floor 3) may be other than those described above. In the following, the maximum excitation force F of the vibration-isolating floor structure 1, in which a support spring 4, a damping element 5, and a rotational inertia mass element 6 are provided in parallel between the support structure 2 and the vibration-isolating floor 3 shown in Figure 1, is described. max This section explains the estimation method.

[0019] The vertical vibration (up and down motion) of people during live concerts is known to be well represented by a sine wave and the sum of its second and third harmonics, as shown in Figure 3. The ratio of their amplitudes is 1:0.4:0.1. The model equation, variables, and numerical values ​​for the vertical vibration are shown below.

[0020]

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[0021] [Table 1]

[0022] Based on the above, without performing time history response analysis, the maximum excitation force F max The method for obtaining this will be explained. The procedure is as follows: The acceleration of the vibration-isolating floor 3 is measured (acceleration measurement process). Maximum acceleration a from the acceleration time series max This is the process of calculating the maximum acceleration. The first natural frequency is determined from the Fourier spectrum of the acceleration time series (first natural frequency calculation process). The transfer function from the input excitation force to the response acceleration of the vibration-isolating floor 3 is determined (transfer function calculation process). The maximum acceleration a obtained in the above process max The maximum excitation force F is derived from the first natural frequency and transfer function. max The maximum excitation force is calculated (maximum excitation force calculation process).

[0023] In the maximum acceleration calculation process and the first natural frequency calculation process, as shown in Figure 4, the maximum acceleration a is calculated from the acceleration time series and its Fourier spectrum. max And read the first natural frequency. Specifically, the maximum acceleration a max This is the maximum absolute value a on the vertical axis in the upper part of Figure 4. max Read the value. In Figure 4, the maximum value a max 60cm / s 2 It is approximately as follows. The primary natural frequency is read from the frequency f1 when the vertical axis in the lower part of Figure 4 is at its maximum. In Figure 4, the frequency f1 is approximately 2.2 Hz. The maximum acceleration calculation process and the primary natural frequency calculation process are performed using the maximum acceleration a max Furthermore, if it is possible to obtain the first natural frequency, this may be done by a method other than the one described above.

[0024] In the transfer function calculation process, the transfer function is determined based on the equations of motion. Below, m: Mass of the vibration-isolating floor b: Inertial mass of rotational inertial mass element c: Damping coefficient of the damping element k: Stiffness of the support spring x: Relative displacement between the support structure and the vibration-isolating floor G(s): Transfer function F max : Maximum excitation force a max :Maximum acceleration ω: Angular frequency j: Imaginary unit t: A variable representing time. s: Laplace operator Let's assume that. First, the equation of motion for the vibration-isolating floor 3 shown in Figure 1 is expressed by the following equation (1).

[0025]

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[0026] Here, by taking the Laplace transform of equation (1), we obtain equation (2). Here, X(s) and F(s) are the Laplace transforms of x(t) and F(t).

[0027]

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[0028] Therefore, the transfer function G(s) from the input excitation force to the response acceleration of the vibration-isolating floor 3 is expressed by the following equation (3).

[0029]

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[0030] In addition, the transfer function calculation process may be carried out by other methods if it is possible to obtain the transfer function G(s).

[0031] In the process of calculating the maximum excitation force, the acceleration is usually a simple sine wave, and its maximum acceleration is a max If the angular frequency is ω, then from equation (3) above, setting s = jω, the amplitude of the excitation force, i.e., the maximum value (maximum excitation force F), is given by the following equation (4). max ) can be calculated, where j is the imaginary unit.

[0032]

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[0033] However, in reality, the vertical excitation force is represented by the sum of three sine waves, from the first to the third order, as shown in Figure 3. This vertical excitation force is expressed as the maximum acceleration a max Two possible methods for obtaining this are (A) and (B) below.

[0034] (A) Approximate the vertical excitation force as a single sine wave and find the maximum value of the excitation force using equation (4) above. In this case, the maximum acceleration a max It is conceivable to set the angular frequency f (=ω / 2π) based on f1 obtained in the first natural frequency calculation process, by setting it to one of the following: 1st (first order), 2nd (second order), or 3rd (third order).

[0035] (B) Maximum acceleration a max The excitation force is decomposed into first, second, and third-order components (a1, a2, a3), and the maximum excitation force is obtained by calculating the value from each component using equation (4) above and adding them together. In this case, the maximum acceleration a max This is divided into two methods: (divide1) the ratio of the amplitudes of each order of the vertical excitation force to 1:0.4:0.1, and abs(G) considering the influence of the transfer function of the target system. -1 (jω):0.4abs(G -1 (2jω): 0.1abs(G -1 One possible method is to divide it into (3jω) (divide2). The above formulas (1) to (4) also correspond to formulas (5) to (8) in the patent claims.

[0036] This section describes a numerical analysis demonstrating the effectiveness of the method for estimating the maximum excitation force of the vibration-isolating floor structure according to this embodiment. The results of a time history response analysis performed on the vibration-isolating floor structure 1 shown in Figure 1, while varying the first frequency of the vertical excitation force, and the obtained maximum acceleration a max Based on the maximum excitation force F max Figure 5 shows a comparison of the estimated results. The dashed line represents the true value we want to predict, and the solid line represents the maximum excitation force F of the vibration-isolating floor structure according to this embodiment. maxThis is the result of the estimation method. Numerical analysis was performed for four frequencies: 1.5 Hz, 2.1 Hz, 2.8 Hz, and 3.5 Hz.

[0037] Figure 5 shows that in both methods, the maximum excitation force F max While it is possible to predict with high accuracy, comparing method (A) and method (B) above, it can be confirmed that method (B) is more accurate, especially at low frequencies such as 1.5 Hz and 2.1 Hz. Method (A) above, which approximates the vertical excitation force to a single sine wave, can estimate the excitation force with high accuracy when the gain (upper part of the same figure) is sufficiently flat, such as 2.5 Hz or higher, as shown in the Bode plot in Figure 6. However, at frequencies where this is not the case, the accuracy of the approximation decreases, resulting in a decrease in the accuracy of the estimation. On the other hand, method (B) estimates by considering the gain of each order, so it is possible to estimate with high accuracy regardless of the frequency. Also, comparing divide1 and divide2 in (B), the system's maximum acceleration a max divide2, which takes into account the influence on the system, always accurately calculates the maximum excitation force F. max It can be seen that this is being estimated. Therefore, method (B) always estimates the maximum excitation force F with high accuracy. max The ability to predict the maximum excitation force F can be predicted with high accuracy even with the simpler method (A) above if the gain is judged to be sufficiently flat. max It has been shown that this can be predicted.

[0038] The operation and effects of the method for estimating the maximum excitation force of the vibration-isolating floor structure according to this embodiment will be explained. In the method for estimating the maximum excitation force of the vibration-isolating floor structure according to this embodiment, the maximum excitation force F is estimated based on the measured acceleration. max This can be easily estimated. Sensors such as load cells that directly measure the excitation force of the vibration-isolating floor 3 are difficult to incorporate into the vibration-isolating floor 3 due to spatial or cost constraints, and are also difficult to install after the vibration-isolating floor 3 is completed. On the other hand, acceleration sensors that measure the acceleration of the vibration-isolating floor 3 are easy to install on the vibration-isolating floor 3, and can also be installed after the vibration-isolating floor 3 is completed or during operation. Using only the information obtained from the acceleration sensor and the model derived from the design values, the maximum value of the excitation force input to the vibration-isolating floor 3 can be easily estimated without performing time history response analysis. This method allows for the estimation of excitation force using a simple technique, enabling verification of the effectiveness of the vibration-isolating floor 3 during operation. Since the actual vertical vibration excitation force during live performances can be obtained from the vibration-isolating floor 3 while it is in operation, it is easy to examine the effectiveness of the vibration-isolating floor 3 and whether the actual excitation force matches the assumptions made during the design phase. In the method for estimating the maximum excitation force of the vibration-isolating floor structure according to this embodiment, the maximum excitation force F is determined regardless of the acceleration waveform. max This can be easily estimated.

[0039] Although embodiments of the method for estimating the maximum excitation force of a vibration-isolating floor structure according to the present invention have been described above, the present invention is not limited to the above embodiments and can be modified as appropriate without departing from the spirit of the invention. For example, in the above embodiment, the maximum excitation force F of the vibration-isolating floor structure is taken as an example, using the vibration-isolating floor structure 1 shown in Figure 1. max Although the method for estimating the maximum excitation force of a vibration-isolating floor structure of the present invention is used to estimate the maximum excitation force F, even in vibration-isolating floor structures other than the vibration-isolating floor structure shown in Figure 2, or the configurations shown in Figures 1 and 2, for example, vibration-isolating floor structures in which one or more of the support spring, damping element (damper), rotational inertia mass element, and vibration-isolating floor (mass body) configurations differ from those shown in Figures 1 and 2. max It is possible to estimate this. The process is as follows: Measure the acceleration of the vibration-isolating floor (acceleration measurement process). Determine the maximum acceleration from the time series of acceleration (maximum acceleration calculation process). Determine the first natural frequency from the Fourier spectrum of acceleration (first natural frequency calculation process). Determine the transfer function from the input excitation force of the vibration-isolating floor to the response acceleration (transfer function calculation process). Calculate the maximum excitation force from the maximum acceleration, first natural frequency and transfer function (maximum excitation force calculation process). Note that the formulas used in each process will be formulas appropriate to the configuration of the vibration-isolating floor structure and may differ from the formulas shown in the above embodiment.

[0040] Acceleration can be measured using displacement sensors or velocity sensors in addition to acceleration sensors. When using displacement sensors or velocity sensors, the transfer function G(s) may be expressed using equation (3)' or equation (3)'' below instead of equation (3) above.

[0041]

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[0042] The Sustainable Development Goals (SDGs) are among the 17 international goals adopted at the UN Summit in September 2015. The method for estimating the maximum excitation force of the vibration-isolating floor structure according to this embodiment may contribute to achieving goals such as "Goal 9: Build resilient infrastructure, promote inclusive and sustainable industrialization and foster innovation," among the 17 Sustainable Development Goals (SDGs). [Explanation of symbols]

[0043] 1 Vibration-proof floor structure 2 Support structure 3. Vibration-isolating floor 4. Support spring 5 Damping elements 6. Rotational Inertia Mass Element

Claims

1. An acceleration measurement step for measuring the acceleration of a vibration-isolating floor provided via a support spring with its spring axis oriented vertically on a support structure, From the aforementioned time series of accelerations, a maximum acceleration calculation process is performed to determine the maximum acceleration, A first-order natural frequency calculation step is performed to determine the first-order natural frequency from the Fourier spectrum of the acceleration, A transfer function calculation step to determine the transfer function from the input excitation force to the response acceleration of the vibration-isolating floor, A method for estimating the maximum excitation force of a vibration-isolating floor structure, comprising a maximum excitation force calculation step of calculating the maximum excitation force from the maximum acceleration, the primary natural frequency, and the transfer function.

2. Between the support structure and the vibration-isolating floor, a damping element and a rotational inertia mass element are provided. In the transfer function calculation process, The equation of motion for the aforementioned vibration-isolating floor is expressed by the following equation (1): From the following equation (2), obtained by Laplace transforming equation (1) above, the transfer function is calculated using the following equation (3): In the process of calculating the maximum excitation force, When the acceleration is a sine wave, in equation (3), the maximum acceleration a ｍaｘ Using angular frequency ω and imaginary unit j, the maximum excitation force is calculated using the following equation (4), where s = jω. A method for estimating the maximum excitation force of a vibration-isolating floor structure according to claim 1, wherein, when the acceleration is expressed as the sum of a first-order sine wave, a second-order sine wave, and a third-order sine wave, the maximum excitation force is calculated from equation (4) by approximating it to one of the first-order sine wave, a second-order sine wave, and a third-order sine wave. [Math 1]

3. Between the support structure and the vibration-isolating floor, a damping element and a rotational inertia mass element are provided. In the transfer function calculation process, The equation of motion for the aforementioned vibration-isolating floor is expressed by the following equation (5): From the following equation (6), obtained by Laplace transforming equation (5) above, the transfer function is calculated using the following equation (7): In the process of calculating the maximum excitation force, When the acceleration is sinusoidal, in equation (7), the maximum acceleration a ｍaｘ Using angular frequency ω and imaginary unit j, the maximum excitation force is calculated using the following equation (8), where s = jω. When the acceleration is expressed by summing a first-order sine wave, a second-order sine wave, and a third-order sine wave, the maximum acceleration a ｍaｘ A method for estimating the maximum excitation force of a vibration-damping floor structure according to claim 1, comprising decomposing the waveform into three components: a first sine wave, a second sine wave, and a third sine wave; calculating the maximum excitation force for each component from equation (8); and summing up the maximum excitation forces for each component to determine the maximum excitation force. [Math 2]

4. A method for estimating the maximum excitation force of a vibration-isolating floor structure according to any one of claims 1 to 3, wherein the acceleration measurement step involves measuring the displacement and velocity of the vibration-isolating floor to calculate the acceleration.

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