Method for measuring damping ratio of building by using solid-borne sound waves

Abstract

The invention provides a method for measuring a damping ratio of a building by using solid-borne sound waves. The method comprises the following steps: calculating an attenuation coefficient alpha of sound waves in the building; obtaining an undamped natural angular frequency omega n of the building according to the physical parameters of the building; and substituting the attenuation coefficient alpha and the undamped natural angular frequency omega n into a formula # imgabs0 #, and calculating a damping ratio zeta. The test device is simple and easy to use, the operation process is simple and convenient, and the test cost and time are greatly reduced. The device is suitable for field testing and application of large-scale structures, and is especially suitable for structures which are difficult to test in a laboratory environment. Through a reasonable data analysis method, the damping ratio of the building can be relatively accurately measured.

Description

Technical Field

[0001] The invention relates to the technical field of earthquake-resistant design of building structures, and in particular to a method for measuring the damping ratio of a building by utilizing solid-borne sound waves. Background Art

[0002] Currently, the main methods for determining the damping ratio of buildings include free decay tests, forced vibration tests, and environmental vibration tests. These methods typically rely on equipment such as accelerometers and laser vibrometers to obtain vibration data, and then calculate the damping ratio through data analysis. However, existing methods have the following problems:

[0003] Free decay testing: This complex testing process requires applying sufficient initial vibration energy to the structure to induce free vibration, and then recording its natural decay process. This process often requires complex experimental setups and a large number of sensors, increasing the cost and difficulty of testing. For large structures, traditional free decay testing is difficult to implement in actual engineering environments due to the difficulty in finding a large enough space to ensure that the structure's free vibration is not disturbed by external factors. Test results may be affected by environmental factors such as temperature fluctuations, humidity, and wind, resulting in unstable test results.

[0004] Forced vibration testing: This testing process is complex. To apply precise periodic excitation, a high-precision vibration table or vibration generator is required. These devices are expensive, making the entire testing process costly. Experimental setup is cumbersome and requires precise control of the frequency and amplitude of the excitation signal, which often requires specialized experimental personnel to set up and adjust, increasing the complexity of the experiment. Due to the specialized experimental equipment and environment required, forced vibration testing can usually only be performed in the laboratory, making it difficult to apply to actual structures in the field.

[0005] Environmental vibration testing: Its test results are highly uncertain. Environmental vibration testing utilizes natural environmental vibrations (such as wind and traffic) as an excitation source. However, these natural vibrations are often random and difficult to control and predict, resulting in significant uncertainty in the test results. Data processing is complex. Because environmental vibration signals contain multiple frequency components, sophisticated signal processing techniques are required to separate and extract useful vibration signals, placing high demands on data analysis. Application to specific frequencies is difficult. If the damping ratio at a specific frequency needs to be tested, environmental vibration testing may not meet the requirements, as the frequency range of natural environmental vibrations is often uncertain.

[0006] In summary, existing methods for determining the damping ratio of buildings have many limitations in practical applications, particularly in terms of testing cost, test environment requirements, and stability of test results. Therefore, it is imperative to develop a simple, efficient, and accurate method for determining the damping ratio of buildings. Summary of the Invention

[0007] The purpose of the present invention is to provide a method for measuring the damping ratio of a building using solid-borne sound waves, which simplifies the test process by utilizing the principle of solid-borne sound transmission, reduces costs, and improves the stability and reliability of the measurement results of the building damping ratio.

[0008] The present invention provides a method for measuring the damping ratio of a building by using solid-borne sound waves, comprising:

[0009] Calculate the attenuation coefficient α of sound waves in buildings;

[0010] The undamped natural angular frequency ω of the building is obtained according to the physical parameters of the building. n ;

[0011] The attenuation coefficient α and the undamped natural angular frequency ω n Substitute into the formula , calculate the damping ratio ζ.

[0012] Optionally, calculating the building attenuation coefficient α includes:

[0013] A sound wave is emitted at a first location in the building, the initial amplitude of the sound wave is A o ;

[0014] The sound wave is received at a second location of the building. The amplitude of the sound wave at the second location is A1. The propagation distance from the first location to the second location is x1. According to the attenuation law of the sound wave, the following formula 1 is obtained: lnA1=lnA0-αx1;

[0015] The sound wave is received at a third position of the building. The amplitude of the sound wave at the third position is A2. The propagation distance from the first position to the third position is x2. According to the attenuation law of the sound wave, the following formula 2 is obtained: lnA2=lnA0-αx2;

[0016] Combining Formula 1 and Formula 2, we can get the attenuation coefficient α:

[0017]

[0018] Optionally, the undamped natural angular frequency ω of the building n Approximately satisfies:

[0019]

[0020] Where m is the mass of the building and k is the stiffness of the building.

[0021] Optionally, it is assumed that the building is a vibration system. The damping ratio ζ is related to the attenuation coefficient α and the undamped natural angular frequency ω. n The relationship satisfies:

[0022]

[0023] Among them, f m (M) is a function that takes into account the material properties M, g s (S) is a function that takes into account the support characteristic S;

[0024] f m (M) takes values ​​of 0 and g s When (S) takes the value of 0, we get:

[0025] Optionally, the material property M includes the elastic modulus E of the material, the loss factor η of the material m ,

[0026] f m (M) Satisfy: Where a1 and a2 are coefficients related to material properties.

[0027] Optional, f m The recommended value range of (M) is between (-0.1, 0.1).

[0028] Optionally, the support characteristic S includes the equivalent stiffness k of the support s and the equivalent damping coefficient c of the support s , g s (S) Satisfy: where b1 and b2 are coefficients related to the support properties.

[0029] Optionally, the g s The recommended value range of (S) is between (-0.15, 0.15).

[0030] Optionally, the damping ratio of the building in different directions is measured according to different orientations from the first position to the second position.

[0031] This method of measuring the damping ratio of a building using solid-borne sound waves has the following advantages:

[0032] 1) Simple and fast: The test device is simple and easy to use, and the operation process is simple, which greatly reduces the test cost and time.

[0033] 2) Strong applicability: Suitable for field testing and large-scale structure applications, especially for structures that are difficult to test in a laboratory environment.

[0034] 3) Accurate and reliable: Through precise data analysis methods and based on the different orientations of the relative measuring points, the damping ratio of the building in different directions can be measured relatively accurately. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 Schematic diagram of the spatial distribution of measuring points;

[0036] Figure 2 Schematic diagram of the distribution of measuring points. DETAILED DESCRIPTION

[0037] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0038] In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "front", "back", "vertical", "horizontal", "inside", "outside" and the like indicating directions or positional relationships are based on the directions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the devices or components referred to must have a specific direction, be constructed and operated in a specific direction, and therefore should not be understood as limiting the present invention; the terms "first", "second", and "third" are only used for descriptive purposes and should not be understood as indicating or implying relative importance; in addition, unless otherwise expressly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a direct connection, an indirect connection through an intermediate medium, or a communication between the internal parts of two components. For those skilled in the art, the specific meanings of the terms in the present invention can be understood according to specific circumstances.

[0039] This embodiment provides a method for measuring the damping ratio of a building using structure-borne sound waves, comprising:

[0040] S1. Calculate the attenuation coefficient α of the sound waves in the building;

[0041] First, suppose we launch a sound wave at one end of a building with an initial amplitude of A0. After propagating a distance x, the amplitude at the other end of the building becomes A. According to the attenuation law of sound waves, the attenuation of the amplitude can be expressed as: A = A0e -αx ;

[0042] Among them, α is the attenuation coefficient of the sound wave in the propagation path of the building.

[0043] Taking the natural logarithm of both sides of the above equation, we can obtain: lnA = lnA0-αx.

[0044] Specifically, the calculation of the building attenuation coefficient α includes:

[0045] S11, emitting a sound wave at a first position of the building, wherein the initial amplitude of the sound wave is A o ;

[0046] S12. Receive the sound wave at a second location in the building. The amplitude of the sound wave at the second location is A1. The propagation distance from the first location to the second location is x1. According to the attenuation law of the sound wave, the following formula 1 is obtained: lnA1=lnA0-αx1;

[0047] S13. Receive the sound wave at a third location of the building. The amplitude of the sound wave at the third location is A2. The propagation distance from the first location to the third location is x2. According to the attenuation law of the sound wave, the following formula 2 is obtained: lnA2=lnA0-αx2;

[0048] S14. Combining Formula 1 and Formula 2, the attenuation coefficient α satisfies:

[0049]

[0050] It should be noted that, during the specific calculation, multiple test points on the building should be selected for test calculation to ensure the accuracy of the α value.

[0051] S2. Obtain the undamped natural angular frequency ω of the building according to the physical parameters of the building n ;

[0052] The undamped natural angular frequency ω of the building n satisfy:

[0053]

[0054] Among them, m is the mass of the building and k is the stiffness of the building. Both values ​​are stable physical parameters of the building.

[0055] S3, the attenuation coefficient α and the undamped natural angular frequency ω n Substitute into the formula , calculate the damping ratio ζ.

[0056] Assuming that building components can be viewed as a vibrating system, from the perspective of vibration theory, the damping ratio is closely related to the system's attenuation characteristics and natural frequency characteristics. Based on the basic description of the relationship between the energy attenuation and natural frequency of a damping system in classical vibration theory, the relationship between the damping ratio ζ and the attenuation coefficient α can be approximately expressed as follows (for low damping):

[0057]

[0058] The formula takes into account the corrections to the damping ratio due to the building's inherent material properties and support characteristics. In actual theoretical derivation, due to the complexity of building structures, it is difficult to obtain a precise theoretical formula to describe the relationship between the damping ratio and all influencing factors. Through extensive theoretical analysis and experimental verification, it was found that this formula can well approximate the actual damping ratio within a certain error range, so a formula that can be approximated was adopted.

[0059] f m (M) is a function that takes into account the material properties M, such as the type, strength, aging degree and other factors of the material to correct the relationship between the damping ratio and the attenuation coefficient.

[0060] Assume that the material properties M mainly include the elastic modulus E of the material, the loss factor η of the material m , then f m (M) can be expressed as:

[0061] Where a1 and a2 are coefficients that can be determined through experimentation or theoretical analysis. The experimental method involves conducting a series of mechanical property tests on the materials used in the building, including elastic modulus and loss factor tests. The material's response characteristics are measured under different stress and frequency conditions. Regression analysis is then performed based on the experimental data to determine coefficients related to the material properties. The theoretical analysis method establishes a mechanical model of the material based on its constitutive relationship and vibration theory. The coefficients are ultimately determined by solving the model equations, combining known material parameters with experimental data for verification and adjustment.

[0062] f m (M) is the material adjustment coefficient, and its value generally ranges from (-0.1, 0.1).

[0063] g s (S) is a function that takes into account the support characteristics S, such as the type of support (fixed support, sliding support, etc.), the stiffness and damping of the support, and other corrections to the relationship.

[0064] Assume that the support characteristics S mainly include the equivalent stiffness k of the support s , equivalent damping coefficient c of the support sBy analyzing calculations and empirical data, the equivalent stiffness and equivalent damping coefficient of the bearing can be obtained. For example, in a finite element model, an axial compressive load is applied to a metal-rubber composite bearing, and the deformation of the bearing is observed. The equivalent stiffness is obtained by calculating the relationship between the deformation and the applied force. At the same time, by analyzing the energy dissipation of the bearing during vibration and combining relevant theories, the equivalent damping coefficient can be calculated. Then g s (S) can be expressed as:

[0065] Among them, b1 and b2 are coefficients that can be determined through experiments or theoretical analysis. The experimental method conducts simulated loading experiments on the support structure, measures the changes in the equivalent stiffness and equivalent damping coefficient of the support under different loads and frequencies, and performs fitting analysis based on the experimental data to obtain the coefficients. This experimental method can measure the characteristic parameters of the support, providing a relatively reliable data basis for the determination of the coefficients. The theoretical analysis method is based on the mechanical model and vibration theory of the support, taking into account the structural form and material properties of the support, and determining the coefficients and by solving relevant equations and verifying and adjusting them in combination with experimental data. Theoretical analysis can provide an in-depth understanding of the characteristics of the support and provide a theoretical basis for the interpretation of experimental results and the determination of coefficients. At the same time, theoretical analysis can also predict the changes in the characteristics of the support under different working conditions, providing guidance for the design and optimization of the structure.

[0066] g s (S) is the support adjustment coefficient, and its value generally ranges from (-0.15, 0.15).

[0067] Substituting the above expression for α into the formula, we can get:

[0068] In order to simplify the measurement method and not affect the measurement accuracy, f m (M) takes the value of 0, g s (S) takes the value of 0, and the simplified formula is obtained:

[0069] In summary, by measuring the amplitude of the sound wave at different distances, the attenuation coefficient α is calculated, and then combined with the undamped natural angular frequency ω calculated by the physical parameters of the building components n , the damping ratio ζ of the building components can be determined.

[0070] The following is a detailed method for determining the damping ratio of a building by propagating sound waves in solids:

[0071] (1) Preparation

[0072] A. Choose a suitable test location:

[0073] Select representative structural components at all angles in the building, such as columns, beams or walls, to ensure that the materials are uniform and free of obvious defects. Figure 1 、 Figure 2 As shown,

[0074] B. Preparation of instruments and equipment:

[0075] Sound wave generator: Use a high-precision sound wave generator with an adjustable frequency range of 20Hz-20kHz and an output power of 5W.

[0076] C. Acoustic wave receiver: It uses a highly sensitive acoustic wave receiver that can measure the amplitude and frequency of acoustic wave signals with an accuracy of ±1μV and ±1Hz respectively.

[0077] D. Data acquisition system: The data acquisition system composed of a data acquisition card and a computer can record the output signal of the sound wave generator and the input signal of the receiver in real time.

[0078] E. Measuring tools: Use measuring tools such as rulers and total stations to accurately measure the distance the sound waves travel with an accuracy of ±1cm.

[0079] (2) Testing process

[0080] A. Install equipment:

[0081] Generator installation: Install the sound wave generator firmly on a pillar on the first floor to ensure that the sound waves can be effectively transmitted into the structure.

[0082] B. Receiver installation: Install the sound wave receiver on the corresponding column on the 6th floor to ensure good contact and fixation.

[0083] Initial parameter settings:

[0084] Frequency selection: Set the initial frequency of the sound wave generator to 100Hz, and select 100Hz, 200Hz, 300Hz, 383Hz (in order to more comprehensively cover the possible frequency range, a non-integer frequency is added here) and 500Hz for testing.

[0085] C. Data Collection

[0086] Signal recording: Start the acoustic wave generator and the data acquisition system at the same time, recording the acoustic wave signal output by the generator and the signal received by the receiver. For each set frequency, keep sending the signal for 10 seconds to obtain sufficient data for analysis.

[0087] D. Change the test location and conditions:

[0088] Floor Variation: Repeat the above test on different columns on floors 2-6 to obtain more comprehensive and reliable data.

[0089] Component Variation: Tests were also conducted on beams and walls on the same floor to compare the damping characteristics of different components.

[0090] E. Testing process

[0091] Calculate the attenuation coefficient:

[0092] Data selection: For each frequency and test location, select the data for the time period when the received signal is stable for analysis.

[0093] (3) Data processing and analysis

[0094] A. Calculate the attenuation coefficient:

[0095] For each frequency and test position, the attenuation coefficient α is calculated using the following formula based on the change in the amplitude of the sound wave received by the receiver with the propagation distance: Where A1 and A2 are the amplitudes of the sound waves received at distances x1 and x2, respectively.

[0096] B. Calculate the undamped natural angular frequency

[0097] According to the physical parameters of building components (such as mass, stiffness), use the formula Calculate the undamped natural angular frequency ω n , where k is the stiffness of the building and m is the mass of the building.

[0098] C. Calculate the damping ratio:

[0099] The calculated attenuation coefficient α and undamped natural angular frequency ω n Substitute into the formula Calculate the damping ratio ζ.

[0100] D. Data integration and evaluation:

[0101] The data from all test positions and frequencies are combined to calculate the average damping ratio and evaluate its reliability and consistency.

[0102] (IV) Result report

[0103] Record all parameters, data and calculation results during the test in detail.

[0104] The test results are analyzed and discussed to illustrate the damping characteristics of the building and their possible impact on structural performance and vibration control.

[0105] In actual testing, the position can be changed and the test can be repeated to reduce external interference, and the data can be carefully screened and processed, and fitting assumptions can be made for the material adjustment coefficient and the support adjustment coefficient based on the measured data to ensure the accuracy and reliability of the measurement results.

[0106] (V) Example

[0107] A. Basic information of the building

[0108] Assume that the building to be measured is a reinforced concrete frame office building with six floors above ground and a total height of 24 meters. The building has a floor plan of 40 meters by 30 meters, with a centrally located core tube measuring 20 meters by 15 meters.

[0109] B. Mass and stiffness calculation

[0110] Quality of each layer:

[0111] Through structural calculation, the mass distribution of each floor is as follows: 1st floor is 2×10 6 kg, 2-6 layers each layer is 1.8×10 6 kg.

[0112] Stiffness of each layer:

[0113] According to the structural design drawings, the stiffness of each layer is calculated as follows: the stiffness of the first layer is 5.0×10 8 N / m, the stiffness of each layer from 2 to 6 is 4.0×10 8 N / m.

[0114] Total structural mass (M):

[0115] The mass of the entire structure is the sum of the masses of each layer, that is, M = 2 × 10 6 +5×1.8×10 6 =11×10 6 kg

[0116] Lateral stiffness (K):

[0117] For frame structures, the lateral stiffness can be approximately calculated using the series spring model. According to the series spring equivalent stiffness formula,

[0118] (n is the number of layers, k i is the stiffness of each layer).

[0119] For 1 layer For 2-6 layers,

[0120] but

[0121] so

[0122] but

[0123] C. Calculate the damping ratio

[0124] Calculate the attenuation coefficient: Calculate the attenuation coefficient according to the formula Where x is the distance between the two measuring points, and A1 and A2 are the amplitudes of the sound waves received by the two measuring points before and after this distance. Taking measuring point 1 at a frequency of 100 Hz as an example, assuming that the amplitude of measuring point 1 at a distance of 10 m is calculated as A1, which is 1.0×10 -3 m, the amplitude A2 at measuring point 2 is 6.0×10 -4 m, then the attenuation coefficient

[0125]

[0126] Calculate the undamped natural angular frequency (ω n ):

[0127] According to the formula Where K is the lateral stiffness of the building and M is the mass of the entire structure.

[0128] It is known that K≈6.9×10 7 N / m, M=11×10 6 kg, then

[0129] Substitute the calculated attenuation coefficient α and the undamped natural angular frequency ω into the formula: n Substitute into the formula to calculate the damping ratio, where f m (M) and g s (S) are adjustment coefficients considering material properties and support properties. In this example, it is assumed that f m (m) = 0.1, g s (S) = 0.1, then

[0130]

[0131] The application areas of this solution are as follows:

[0132] Earthquake-resistant and seismic isolation design of building structures: By measuring the damping of buildings of the same type, a relatively accurate damping ratio is used to carry out earthquake-resistant and seismic isolation design that is safer, more economical and reasonable.

[0133] Building structure reinforcement: The method of the present invention can be used to quickly and relatively accurately determine the damping ratio of existing buildings, providing important data for the seismic design, seismic reinforcement and renovation of the structure.

[0134] Calculation and analysis of complex structures: In the vibration analysis of ultra-high, large-span and complex composite structures, the vibration working conditions of the structure can be monitored in real time, providing important reference for operation and maintenance.

[0135] The above-described embodiments merely illustrate several implementations of the present invention, and while their descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the spirit of the present invention, all of which fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be determined by the appended claims.

Claims

1. A method for measuring the damping ratio of a building using solid-borne sound waves, characterized in that: include: Calculate the attenuation coefficient α of sound waves in the building; The undamped natural angular frequency ω of the building is obtained according to the physical parameters of the building. n ; The attenuation coefficient α and the undamped natural angular frequency ω n Substitute into the formula , calculate the damping ratio ζ.

2. The method for measuring the damping ratio of a building by using solid-borne sound waves according to claim 1, characterized in that: The calculation of the building attenuation coefficient α comprises: A sound wave is emitted at a first location in the building, the initial amplitude of the sound wave is A o ; The sound wave is received at a second position of the building, the amplitude of the sound wave at the second position is A1, the propagation distance from the first position to the second position is x1, and according to the attenuation law of the sound wave, the following formula 1 is obtained: lnA1=lnA0-αx1; The sound wave is received at a third position of the building, the amplitude of the sound wave at the third position is A2, the propagation distance from the first position to the third position is x2, and according to the attenuation law of the sound wave, the following formula 2 is obtained: lnA2=lnA0-αx2; Combining Formula 1 and Formula 2, we can get the attenuation coefficient α to satisfy:

3. The method for measuring the damping ratio of a building by using solid-borne sound waves according to claim 1, characterized in that: The undamped natural angular frequency ω of the building n Approximately meets: Where m is the mass of the building and k is the stiffness of the building.

4. The method for measuring the damping ratio of a building by using solid-borne sound waves according to claim 1, characterized in that: Assume that the building is a vibration system; the damping ratio ζ is related to the attenuation coefficient α and the undamped natural angular frequency ω n The relationship satisfies: Among them, f m (M) is a function of the material property M, g s (S) is a function that takes into account the support characteristic S; f m (M) takes values ​​of 0 and g s When (S) takes the value of 0, we get:

5. The method for measuring the damping ratio of a building by using solid-borne sound waves according to claim 4, characterized in that: The material property M includes the elastic modulus E of the material, the loss factor η of the material m , f m (M) Satisfy: Where a1 and a2 are coefficients related to material properties.

6. The method for measuring the damping ratio of a building by using solid-borne sound waves according to claim 4, characterized in that: f m (M) value range is between (-0.1,0.1).

7. The method for measuring the damping ratio of a building by using solid-borne sound waves according to claim 4, characterized in that: The support characteristics S include the equivalent stiffness k of the support s and the equivalent damping coefficient c of the support s , g s (S) Satisfy: where b1 and b2 are coefficients related to the support properties.

8. The method for measuring the damping ratio of a building by using solid-borne sound waves according to claim 4, characterized in that: The g s The value range of (S) is between (-0.15, 0.15).

9. The method for measuring the damping ratio of a building by using solid-borne sound waves according to claim 2, characterized in that: According to different orientations from the first position to the second position, the damping ratio of the building in different directions is measured.

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