A method for determining the damping ratio of a structure using solid-borne sound

Abstract

The application provides a method for measuring damping ratio of a building by using solid sound waves, which comprises calculating an attenuation coefficient α of sound waves in the building; obtaining an undamped natural angular frequency ω n of the building according to physical parameters of the building; and calculating a damping ratio ζ by bringing the attenuation coefficient α and the undamped natural angular frequency ω n into a formula. The method has the advantages of simple testing device, easy operation, simple operation process, greatly reduced testing cost and time, and suitability for on-site testing and large-scale structure application, especially for structures difficult to test in a laboratory environment. Through reasonable data analysis method, the damping ratio of the building can be relatively accurately measured.

Description

Technical Field

[0001] This invention relates to the technical field of seismic design of building structures, and in particular to a method for determining the damping ratio of a building using solid-borne sound waves. Background Technology

[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 acquire vibration data, and then calculate the damping ratio through data analysis. However, existing methods have the following problems:

[0003] Free decay testing: This test is complex, requiring the application of sufficient initial vibrational energy to the structure to induce free vibration, followed by recording its natural decay process. This process often necessitates sophisticated experimental setups and numerous sensors, increasing both cost and difficulty. For large structures, traditional free decay testing is difficult to implement in real-world engineering environments because it is challenging to find a sufficiently large space to ensure that the structure's free vibration is unaffected by external factors. Test results may be influenced by environmental factors such as temperature variations, humidity, and wind, leading to instability.

[0004] Forced vibration testing: The testing process is complex. To apply precise periodic excitation, high-precision vibration tables or vibration generators are required, which are expensive, making the entire testing process costly. The experimental setup is also cumbersome, requiring precise control of the frequency and amplitude of the excitation signal. This often necessitates specialized personnel for setup and adjustment, further increasing the complexity of the experiment. Due to the need for specialized experimental equipment and environments, forced vibration testing can typically only be conducted in a laboratory and is difficult to apply to actual structures in the field.

[0005] Environmental vibration testing presents significant uncertainties in its results. While it utilizes natural environmental vibrations (such as wind and traffic) as excitation sources, these vibrations are typically random, difficult to control and predict, leading to substantial uncertainty in the test results. Data processing is complex; environmental vibration signals contain multiple frequency components, requiring sophisticated signal processing techniques to separate and extract useful vibration signals, placing high demands on data analysis. Furthermore, it is difficult to apply to specific frequencies. If testing the damping ratio at a specific frequency is required, environmental vibration testing may not be suitable because the frequency range of natural environmental vibrations is often unpredictable.

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

[0007] The purpose of this invention is to provide a method for determining the damping ratio of a building using solid-borne sound waves. By utilizing the principle of solid-borne sound transmission, the testing process is simplified, costs are reduced, and the stability and reliability of the measured damping ratio of the building are improved.

[0008] This invention provides a method for determining the damping ratio of a building using solid-borne sound waves, comprising:

[0009] Calculate the attenuation coefficient α of sound waves inside the building;

[0010] The undamped natural angular frequency ω of the building is obtained based on the building's physical parameters. n ;

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

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

[0013] A sound wave is emitted from the first location on the building, the initial amplitude of which is A. o ;

[0014] The sound wave is received at a second location on the building, with an amplitude of A1. The propagation distance from the first location to the second location is x1. Based on the attenuation law of sound waves, the following formula is obtained: ;

[0015] The sound wave is received at a third location on the building, with an amplitude of A2. The propagation distance from the first location to the third location is x2. Based on the attenuation law of sound waves, the following formula is obtained: ;

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

[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 vibrating 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] in, It takes into account the material properties The function, It takes into account the support characteristics The function;

[0024] The values ​​are 0 and When the value is 0, we get: .

[0025] Optionally, the material property M includes the material's elastic modulus. Material loss factor ,

[0026] satisfy: ,in and It is a coefficient related to material properties.

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

[0028] Optionally, the support characteristic S includes the equivalent stiffness of the support. Equivalent damping coefficient of the support ,

[0029] satisfy: ,in and It is a coefficient related to the support characteristics.

[0030] Optionally, the The recommended value range is between (-0.15, 0.15).

[0031] Optionally, the damping ratio of the building in different directions can be determined based on the different orientations of the first to second positions.

[0032] This method, which uses solid-borne sound waves to determine the damping ratio of a building, has the following advantages:

[0033] 1) Simple and quick: The testing device is simple and easy to use, and the operation process is simple, which greatly reduces the testing cost and time.

[0034] 2) High applicability: Suitable for field testing and large-scale structural applications, especially for structures that are difficult to test in a laboratory environment.

[0035] 3) Accurate and reliable: Through precise data analysis methods and based on the different orientations of relative measuring points, the damping ratio of a building in different directions can be determined relatively accurately. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of the spatial distribution of the measuring points;

[0037] Figure 2 This is a schematic diagram of the elevation distribution of the measuring points. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of this invention clearer, the 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 merely illustrative and not intended to limit the invention.

[0039] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "front," "rear," "vertical," "horizontal," "inner," and "outer," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention; the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance; furthermore, unless otherwise explicitly specified and limited, the terms "installed," "connected," and "linked" should be interpreted broadly, for example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a direct connection or an indirect connection through an intermediate medium, or they can refer to the internal communication of two components. For those skilled in the art, the specific meaning of the terms in this invention can be understood according to the specific circumstances.

[0040] This embodiment provides a method for determining the damping ratio of a building using solid-borne sound waves, including:

[0041] S1. Calculate the attenuation coefficient α of sound waves inside the building;

[0042] First, suppose we emit a sound wave at one end of a building, with an initial amplitude of... After a distance After propagation, the amplitude at the other end of the building becomes According to the attenuation law of sound waves, the attenuation of amplitude can be expressed as: ;

[0043] in, It is the attenuation coefficient of the sound wave in this propagation path of the building.

[0044] Taking the natural logarithm of both sides of the above expression, we get: .

[0045] Specifically, the calculation of the building attenuation coefficient α includes:

[0046] S11. A sound wave is emitted at the first location on the building, the initial amplitude of the sound wave being A. o ;

[0047] S12. The sound wave is received at a second location on the building. The amplitude of the sound wave at the second location is A1, and the propagation distance from the first location to the second location is x1. Based on the attenuation law of sound waves, the following formula is obtained: ;

[0048] S13. The sound wave is received at the third position of the building, the amplitude of the sound wave at the third position is A2, and the propagation distance from the first position to the third position is x2. According to the attenuation law of sound waves, the following formula is obtained: ;

[0049] S14. Combining Formula 1 and Formula 2, we can obtain that the attenuation coefficient α satisfies:

[0050] .

[0051] It should be noted that, in the specific calculation, multiple test points on the building should be selected for testing and calculation to ensure the accuracy of the value of α.

[0052] S2. Obtain the undamped natural angular frequency ω of the building based on its physical parameters. n ;

[0053] The undamped natural angular frequency ω of the building n satisfy:

[0054] ;

[0055] Where m is the mass of the building and k is the stiffness of the building, both of which are stability physical parameters of the building.

[0056] S3, combine the attenuation coefficient α and the undamped natural angular frequency ω n Substitute into the formula In the process, the damping ratio ζ is calculated.

[0057] Assuming that building components can be considered as a vibrating system, from the perspective of vibration theory, when considering a building as a vibrating system, 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 energy attenuation and natural frequency in a damped system in classical vibration theory, its damping ratio... With attenuation coefficient The relationship can be approximated as (for the case of small damping): ,

[0058] The formula takes into account the corrections to the damping ratio based on the building's material properties and support characteristics. In the 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 form of formula can approximate the actual damping ratio well within a certain error range; therefore, an approximate formula was adopted.

[0059] It takes into account the material properties The function, such as the correction of the relationship between damping ratio and attenuation coefficient by factors such as material type, strength, and aging degree.

[0060] Assuming material properties Mainly includes the elastic modulus of the material Material loss factor ,but It can be represented as:

[0061] ,in and These are coefficients that can be determined through experiments or theoretical analysis. Experimental methods involve conducting a series of mechanical property tests on the materials used in the building, including elastic modulus testing and loss factor testing. Under different stress and frequency conditions, the material's response characteristics are measured, and then regression analysis is performed based on the experimental data to obtain coefficients related to the material properties. Theoretical analysis methods are based on the material's constitutive relations and vibration theory, establishing a mechanical model of the material, solving the model equations, and verifying and adjusting them using known material parameters and experimental data to ultimately determine the coefficients.

[0062] As a material adjustment factor, its value generally ranges from -0.1 to 0.1.

[0063] It takes into account the support characteristics Functions such as the type of support (fixed support, sliding support, etc.), the stiffness and damping of the support, etc., modify the relationship.

[0064] Assuming support characteristics This mainly includes the equivalent stiffness of the supports. The equivalent damping coefficient of the support By 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. Simultaneously, by analyzing the energy dissipation of the bearing during vibration and combining relevant theories, the equivalent damping coefficient is calculated. It can be represented as:

[0065] ,in and These coefficients can be determined through experiments or theoretical analysis. The experimental method involves conducting simulated loading experiments on the support structure, measuring the changes in the equivalent stiffness and equivalent damping coefficients of the support under different loads and frequencies, and obtaining the coefficients through fitting analysis based on the experimental data. This experimental method can measure the characteristic parameters of the support, providing a relatively reliable data foundation for determining the coefficients. The theoretical analysis method, based on the mechanical model of the support and vibration theory, considers the structural form and material properties of the support. By solving relevant equations and verifying and adjusting them in conjunction with experimental data, the coefficients are determined. Theoretical analysis can provide a deeper understanding of the support characteristics and provide a theoretical basis for interpreting experimental results and determining the coefficients. Simultaneously, theoretical analysis can also predict the changes in support characteristics under different working conditions, providing guidance for structural design and optimization.

[0066] As a support adjustment coefficient, its value is generally between (-0.15, 0.15).

[0067] Then the above about Substituting the expression into the formula, we get:

[0068] To simplify the measurement method without significantly affecting the measurement accuracy, The value is 0. Taking the value as 0, we get the simplified formula: .

[0069] In summary, the attenuation coefficient can be calculated by measuring the sound wave amplitude at different distances. Then, combined with the undamped natural angular frequency calculated from the physical parameters of the building components... This allows for the determination of the damping ratio of building components. .

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

[0071] (a) Preparatory work

[0072] A. Select a suitable test location:

[0073] Select representative structural components from various corners of the building, such as columns, beams, or walls, ensuring that the materials are uniform and free of obvious defects. For example... Figure 1 , Figure 2 As shown,

[0074] B. Preparation of instruments and equipment:

[0075] Sound wave generator: Uses 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: A high-sensitivity acoustic wave receiver is used to measure the amplitude and frequency of acoustic wave signals with accuracies of ±1μV and ±1Hz, respectively.

[0077] D. Data Acquisition System: A data acquisition system consisting of a data acquisition card and a computer is used to 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 of sound wave propagation with an accuracy of ±1cm.

[0079] (II) Testing Process

[0080] A. Equipment installation:

[0081] Generator installation: Securely install the sound wave generator on a column on the first floor to ensure that the sound waves can be effectively transmitted to the component.

[0082] B. Receiver Installation: Install the acoustic receiver on the corresponding column on the 6th floor, ensuring good contact and fixation.

[0083] Initial parameter settings:

[0084] Frequency selection: Set the initial frequency of the sound wave generator to 100Hz, and select 5 frequencies for testing: 100Hz, 200Hz, 300Hz, 383Hz (to more comprehensively cover the possible frequency range, a non-100Hz frequency is added here) and 500Hz.

[0085] C. Data Acquisition:

[0086] Signal recording: Start the sound wave generator and simultaneously start the data acquisition system to record the sound wave signal output by the generator and the signal received by the receiver. For each set frequency, maintain signal transmission 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, data from periods when the received signal is stable are selected for analysis.

[0093] (III) Data Processing and Analysis

[0094] A. Calculate the attenuation coefficient:

[0095] For each frequency and test location, the attenuation coefficient is calculated using the following formula, based on the variation of the acoustic wave amplitude received by the receiver with propagation distance. : in, and They are at the distance and The amplitude of the sound waves received at the location.

[0096] B. Calculate the undamped natural angular frequency.

[0097] Based on the physical parameters of the building components (such as mass and stiffness), use the formula Calculate the undamped natural angular frequency ,in It is the rigidity of the building. It refers to the quality of the building.

[0098] C. Calculate the damping ratio:

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

[0100] D. Data Synthesis and Evaluation:

[0101] By combining data from all test locations and frequencies, the average damping ratio is calculated, and its reliability and consistency are evaluated.

[0102] (iv) Results Report

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

[0104] The test results are analyzed and discussed to explain the damping characteristics of the building and its potential impact on structural performance and vibration control.

[0105] In actual testing, the positions can be changed and the tests repeated. This can reduce external interference, and the data can be carefully screened and processed. Based on the measured data, the material adjustment coefficient and the support adjustment coefficient can be fitted and assumed to ensure the accuracy and reliability of the measurement results.

[0106] (V) Calculation Examples

[0107] A. Basic Building Information

[0108] Assume the building to be measured is a reinforced concrete frame office building with 6 floors above ground and a total height of 24m. The building's plan dimensions are 40m × 30m, with a centrally located core tube measuring 20m × 15m.

[0109] B. Mass and Stiffness Calculation

[0110] Quality per layer:

[0111] Through structural calculations, the mass distribution of each floor is obtained as follows: Floor 1 is... kg, 2-6 layers, each layer is kg.

[0112] Stiffness per layer:

[0113] Based on the structural design drawings, the stiffness of each floor is calculated as follows: Floor 1 stiffness is... N / m, stiffness of each of the 2nd to 6th floors is N / m.

[0114] Overall structural mass ( ):

[0115] The total mass of the structure is the sum of the masses of each layer, that is... kg

[0116] Lateral stiffness ( ):

[0117] For frame structures, the lateral stiffness can be approximated by a series spring model, based on the equivalent stiffness formula for series springs.

[0118] ( For the number of floors, (Stiffness of each layer).

[0119] For floor 1 For floors 2-6, .

[0120] but

[0121] so

[0122] but N / m

[0123] C. Calculate the damping ratio

[0124] Calculate the attenuation coefficient: Calculate the attenuation coefficient according to the formula. ,in The distance the sound wave travels between the two measurement points. and These represent the sound wave amplitudes received at two measurement points at this distance. Taking measurement point 1 at a frequency of 100Hz as an example, assuming the amplitude at measurement point 1, located 10m apart, is calculated based on the amplitude length... for The amplitude at measuring point 2 for Then the attenuation coefficient .

[0125] Calculate the undamped natural angular frequency ( ):

[0126] According to the formula ,in For the lateral stiffness of the building, For the overall structural mass.

[0127] Known N / m, kg, then ;

[0128] Substitute into the formula: Calculate the attenuation coefficient and undamped natural angular frequency Substitute into the formula to calculate the damping ratio, where and These are adjustment factors considering material properties and support properties, respectively. In this example, it is assumed that... , ,but

[0129] .

[0130] The application areas of this solution are as follows:

[0131] Seismic design and vibration isolation of building structures: By measuring the damping of similar buildings, a more accurate damping ratio is used to design a safer, more economical and reasonable seismic design and vibration isolation system.

[0132] Building structure reinforcement: The method of this invention can quickly and relatively accurately determine the damping ratio of existing buildings, providing important data for seismic design, seismic reinforcement and renovation of structures.

[0133] Computational analysis of complex structures: In the vibration analysis of ultra-high, long-span and complex combined structures, the vibration status of the structure can be monitored in real time, providing important reference for operation and maintenance.

[0134] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A method for determining the damping ratio of a structure using solid-borne sound, characterized in that Comprising: calculating the attenuation coefficient a of sound wave in the building; obtaining a damped natural angular frequency ωdof the building from the physical parameters of the building n ; The attenuation coefficient a and the undamped natural angular frequency ω n Substituting the formula The damping ratio ζ is calculated The calculation of the attenuation coefficient a of sound wave in the building comprises: emitting a sound wave at a first location of a building, the initial amplitude of the sound wave being A o ; receiving the sound wave at a second position of the building, the amplitude of the sound wave at the second position being A1, the propagation distance from the first position to the second position being x1, and according to the attenuation law of the sound wave, the following formula one is obtained: ; receiving the sound wave at a third position of the building, the amplitude of the sound wave at the third position being A2, the propagation distance from the first position to the third position being x2, and according to the attenuation law of the sound wave, the following Formula Two is obtained: ; The attenuation coefficient a satisfies: ； the undamped natural angular frequency ω of the building n approximately satisfies: ； Wherein, m is the mass of the building, and k is the stiffness of the building; assuming that the building is a vibrating system; the relationship of the damping ratio ζ and the attenuation coefficient α and the undamped natural angular frequency ω n of the building satisfies: ， ； wherein, is a function taking into account the material properties , is a function taking into account the support properties , has a value ranging between (-0.15, 0.15); = 0 and = 0, we get ; The material properties M comprise the elastic modulus of the material , the loss factor of the material , satisfies: wherein and are material property dependent coefficients.

2. The method of determining the damping ratio of a structure using solid-borne sound according to claim 1, characterized in that The value range is between (-0.1, 0.1).

3. The method of determining the damping ratio of a structure using solid-borne sound according to claim 1, wherein, The support characteristics S comprise an equivalent stiffness of the support and an equivalent damping coefficient of the support , satisfies: , wherein and are coefficients related to the properties of the support.

4. The method of determining the damping ratio of a structure using solid-borne sound according to claim 1, wherein, According to the different orientations from the first position to the second position, the damping ratio of the building in different directions is determined.

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