Vibration wave propagation calculation method based on WPA method and application thereof

Abstract

The invention provides a vibration wave propagation calculation method based on a WPA method and application thereof, and the calculation method comprises the steps: S1, supplementing the propagation and reflection parameters of vibration waves at the joints of a beam, a plate and a column based on the classical theory of the WPA method; s2, compiling a code by adopting matlab software, and calculating the response of the vibration wave at any moment and any position in the structure according to the obtained propagation and reflection parameters of the vibration wave; s3, calculating the actual structure by using the written code, performing field test, verifying the code calculation accuracy, and calculating the response of the vibration wave at any moment and any position in the structure according to the verified code; and S4, calculating acceleration peak values of different positions of each layer under excitation of different points of each layer, and further returning a vibration propagation rule of vibration waves between the same layer and different layers. According to the technical scheme, vibration wave propagation analysis and calculation are expanded to the overall structure and are closer to the actual situation.

Description

Technical Field

[0001] The present invention relates to the technical field of building vibration analysis, and in particular to a vibration wave propagation calculation method based on a WPA method and an application thereof. Background Art

[0002] The existing research on vibration wave propagation calculation is mainly aimed at a single component, such as the propagation of vibration waves in beams, plates or columns in a structure. Commonly used methods include the transfer matrix method using boundary approximation, the admittance method using indirect parameters, and the spectrum analysis method in the frequency domain. The above methods can be used to calculate the vibration response of vibration waves at any time and any position in a single component. However, there are some problems with this method: (1) It rarely involves structures composed of multiple components, or ignores the reflection and refraction of vibration waves at the joints of beams, plates and columns; (2) For the specific method using boundary approximation, there is often a difference between the actual boundary conditions, making the calculation results inaccurate; (3) For the specific method using indirect parameters, the selection of indirect parameters has a greater impact on the calculation accuracy, and the calculation selection of this parameter often has errors; (4) For the analysis method in the frequency domain, its calculation is relatively complicated, and the requirements for boundary conditions are vague, which is more suitable for the calculation of a single component. Summary of the invention

[0003] In response to the above technical problems, the present invention discloses a vibration wave propagation calculation method based on the WPA method and its application. The obtained vibration propagation law of the vibration wave between the same layer and different layers is more accurate, and the response of the target position can be quickly judged.

[0004] To this end, the technical solution adopted by the present invention is:

[0005] A vibration wave propagation calculation method based on the WPA method comprises the following steps:

[0006] Step S1, based on the classical theory of WPA method and according to the dynamic characteristics of the connection between beams, plates and columns, supplement the propagation and reflection parameters of the vibration waves at the connection between beams, plates and columns;

[0007] Step S2, based on the WPA method theory, using Matlab software to write code, according to the obtained propagation and reflection parameters of the vibration wave, calculate the response of the vibration wave at any time and any position in the structure;

[0008] Step S3, using the written code to calculate the actual structure, and conducting field tests to verify the accuracy of the code calculation, and calculating the response of the vibration wave at any time and any position in the structure according to the verified code;

[0009] Step S4, calculate the acceleration peaks at different positions of each layer under the excitation of different points of each layer, and regress to obtain the vibration propagation law of the vibration wave in the same layer and between different layers.

[0010] This technical solution takes into account the reflection and refraction of vibration waves at the connections of beams, plates and columns, so that the vibration wave propagation analysis and calculation is not limited to the components, but expanded to the overall structure, making the calculated rules more in line with the actual situation.

[0011] As a further improvement of the present invention, in step S1, the beam and slab are divided into middle simple support, end simple support and end fixed support at the connection;

[0012] Among them, the four structural wave amplitudes of the plate-beam structure in the case of intermediate simple support are:

[0013]

[0014] Among them, A r is the amplitude of the reflected wave, A nl is the amplitude of the reflected near-field wave, A t , A nr are the amplitudes of the transmitted propagation wave and the near-field wave, A i is the amplitude of the incident bending wave, j is the initial phase angle;

[0015] Two reflected wave amplitudes A of the plate-beam structure with simply supported ends r , A nl They are:

[0016]

[0017] Among them, A i is the amplitude of the normally incident bending wave;

[0018] Two reflected wave amplitudes A of the plate-beam structure under the condition of end clamping r , A nl They are:

[0019]

[0020] Among them, A i is the amplitude of the forward incident bending wave, and j is the initial phase angle.

[0021] As a further improvement of the present invention, in step S1, for the connection between the plate and column, if the connection between the plate and column is a rigid connection, the reflection of the wave is ignored;

[0022] If the plate-column connection is semi-rigid, solve the following equation to obtain the reflection wave parameters:

[0023]

[0024]

[0025] w 板 =w 柱

[0026] M 板 -M 柱 =K θ (θ 柱 -θ 板 )

[0027] Among them, M 连接 is the bending moment at the connection, θ 柱 ,θ 板 is the rotation angle of the plate column at the connection. 柱 ,θ 板 M is the rotation angle of the plate column at the connection point; 板 is the bending moment of the plate, M 柱 is the bending moment of the column, W 板 is the displacement of the plate, W 柱 is the displacement of the column; K θ is the stiffness of the corner of the connection;

[0028] If the plate-column joint is hinged at the connection, rotation is allowed, no bending moment is transmitted, only shear force and axial force are transmitted, and the reflected wave parameters are obtained by solving the following equation:

[0029] M 连接 =0

[0030] w 板 =w 柱

[0031] M 板 =0,M 柱 =0

[0032] Among them, M 连接 is the bending moment at the connection.

[0033] As a further improvement of the present invention, step S2 is calculated using the following steps:

[0034] Step S21, considering the damping loss factor and the damping bending stiffness, defining the physical and geometric parameters of the beam, plate and column;

[0035] Step S22, defining excitation parameters and extracting measurement point locations, wherein the excitation parameters include excitation load type, frequency, amplitude, and location;

[0036] Step S23, performing meshing, setting the number of modes, initializing the displacement response matrix, calculating the mechanical impedance of the beam, plate, and column, and initializing the displacement and acceleration matrices;

[0037] Step S24, determining the boundary conditions at the connection between the beam and the plate, and calculating the reflection and transmission coefficients between the beam and the plate, and between the plate and the column;

[0038] Step S25, calculating the displacement response;

[0039] Step S26, calculating acceleration;

[0040] Step S27, calculating the peak acceleration.

[0041] As a further improvement of the present invention, step S3 includes: for the standard layer plan of the structure to be tested, using the code of step S2 to excite a layer in the structure with a simple harmonic load, and obtaining the acceleration time history curve diagram of each layer of the structure to be tested; using an exciter to apply the same simple harmonic load in the code, conducting a field test, collecting the acceleration time history curve of the same point on each layer, and comparing them with the acceleration time history curve diagram obtained by the code to verify the accuracy of the code calculation.

[0042] As a further improvement of the present invention, in step S4, based on the verified code, the acceleration peak values ​​at different positions of each layer of the structure to be tested under the excitation of different points on each layer are calculated, and then the vibration propagation law of the vibration wave between the same layer and different layers is regressed, and the acceleration peak prediction equation of the vibration wave at any time and any position in the structure is obtained.

[0043] As a further improvement of the present invention, the acceleration peak prediction equation is:

[0044] α=-7.868Y 2 -9.796Z 2 -17.799x 2 -00.758y 2 -9.969z 2 +5.657XY+56.854ZY+12xY-0.955yY

[0045] +.794zY+0.928XZ+0.857YZ+1.133xZ-1.4yZ+19.691zZ+0.128Xx-0.982xY+1.281xZIn the formula, α is the peak acceleration, x, y, z are the coordinates of the measuring point, and X, Y, Z are the coordinates of the excitation source.

[0046] The present invention also discloses the application of the vibration wave propagation calculation method based on the WPA method as described above, which is applied to determine the response of the target position.

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] By adopting the technical solution of the present invention, on the basis of the existing WPA classical theory, the reflection and refraction analysis theory of vibration waves at the connection of beams, plates and columns is supplemented, so that the vibration wave propagation analysis calculation is not only limited to the components, but expanded to the overall structure, which is closer to the actual situation; the written matlab code is used to more accurately and efficiently realize the calculation of any working condition; further, according to the obtained acceleration peak prediction equation, the response of the target position can be quickly judged. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a flow chart of a vibration wave propagation calculation method based on the WPA method according to an embodiment of the present invention.

[0050] Figure 2 Schematic diagram of wave propagation at a discontinuous point of a plate-beam structure according to an embodiment of the present invention.

[0051] Figure 3 It is a schematic diagram of wave propagation in a plate-beam structure with a simple support in the middle according to an embodiment of the present invention.

[0052] Figure 4 It is a schematic diagram of wave propagation of a plate-beam structure simply supported at the ends according to an embodiment of the present invention.

[0053] Figure 5 It is a schematic diagram of wave propagation of a plate-beam structure fixed at the ends according to an embodiment of the present invention.

[0054] Figure 6 It is a code calculation flow chart of an embodiment of the present invention.

[0055] Figure 7 It is a code content diagram of an embodiment of the present invention.

[0056] Figure 8 It is a standard floor plan of the actual structure of an embodiment of the present invention.

[0057] Fig. 9 It is the acceleration time history curve of 8 points on the 1-13th floor calculated by the embodiment of the present invention.

[0058] Fig.10 It is the comparison result of the acceleration curve obtained by code calculation and the acceleration curve obtained by test in the embodiment of the present invention.

[0059] Fig.11 This is a regression prediction peak acceleration diagram obtained by an embodiment of the present invention.

[0060] Fig.12 is the residual of the regression prediction obtained in the embodiment of the present invention. DETAILED DESCRIPTION

[0061] The preferred embodiments of the present invention are described in further detail below.

[0062] A calculation method for vibration wave propagation based on the WPA method, such as Figure 1 As shown, the following steps are included:

[0063] S1. Based on the classical theory of WPA method, the dynamic characteristics of the connection between beams, plates and columns are supplemented to describe the propagation and reflection of vibration waves as accurately as possible;

[0064] S2. Use Matlab software to write a code that can calculate the response of vibration waves at any time and any position in the structure under simple harmonic loads;

[0065] S3. Use the above code to calculate the actual structure and conduct field tests to verify the accuracy of the code calculation;

[0066] S4. Based on the verified code, the vibration propagation law of the vibration wave in the same layer and between different layers can be calculated, thereby realizing the response calculation of the vibration wave at any time and any position in the structure.

[0067] Wherein, step S1 specifically includes:

[0068] (I) Analysis of beam-slab joints

[0069] Assume that the beam-slab structure is discontinuous at x = 0, such as Figure 2 As shown. In the region x<0, there is an incident bending wave for

[0070]

[0071] Among them, A i is the amplitude of the incident bending wave, w is the angular frequency, t is the time, k is the proportionality coefficient, and x is the displacement.

[0072] Since the beam-slab structure is discontinuous at x=0, the structure reflects and transmits structural waves at this point. The reflected wave can be expressed as

[0073]

[0074] Where A r is the amplitude of the reflected wave.

[0075] The near-field wave generated by the reflection interface is

[0076]

[0077] Where A nl is the amplitude of the reflected near-field wave.

[0078] In the region of x>0, the transmitted propagation wave and the near-field wave are

[0079]

[0080]

[0081] Where A t , A nr are the amplitudes of the transmitted propagating wave and the near-field wave, respectively.

[0082] Therefore, the movement of the beam-slab structure in the area around x=0 can be described as

[0083]

[0084] In beam-slab structures, there are several cases for boundary conditions at discontinuous points:

[0085] (1) Consider the beam-slab model with simple support in the middle of the slab, such as Figure 3 As shown, there is a normal incident bending wave propagates in the plate. According to the equilibrium condition,

[0086]

[0087] M + With M - is the bending moment around the discontinuity point.

[0088] Substituting the wave expression into the continuity condition, we can get the 4 structural wave amplitudes A r , A nl , A t , A nr They are

[0089]

[0090] (2) Considering the simply supported plate at the end, the model is as follows Figure 4 As shown, there is a normal incident bending wave propagates in the plate. According to the equilibrium condition,

[0091]

[0092] Substituting the wave expression into the continuity condition, we can get the two reflected wave amplitudes A r , A nl , respectively

[0093]

[0094] (3) Considering the end fixed plate, the model is as follows Figure 5 As shown, there is a normal incident bending wave propagates in the plate. According to the equilibrium condition,

[0095]

[0096] Substituting the wave expression into the continuity condition, we can get the two reflected wave amplitudes A r , A nl , respectively

[0097]

[0098] (II) Analysis of the connection between slabs and columns

[0099] (1) If the plate and column are rigidly connected at the joint, then the displacement and rotation are continuous. For the joint surface z = 0 between the plate and the column, there is displacement continuity, and the deflection w(x, y, t) of the plate is equal to the lateral displacement v(0, t) of the column top, that is,

[0100] w(x,y,t)=v(0,t) (13)

[0101] And there is also rotational continuity, the rotation angle of the plate is equal to the rotation angle of the column top, that is

[0102]

[0103] θ(0,t) is the rotation angle of the top of the column.

[0104] In this case, the reflection of the wave is minimal and can be ignored.

[0105] (2) If the plate-column connection is semi-rigid, it can be simulated by using rotation springs (bending moment springs) and shear springs, indicating that the connection has limited stiffness and allows a certain degree of rotation and displacement.

[0106] The horizontal and vertical displacements at the plate-column connection must still be continuous. Since the connection has a rotation spring, the rotation angle is no longer strictly continuous, but meets the requirement of

[0107] M 连接 =K θ (θ 柱 -θ 板 ) (15)

[0108] Where M 连接 is the bending moment at the connection, θ 柱 ,θ 板 is the rotation angle of the slab-column connection.

[0109]

[0110]

[0111] Substitute the boundary conditions

[0112] w 板 =w柱 (18)

[0113] M 板 -M 柱 =K θ (θ 柱 -θ 板 ) (19)

[0114] Solving the equation gives the reflected wave. 柱 ,θ 板 M is the rotation angle of the plate column at the connection point; 板 is the bending moment of the plate, M 柱 is the bending moment of the column, W 板 is the displacement of the plate, W 柱 is the displacement of the column; K θ is the stiffness of the corner of the connection;

[0115] (3) If the slab-column connection is hinged, rotation is allowed and no bending moment is transmitted, only shear force and axial force are transmitted.

[0116] The horizontal displacement and vertical displacement of the plate-column connection must still be continuous. The angle is discontinuous, and sudden changes in the angle are allowed, that is,

[0117] M 连接 =0 (20)

[0118] According to the boundary conditions

[0119] w 板 =w 柱 (twenty one)

[0120] M 板 =0,M 柱 =0 (22)

[0121] Solving the equation gives the reflected wave.

[0122] In step S2, according to the above-mentioned perfect WPA theory, the code is written using matlab software to calculate the response of the vibration wave at any time and any position in the structure. The flow chart is as follows: Figure 6 As shown, the code content is as follows Figure 7 As shown, Figure 7 Each line of code is commented, and the parameters, extraction point locations, and mesh divisions in the code can be changed according to specific circumstances.

[0123] In step S3, Figure 8 is the standard floor plan of the actual structure. According to the above code, simple harmonic load excitation is performed on 8 points on the 1st floor of the structure to be tested, and the acceleration time history curve of 8 points on the 1st to 13th floors is obtained, as shown in Fig. 9A field test was conducted, using an exciter to apply the same simple harmonic load in the code, and using an acquisition system to collect the acceleration time history curves of the same points on each layer, and compared with the curves obtained by the code. The results are shown in Fig.10 As shown, the calculation accuracy of the code is verified.

[0124] In step S4, based on the verified code, the acceleration peaks at different positions of each layer under the excitation of different points on each layer can be calculated, and then the vibration propagation law of the vibration wave between the same layer and different layers can be regressed. The statistical results of the acceleration peaks at different points on each layer under the three-layer 8-point excitation are shown in Table 1. Fig.11 and Fig.12 The result of regression prediction based on the data calculated by the code.

[0125] Table 1

[0126]

[0127] Finally, the acceleration peak prediction equation of the vibration wave at any time and any position in the structure can be sorted out as follows: α = -7.868Y 2 -9.796Z 2 -17.799x 2 -00.758y 2 -9.969z 2 +5.657XY+56.854ZY+12xY-0.955yY+.794zY+0.928XZ+0.857YZ+1.133xZ-1.4yZ+19.691zZ+0.128Xx-0.982xY+1.281xZ (twenty three)

[0129] Where α is the peak acceleration, x, y, z are the coordinates of the measuring point, and X, Y, Z are the coordinates of the excitation source.

[0130] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims

1. A vibration wave propagation calculation method based on the WPA method, characterized in that: The steps include: Step S1, based on the classical theory of WPA method and according to the dynamic characteristics of the connection between beams, plates and columns, supplement the propagation and reflection parameters of the vibration waves at the connection between beams, plates and columns; Step S2, based on the WPA method theory, using Matlab software to write code, according to the obtained propagation and reflection parameters of the vibration wave, calculate the response of the vibration wave at any time and any position in the structure; Step S3, using the written code to calculate the actual structure, and conducting field tests to verify the accuracy of the code calculation, and calculating the response of the vibration wave at any time and any position in the structure according to the verified code; Step S4, calculate the acceleration peaks at different positions of each layer under the excitation of different points of each layer, and regress to obtain the vibration propagation law of the vibration wave in the same layer and between different layers.

2. The vibration wave propagation calculation method based on the WPA method according to claim 1, characterized in that: In step S1, for the connection between beam and plate, the amplitudes of the four structural waves of the plate-beam structure in the middle simply supported condition are: Among them, A r is the amplitude of the reflected wave, A nl is the amplitude of the reflected near-field wave, A t , A nr are the amplitudes of the transmitted propagation wave and the near-field wave, A i is the amplitude of the incident bending wave, j is the initial phase angle; Two reflected wave amplitudes A of the plate-beam structure with simply supported ends r , A nl They are: Among them, A i is the amplitude of the normally incident bending wave; The two reflected wave amplitudes A of the plate-beam structure under the condition of end clamping r , A nl They are: Among them, A i is the amplitude of the forward incident bending wave, and j is the initial phase angle.

3. The vibration wave propagation calculation method based on the WPA method according to claim 2, characterized in that: In step S1, for the connection between the plate and column, if the connection between the plate and column is a rigid connection, the reflection of the wave is ignored; If the plate-column connection is semi-rigid, solve the following equation to obtain the reflection wave parameters: In 板 =in 柱 M 板 -M 柱 =K θ (i 柱 -θ 板 ) Among them, M 连接 is the bending moment at the connection, θ 柱 ,θ 板 M is the rotation angle of the plate column at the connection point; 板 is the bending moment of the plate, M 柱 is the bending moment of the column, W 板 is the displacement of the plate, W 柱 is the displacement of the column; K θ is the stiffness of the corner of the connection; If the plate-column joint is hinged at the connection, rotation is allowed, no bending moment is transmitted, only shear force and axial force are transmitted, and the reflected wave parameters are obtained by solving the following equation: M 连接 ＝0 In 板 =in 柱 M 板 =0,M 柱 =0 Among them, M 连接 is the bending moment at the connection.

4. The vibration wave propagation calculation method based on the WPA method according to claim 3 is characterized in that: Step S2 is calculated using the following steps: Step S21, considering the damping loss factor and the damping bending stiffness, defining the physical and geometric parameters of the beam, plate and column; Step S22, defining excitation parameters and extracting measurement point locations, wherein the excitation parameters include excitation load type, frequency, amplitude, and location; Step S23, performing meshing, setting the number of modes, initializing the displacement response matrix, and calculating the machine initialization displacement and acceleration matrix of the beam, plate, and column; Step S24, determining the boundary conditions at the connection between the beam and the plate, and calculating the reflection and transmission coefficients between the beam and the plate, and between the plate and the column; Step S25, calculating the displacement response; Step S26, calculating acceleration; Step S27, calculating the peak acceleration.

5. The vibration wave propagation calculation method based on the WPA method according to claim 4 is characterized in that: Step S3 includes: for the standard layer plan of the structure to be tested, using the code of step S2 to excite a layer of the structure with a simple harmonic load, and obtaining the acceleration time history curve diagram of each layer of the structure to be tested; using an exciter to apply the same simple harmonic load in the code, conducting a field test, collecting the acceleration time history curve of the same point of each layer, and comparing it with the acceleration time history curve diagram obtained by the code to verify the accuracy of the code calculation.

6. The vibration wave propagation calculation method based on the WPA method according to claim 5, characterized in that: In step S4, based on the verified code, the peak acceleration values ​​at different positions of each layer of the structure to be tested under the excitation of different points on each layer are calculated, and then the vibration propagation law of the vibration wave between the same layer and different layers is regressed to obtain the peak acceleration prediction equation of the vibration wave at any time and any position in the structure.

7. The vibration wave propagation calculation method based on the WPA method according to claim 6 is characterized in that: The acceleration peak prediction equation is: α=-7.868Y 2 -9.796Z 2 -17,799x 2 -00.758y 2 -9.969z 2 +5.657XY+56.854ZY+12xY-0.955yY+.794zY+0.928XZ+0.857YZ+1.133xZ-1.4yZ+19.691zZ+0.128Xx-0.982xY+1.281xZ Where α is the peak acceleration, x, y, z are the coordinates of the measuring point, and X, Y, Z are the coordinates of the excitation source.

8. The application of the vibration wave propagation calculation method based on the WPA method according to any one of claims 1 to 7, characterized in that: Used to determine the response status of the destination.

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