Calculation Method for Acoustic Characteristics of Periodic Ribbed Bridge Deck Based on Advanced Statistical Energy Analysis

Abstract

The present invention discloses a calculation method for the acoustic characteristics of a periodic ribbed bridge deck based on advanced statistical energy analysis, comprising the following steps: S1. Divide the periodic ribbed bridge deck into subsystems to obtain a number of subsystems; S2. Calculate the average transmission coefficient and the average internal loss coefficient of the periodic ribbed bridge deck according to the subsystems; S3. Calculate the free power matrix and the fixed power matrix in the advanced statistical analysis power flow equation according to the average transmission coefficient and the average internal loss coefficient of the periodic ribbed bridge deck; S4. Substitute the free power matrix and the fixed power matrix into the power flow equation to obtain the vibration energy vectors of each subsystem; S5. Calculate the sound radiation efficiency of each subsystem based on the sound radiation principle; S6. Calculate the acoustic characteristics of the periodic ribbed bridge deck according to the sound radiation efficiency and the vibration energy vectors of each subsystem. The present invention improves the accuracy of calculating various acoustic characteristics of the periodic ribbed bridge deck, and provides technical support for the design of the periodic ribbed bridge deck and the research on its acoustic characteristics.

Description

Technical Field

[0001] The present invention belongs to the technical field of vibration and noise reduction of rail transit bridges, and particularly relates to a calculation method for acoustic characteristics of a periodic rib bridge deck based on advanced statistical energy analysis. Background Art

[0002] The periodic rib bridge deck has excellent mechanical properties and is widely used in bridge structures. At the same time, it is also an important noise source of bridge structures. For thin steel plate structures, the main frequencies of their vibration and noise are usually relatively high. When using the finite element method to calculate their acoustic characteristics, the calculation efficiency is extremely low due to excessive meshes. Therefore, the statistical energy analysis method is usually used for calculation. However, when calculating a periodic structure with complex coupling such as a periodic rib bridge deck, the statistical energy analysis method has a large calculation error due to ignoring the indirect coupling between subsystems. Therefore, how to accurately obtain the acoustic responses of each plate member of the periodic rib bridge deck is an urgent problem to be solved by those skilled in the art. Summary of the Invention

[0003] Aiming at the above deficiencies in the prior art, the calculation method for acoustic characteristics of a periodic rib bridge deck based on advanced statistical energy analysis provided by the present invention solves the problem of large calculation errors existing in the statistical energy analysis method due to ignoring the indirect coupling between subsystems.

[0004] In order to achieve the above invention purpose, the technical solution adopted by the present invention is as follows: A calculation method for acoustic characteristics of a periodic rib bridge deck based on advanced statistical energy analysis, including the following steps:

[0005] S1. Divide the periodic rib bridge deck into subsystems to obtain a number of subsystems;

[0006] S2. Calculate the average transmission coefficient and average internal loss coefficient of the periodic rib bridge deck according to the subsystems;

[0007] S3. Calculate the free power matrix and fixed power matrix in the advanced statistical analysis power flow equation according to the average transmission coefficient and average internal loss coefficient of the periodic rib bridge deck;

[0008] S4. Substitute the free power matrix and fixed power matrix into the power flow equation to obtain the vibration energy vector of each subsystem;

[0009] S5. Calculate the sound radiation efficiency of each subsystem based on the sound radiation principle;

[0010] S6. Calculate the acoustic characteristics of the periodic rib bridge deck according to the sound radiation efficiency and vibration energy vector of each subsystem.

[0011] Further: In the S1, the method for dividing the periodic rib bridge deck into subsystems is specifically as follows:

[0012] Taking the stiffeners as the boundaries, the periodic ribbed bridge deck is divided into several base plates, and each base plate is regarded as a subsystem.

[0013] Furthermore, in step S2, the specific expressions for calculating the average transmission coefficient τ and the average internal loss coefficient D of the periodic ribbed bridge deck are as follows:

[0014]

[0015] In the formula, i1 is the imaginary unit, θ is the incident wave angle, ψ' is the moment of inertia per unit length of the stiffener, k Bp is the flexural wave number of the subsystem, k Bb and k Tb are the flexural wave number and torsional wave number of the stiffener respectively, m' and m” are the mass per unit length and mass per unit area of a single subsystem respectively, ω is the circular frequency, η is the internal loss factor of the subsystem, c g is the group velocity of the flexural wave, l and L are the width and length of the subsystem respectively.

[0016] Furthermore, step S3 includes the following sub-steps:

[0017] S31. Generate a first all-zero matrix and a second all-zero matrix with a set size according to the number of subsystems. Among them, the sizes of the first to second all-zero matrices are both N×N, and N is the number of subsystems;

[0018] S32. Trace the flexural wave power of all boundaries of all subsystems, and adjust the values of the corresponding elements in the first to second all-zero matrices during the tracing process to establish a free power matrix and a fixed power matrix.

[0019] Furthermore, in step S32, the method for tracing the flexural wave power of any boundary of the i-th subsystem is as follows:

[0020] S321. Select any side of the i-th subsystem as the starting point for flexural wave tracing, calculate the starting available power, and add the starting available power to the value of the element position (i, i) of the first all-zero matrix corresponding to the i-th subsystem;

[0021] Among them, the expression for the starting available power W a,i is as follows:

[0022]

[0023] In the formula, k is the flexural wave number of the subsystem;

[0024] S322. When the flexural wave is transmitted from the $i$-th subsystem to the $j$-th subsystem through the first junction, calculate the available power flowing into the $j$-th subsystem; when tracking the reflected power reflected back to the $i$-th subsystem, calculate the reflected power, and subtract the reflected power from the value of the element at position $(j, i)$ of the first all-zero matrix;

[0025] wherein, the available power $W$ flowing into the $j$-th subsystem s,j has the specific expression as follows:

[0026] $W$ s,j $=\tau W$ a,j

[0027] The reflected power $W$ reflected back to the $i$-th subsystem s,i has the specific expression as follows:

[0028] $W$ s,i $=W$ a,i $-W$ s,j

[0029] S323. When the flexural wave is transmitted through the $j$-th subsystem to the second junction, calculate the remaining available power, subtract the remaining available power from the reflected power of the $i$-th subsystem to obtain the lost power, and subtract the lost power from the value of the element at position $(j, i)$ of the second all-zero matrix;

[0030] wherein, the remaining available power $W$ e,j has the specific expression as follows:

[0031] $W$ e,j $=DW$ s,j

[0032] S324. Take the remaining available power as the new starting available power, add the new starting available power to the value of the element at position $(j, j)$ of the first all-zero matrix corresponding to the $j$-th subsystem, repeat the methods of S322 - S323 to calculate the available power of the flexural wave propagating in the subsequent subsystems, and update the values of the element positions of the first - second all-zero matrices corresponding to the subsystems; when either the number of transmissions of the flexural wave in each subsystem reaches the set threshold or the remaining available power is less than the energy threshold, subtract the remaining available power from the value of the element position of the first all-zero matrix corresponding to the subsystem, and complete the tracking of the flexural wave power at any boundary of the $i$-th subsystem.

[0033] Furthermore: In the above S4, the specific expression for calculating the vibration energy vector $\{E\}$ of any subsystem is:

[0034] $\{E\}=([M]-[B])([M]+[A])$ -1 $\{P\}$

[0035] Wherein, {P} is the input power vector, and [M] is the modal density matrix, and its expression is specifically:

[0036]

[0037] Wherein, n is the modal density of the subsystem.

[0038] Furthermore: In the step S5, the expression for calculating the acoustic radiation efficiency σ of any subsystem is specifically:

[0039]

[0040] Wherein, a and b are the sizes of the subsystem, f is the Hertz frequency, c0 is the speed of sound in air, D e is the bending stiffness of the subsystem, ρ s is the material density of the subsystem, h is the thickness of the subsystem, P is the perimeter of the subsystem, f1, f e and f c are the preset Hertz frequency thresholds, α is the Hertz frequency adjustment parameter, and The expression for the preset Hertz frequency threshold is:

[0041]

[0042] f e = 3c0 / P

[0043]

[0044] Furthermore: In the step S6, the acoustic characteristics of the periodic ribbed bridge deck include sound power, sound pressure level at the field point, and sound power level difference. The step S6 is specifically:

[0045] (1) Calculate the sound power of each subsystem to obtain the sound power of the periodic ribbed bridge deck. Among them, the expression for calculating the sound power W j of the jth subsystem is specifically:

[0046] W j = ρ0c0σ j S j E j / m j

[0047] Wherein, ρ0 is the air density, S j is the area of the jth subsystem, E j is the vibration energy of the jth subsystem, σ j is the acoustic radiation efficiency of the jth subsystem, and m j is the mass of the jth subsystem;

[0048] (2) Calculate the sound pressure of the periodic ribbed bridge deck, and express the sound pressure of the periodic ribbed bridge deck in terms of sound pressure level to obtain the sound pressure level at the field point. Among them, when calculating the sound pressure <p 2 >, the specific expression is:

[0049]

[0050] In the formula, A j is the area through which the energy flow radiated by the j-th subsystem passes, and its specific expression is:

[0051]

[0052] In the formula, d j is the distance from the center of the subsystem with width a j and length b j to the observation point, where a j < b j ;

[0053] The specific expression of the sound pressure level SPL at the field point of the periodic ribbed bridge deck is:

[0054]

[0055] In the formula, p0 is the reference sound pressure;

[0056] (3) Calculate the sound power level difference according to the sound power of each subsystem. Among them, when calculating the sound power level difference DSWL i,j between the i-th subsystem and the j-th subsystem, the specific expression is:

[0057] DSWL i,j = 10lg(W i / W j ).

[0058] The beneficial effects of the present invention are:

[0059] (1) The present invention proposes a calculation method for the acoustic characteristics of a periodic ribbed bridge deck based on advanced statistical energy analysis. By calculating the vibration energy vectors of each plate member of the periodic ribbed bridge deck through advanced statistical energy analysis, and then applying the sound radiation theory to calculate the acoustic characteristics of the periodic ribbed bridge deck, the accuracy of calculating various acoustic characteristics of the periodic ribbed bridge deck is improved, and the problem of large calculation errors existing in the statistical energy analysis method due to ignoring the indirect coupling between subsystems is solved.

[0060] (2) The present invention provides technical support for the design of the periodic ribbed bridge deck and the research on its acoustic characteristics. Description of the Drawings

[0061] Figure 1Flow chart of the calculation method for the acoustic characteristics of a periodic ribbed bridge deck based on advanced statistical energy analysis of the present invention.

[0062] Figure 2 Schematic diagram of the structure for subsystem division.

[0063] Figure 3 Result diagram of the average transmission coefficient.

[0064] Figure 4 Result diagram of the calculated sound power.

[0065] Figure 5 Result diagram of the sound pressure at the field point.

[0066] Figure 6 Result diagram of the calculated sound power difference. Specific implementation manners

[0067] The specific implementation manners of the present invention will be described below to facilitate those skilled in the art of the present technology to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation manners. For those of ordinary skill in the art of the present technology, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions made using the concept of the present invention are within the scope of protection.

[0068] Example 1:

[0069] As Figure 1 shown, in an embodiment of the present invention, the calculation method for the acoustic characteristics of a periodic ribbed bridge deck based on advanced statistical energy analysis includes the following steps:

[0070] S1. Divide the periodic ribbed bridge deck into subsystems to obtain a number of subsystems;

[0071] S2. Calculate the average transmission coefficient and average internal loss coefficient of the periodic ribbed bridge deck according to the subsystems;

[0072] S3. Calculate the free power matrix and fixed power matrix in the advanced statistical analysis power flow equation according to the average transmission coefficient and average internal loss coefficient of the periodic ribbed bridge deck;

[0073] S4. Substitute the free power matrix and fixed power matrix into the power flow equation to obtain the vibration energy vectors of each subsystem;

[0074] S5. Calculate the sound radiation efficiency of each subsystem based on the sound radiation principle;

[0075] S6. Calculate the acoustic characteristics of the periodic ribbed bridge deck according to the sound radiation efficiency and vibration energy vectors of each subsystem.

[0076] In S1, the method for dividing the periodic ribbed bridge deck into subsystems is specifically as follows:

[0077] Taking the stiffening rib as the boundary, the periodic ribbed bridge deck is divided into several base plates, and each base plate is taken as a subsystem. The division result is as Figure 2 shown.

[0078] In S2, the expressions for calculating the average transmission coefficient τ and the average internal loss coefficient D of the periodic ribbed bridge deck are specifically as follows:

[0079]

[0080] In the formula, i1 is the imaginary unit, θ is the incident wave angle, ψ' is the moment of inertia per unit length of the stiffening rib, k Bp is the flexural wave number of the subsystem, k Bb and k Tb are respectively the flexural wave number and the torsional wave number of the stiffening rib, m' and m” are respectively the mass per unit length and the mass per unit area of a single subsystem, ω is the circular frequency, η is the internal loss factor of the subsystem, which can be equivalent to material damping, c g is the group velocity of the flexural wave, and l and L are respectively the width and length of the subsystem.

[0081] In this embodiment, the specific method for calculating the free power matrix and the fixed power matrix in the advanced statistical analysis power flow equation is: using the ray tracing method to trace the transmission of flexural waves in the periodic ribbed bridge deck. S3 includes the following sub-steps:

[0082] S31. Generate a first all-zero matrix and a second all-zero matrix with a set size according to the number of subsystems. Among them, the sizes of the first to second all-zero matrices are both N×N, and N is the number of subsystems;

[0083] S32. Trace the flexural wave power of all boundaries of all subsystems, and adjust the values of the corresponding element positions in the first to second all-zero matrices during the tracing process to establish the free power matrix and the fixed power matrix.

[0084] In this embodiment, it can be known from Figure 2 that a subsystem includes at most two boundaries, and the methods for tracing the flexural wave power of any boundary of the subsystem are the same. Therefore, the method for tracing the flexural wave power of the other boundary will not be elaborated. In S32, the method for tracing the flexural wave power of any boundary of the i-th subsystem is specifically as follows:

[0085] S321. Select any side of the i-th subsystem as the starting point for flexural wave tracing, calculate the starting available power, and add the starting available power to the value of the element position (i, i) of the first all-zero matrix corresponding to the i-th subsystem;

[0086] Among them, the starting available power W a,i has the following specific expression:

[0087]

[0088] where k is the bending wave number of the subsystem;

[0089] S322. When the bending wave is transmitted from the i-th subsystem to the j-th subsystem through the first junction, calculate the available power flowing into the j-th subsystem; when tracking the reflected power back to the i-th subsystem, calculate the reflected power, and subtract the reflected power from the value at the element position (j, i) of the first all-zero matrix.

[0090] Among them, the available power W s,j flowing into the j-th subsystem has the following specific expression:

[0091] W s,j = τW a,j

[0092] The reflected power W s,i reflected back to the i-th subsystem has the following specific expression:

[0093] W s,i = W a,i - W s,j

[0094] S323. When the bending wave is transmitted through the j-th subsystem to the second junction, calculate the remaining available power, subtract the remaining available power from the reflected power of the i-th subsystem to obtain the lost power, and subtract the lost power from the value at the element position (j, i) of the second all-zero matrix.

[0095] Among them, the remaining available power W e,j has the following specific expression:

[0096] W e,j = DW s,j

[0097] S324. Take the remaining available power as the new starting available power, add the new starting available power to the value at the element position (j, j) of the first all-zero matrix corresponding to the j-th subsystem, repeat the methods of S322 to S323 to calculate the available power of the bending wave propagating in the subsequent subsystems, and update the values at the element positions of the first to second all-zero matrices corresponding to the subsystems; when either the number of transmissions of the bending wave in each subsystem reaches the set threshold or the remaining available power is less than the energy threshold, subtract the remaining available power from the value at the element position of the first all-zero matrix corresponding to the subsystem to complete the tracking of the bending wave power at any boundary of the i-th subsystem.

[0098] In the above-mentioned S4, the specific expression for calculating the vibration energy vector {E} of any subsystem is as follows:

[0099] {E} = ([M] - [B])([M] + [A]) -1 {P}

[0100] In the formula, {P} is the input power vector, which is a known vector, and [M] is the modal density matrix, and its specific expression is:

[0101]

[0102] In the formula, n is the modal density of the subsystem. Since the materials and geometric properties of each subsystem of the periodic ribbed bridge deck are the same, the diagonal elements of the modal density matrix are all equal.

[0103] In the above-mentioned S5, the specific expression for calculating the sound radiation efficiency σ of any subsystem is as follows:

[0104]

[0105] In the formula, a and b are the sizes of the subsystem, f is the Hertz frequency, c0 is the speed of sound in air, D e is the bending stiffness of the subsystem, ρ s is the material density of the subsystem, h is the thickness of the subsystem, P is the perimeter of the subsystem, f1, f e and f c are the preset Hertz frequency thresholds, α is the Hertz frequency adjustment parameter, and The expression for the preset Hertz frequency threshold is:

[0106]

[0107] f e = 3c0 / P

[0108]

[0109] In the above-mentioned S6, the acoustic characteristics of the periodic ribbed bridge deck include sound power, sound pressure level at the field point, and sound power level difference. The specific content of S6 is as follows:

[0110] (1) Calculate the sound power of each subsystem to obtain the sound power of the periodic ribbed bridge deck. Among them, the specific expression for calculating the sound power W j of the jth subsystem is:

[0111] W j = ρ0c0σ j S j E j / m j

[0112] In the formula, ρ0 is the air density, Sj is the area of the j-th subsystem, E j is the vibration energy of the j-th subsystem, σ j is the sound radiation efficiency of the j-th subsystem, m j is the mass of the j-th subsystem;

[0113] (2) Calculate the sound pressure of the periodic ribbed bridge deck. Express the sound pressure of the periodic ribbed bridge deck in terms of sound pressure level to obtain the sound pressure level at the field point. Among them, the expression for calculating the sound pressure <p 2 > is specifically:

[0114]

[0115] In the formula, A j is the area through which the energy flow radiated by the j-th subsystem passes, and its expression is specifically:

[0116]

[0117] In the formula, d j is the distance from the center of the subsystem with width a j , length b j to the observation point, where a j < b j ;

[0118] The expression for the sound pressure level SPL at the field point of the periodic ribbed bridge deck is specifically:

[0119]

[0120] In the formula, p0 is the reference sound pressure, generally taken as 2×10 -5 Pa;

[0121] (3) Calculate the sound power level difference according to the sound power of each subsystem. Among them, the expression for calculating the sound power level difference DSWL i,j between the i-th subsystem and the j-th subsystem is specifically:

[0122] DSWL i,j = 10lg(W i / W j ).

[0123] Example 2:

[0124] This example is a specific experimental case provided for Example 1 to prove the accuracy of the method of the present invention for calculating the acoustic characteristics of the periodic ribbed bridge deck.

[0125] Taking Figure 2 the periodic ribbed bridge deck shown as an example, its geometric parameters and material parameters are given in Table 1 and Table 2 respectively.

[0126] Table 1 Geometric parameters of the periodic rib bridge deck

[0127]

[0128] Table 2 Material parameters of the periodic rib bridge deck

[0129]

[0130] 1. According to step S1, the structure of the subsystem division of the periodic rib bridge deck is as Figure 2 shown.

[0131] 2. According to step S2, calculate the average transmission coefficient τ and the average internal loss coefficient D of the periodic rib bridge deck. The result of the average transmission coefficient is as Figure 3 shown.

[0132] 3. According to step S3, calculate the free power matrix [A] and the fixed power matrix [B] in the advanced statistical analysis power flow equation.

[0133] 4. According to step S4, substitute the [A], [B] matrices and the input power vector {P} into the power flow equation to solve the vibration energy vector {E} of each subsystem.

[0134] 5. According to step S5, calculate the sound radiation efficiency σ of each subsystem based on the sound radiation principle.

[0135] 6. According to step S5, the sound power (sound power level), the sound pressure level at a certain field point, and the sound power level difference between the 5th subsystem and the 1st subsystem of the periodic rib bridge deck are calculated. The calculation results are as Figures 4 - 6 shown.

[0136] In summary, the present invention accurately calculates various acoustic characteristics of the periodic rib bridge deck through the advanced statistical energy analysis method and the sound radiation theory, providing technical support for the design of the periodic rib bridge deck and the research on its acoustic characteristics.

[0137] The beneficial effects of the present invention are as follows: The present invention proposes a method for calculating the acoustic characteristics of the periodic rib bridge deck based on the advanced statistical energy analysis. The vibration energy vector of each plate of the periodic rib bridge deck is calculated through the advanced statistical energy analysis, and then the acoustic characteristics of the periodic rib bridge deck are calculated by using the sound radiation theory, improving the accuracy of the calculation of various acoustic characteristics of the periodic rib bridge deck and solving the problem that the statistical energy analysis method has a large calculation error due to ignoring the indirect coupling between subsystems.

[0138] The present invention provides technical support for the design of the periodic rib bridge deck and the research on its acoustic characteristics.

[0139] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by terms such as "center", "thickness", "upper", "lower", "horizontal", "top", "bottom", "inner", "outer", "radial", etc. is based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, it should not be construed as a limitation to the present invention. In addition, the terms "first", "second", and "third" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly specifying the quantity of technical features. Therefore, the features defined by "first", "second", and "third" may explicitly or implicitly include one or more of such features.

Claims

1. A calculation method for the acoustic characteristics of a periodic ribbed bridge deck based on advanced statistical energy analysis, characterized in that, It includes the following steps: S1. Subdivide the periodic ribbed bridge deck into several subsystems; S2. Calculate the average transmission coefficient and average internal loss coefficient of the periodic ribbed bridge deck according to the subsystems; Calculating the average transmission coefficient of the periodic ribbed bridge deck τ and the average internal loss coefficient D The specific expressions are as follows: In the formula, i 1 is the imaginary unit, is the incident wave angle, is the moment of inertia of the stiffener per unit length, k Bp is the flexural wave number of the subsystem, k Bb and k Tb are the flexural wave number and torsional wave number of the stiffener respectively, and are the mass per unit length and mass per unit area of a single subsystem respectively, ω is the circular frequency, η is the internal loss factor of the subsystem, c g is the group velocity of the flexural wave, l and L are the width and length of the subsystem respectively; S3. Calculate the free power matrix and fixed power matrix in the advanced statistical analysis power flow equation according to the average transmission coefficient and average internal loss coefficient of the periodic ribbed bridge deck, specifically: S31. Generate a first all-zero matrix of a set size according to the number of subsystems and a second all-zero matrix , where the sizes of the first to second all-zero matrices are both N × N , N being the number of subsystems; S32. Trace the bending wave power of all boundaries of all subsystems, and adjust the values at the corresponding element positions in the first to second all-zero matrices during the tracing process to establish the free power matrix and fixed power matrix; S4. Substitute the free power matrix and fixed power matrix into the power flow equation to obtain the vibration energy vector of each subsystem; S5. Calculate the sound radiation efficiency of each subsystem based on the sound radiation principle; S6. Calculate the acoustic characteristics of the periodic ribbed bridge deck according to the sound radiation efficiency and vibration energy vector of each subsystem.

2. The calculation method for the acoustic characteristics of a periodic ribbed bridge deck based on advanced statistical energy analysis according to claim 1, wherein In the above S1, the method for subdividing the periodic ribbed bridge deck into subsystems is specifically: Taking the stiffeners as the boundaries, divide the periodic ribbed bridge deck into several base plates, and take each base plate as a subsystem.

3. The acoustic characteristic calculation method of the periodic ribbed bridge deck based on advanced statistical energy analysis according to claim 1, characterized in that In S32, the method for tracking the flexural wave power of any boundary of the i th subsystem is specifically as follows: S321. Select any side of the i th subsystem as the starting point for flexural wave tracking, calculate the starting available power, and add the value of the starting available power to the element position ( i th subsystem's corresponding all-zero matrix element position i , i ); Among them, the starting available power The specific expression is as follows: In the formula, k is the flexural wave number of the subsystem; S322. When the flexural wave is transmitted from the i th subsystem to the j th subsystem through the first junction, calculate the available power flowing into the j th subsystem; when tracking the reflected power back to the i th subsystem, calculate the reflected power, and subtract the value of the reflected power from the element position ( j , i ) of the first all-zero matrix; Among them, the available power flowing into the j th subsystem is specifically expressed as: The reflected power returned to the i subsystem is specifically as follows: W s,i The expression is specifically: S323. When the flexural wave is transmitted to the second junction through the j th subsystem, calculate the remaining available power. Subtract the remaining available power from the reflected power of the i th subsystem to obtain the lost power, and subtract the value of the lost power from the element position ( j , i ) of the second all-zero matrix; wherein, the remaining available power is specifically expressed as: S324, taking the remaining available power as the new starting available power, and j The element position of the first all-zero matrix corresponding to the subsystem ( j , j ) plus the new starting available power, repeat the method of S322-S323 to calculate the available power of the bending wave propagating in the subsequent subsystem, and update the values ​​of the element positions of the first to second all-zero matrices corresponding to the subsystem; when the number of transmissions of the bending wave in each subsystem reaches a set threshold and the remaining available power is less than the energy threshold, the value of the element position of the first all-zero matrix corresponding to the subsystem is subtracted from the remaining available power, and the calculation of the first to second all-zero matrices is completed. i Tracking of the bending wave power at any boundary of a subsystem.

4. The method for calculating the acoustic characteristics of a periodic ribbed bridge deck based on advanced statistical energy analysis according to claim 3, wherein In S4, calculate the vibration energy vector of any subsystem The specific expression is as follows: where, { P} is the input power vector, M is the modal density matrix, and its expression is specifically: In the formula, n is the modal density of the subsystem.

5. The method for calculating the acoustic characteristics of a periodic ribbed bridge deck based on advanced statistical energy analysis according to claim 4, wherein In S5, calculate the acoustic radiation efficiency of any subsystem The specific expression is as follows: In the formula, a and b are the dimensions of the subsystem, f is the Hertz frequency, c 0 is the speed of sound in air, D e is the bending stiffness of the subsystem, ρ s is the material density of the subsystem, h is the thickness of the subsystem, P is the perimeter of the subsystem, f 1, f e and f c are the preset Hertz frequency thresholds, is the Hertz frequency adjustment parameter, and , the expression of the preset Hertz frequency threshold is: 。 6. The method for calculating the acoustic characteristics of a periodic ribbed bridge deck based on advanced statistical energy analysis according to claim 5, characterized in that, In the above S6, the acoustic characteristics of the periodic ribbed bridge deck include sound power, sound pressure level at the field point, and sound power level difference. The above S6 is specifically: (1) Calculate the sound power of each subsystem to obtain the sound power of the periodic ribbed bridge deck. Among them, when calculating the sound power of the j th subsystem the specific expression is: Wherein, ρ 0 is the air density, S j is the area of the j nth subsystem, E j is the vibration energy of the j nth subsystem, is the sound radiation efficiency of the j nth subsystem, m j is the mass of the j nth subsystem; (2)Calculate the sound pressure of the periodic ribbed bridge deck, express the sound pressure of the periodic ribbed bridge deck in terms of sound pressure level to obtain the sound pressure level at the field point. Among them, calculate the sound pressure of the periodic ribbed bridge deck The specific expression is as follows: Wherein, A j is the area through which the energy flow radiated by the j th subsystem passes, and its specific expression is: In the formula, d j is for a subsystem with a width of a j and a length of b j , which is the distance from the center to the observation point, where a j < b j ; Sound pressure level at field points of periodic ribbed bridge deck The specific expression is as follows: wherein, p 0 is the reference sound pressure; (3) Calculate the sound power level difference based on the sound power of each subsystem. Among them, when calculating the sound power level difference between the i th subsystem and the j th subsystem, the specific expression of the sound power level difference is as follows: 。

Images