CN108663116B - Method for determining main sound conduction radiation mode of coupled closed sound cavity - Google Patents
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Abstract
The invention relates to a method for determining a main sound conduction radiation mode of a coupled closed sound cavity, which is used for calculating and comparing radiation efficiency coefficients lambda of various orders of sound radiation modes of the coupled closed sound cavitymPrimarily selecting possible main sound radiation modes; fully considering the effect of modal amplitude, amplifying the primary selection order to reserve allowance; arranging a sensor array on a structural vibration surface to measure vibration velocity data and acquiring possible leading acoustic radiation modal amplitude y of the previous J orderi(ii) a And calculating and comparing the acoustic potential energy contributed by the previous J-order possible leading acoustic radiation modes respectively, and finally determining the leading acoustic radiation mode. The method comprehensively considers two factors of radiation efficiency and modal amplitude, can accurately identify the dominant acoustic radiation mode, realizes the truncation of the modal order through a primary selection link, greatly reduces the workload, does not need to use the structural modal information of the radiator in the determination process, and is convenient for engineering realization.
Description
Technical Field
The invention relates to the technical field of active structure acoustic control of a coupled closed acoustic cavity, in particular to a method for determining a main acoustic radiation mode of the coupled closed acoustic cavity.
Background
In practice, the problem of radiating noise from structural vibrations into a closed acoustic cavity is widespread in various industrial and domestic applications, such as ship, aircraft and vehicle cabins, as well as working and living rooms. The problem of analyzing and controlling the acoustic radiation of such coupled closed acoustic cavities is of great engineering importance. The active structure sound control technology has the advantages that the actuator directly acts on the structure, so that the intervention of a secondary sound source is avoided, a better control effect can be obtained by using fewer actuators, and the like, and the active structure sound control technology is widely concerned by various scholars. The acoustic radiation mode of the coupled closed acoustic cavity eliminates complex coupling terms when the structural mode is used for representing the sound potential energy of the closed acoustic cavity, and only one-order or several-order modes generally play a main role in the contribution of the sound potential energy of the closed acoustic cavity at medium and low frequencies, so that the analysis and control of the acoustic radiation problem are simpler. Therefore, active structure acoustic control using acoustic radiation modes for coupling closed acoustic cavities has been a focus of research in the field of structural acoustics in recent years.
When an active structure sound control system of a coupled closed sound cavity based on a sound radiation mode is actually designed, if the sound radiation mode which mainly contributes to sound potential energy can be accurately determined, the control target is selected with very clear pertinence, so that the control effect is directly determined, and the number of control channels can be effectively reduced.
At present, most of coupled closed acoustic cavity active structure acoustic control systems based on acoustic radiation modes arrange the acoustic radiation modes from large to small according to radiation efficiency coefficients, and then select the previous-order or previous-order acoustic radiation modes for control, which considers the effect of radiation efficiency but neglects the influence of mode amplitude. There are some scholars who propose in free space active structure acoustic control research that the dominant acoustic radiation mode of the structure can be effectively determined by using the internal relation between the acoustic radiation mode and the structure mode, but this method needs the structure mode information, and it is not easy to obtain the structure mode information of the radiator accurately in practice, so this method has inconvenience in application.
Therefore, finding an accurate method convenient for engineering application for determining the acoustic radiation mode mainly contributing to the acoustic potential energy of the closed acoustic cavity, especially considering comprehensively the two factors of radiation efficiency and mode amplitude, is an urgent problem to be solved.
Disclosure of Invention
The invention aims to provide a method which is convenient for engineering application and can accurately determine a main sound conduction radiation mode of a coupled closed sound cavity and mainly contributes to the sound potential energy of the closed sound cavity.
The invention aims to realize a method for determining a main sound guide radiation mode of a coupled closed sound cavity, which comprises the following specific steps of:
1) calculating and comparing radiation efficiency coefficients lambda of all orders of acoustic radiation modes of the coupled closed acoustic cavitymThe order M is 1,2, …, M, and the former j orders of sound radiation modes are initially selected as possible main sound radiation modes; m is the number of discrete surface elements of the structural vibration surface, which is also called the degree of freedom of an acoustic radiation mode;
primarily selecting possible dominant sound radiation modes, calculating radiation efficiency coefficients corresponding to the sound radiation modes of all orders during single-frequency analysis, then calculating the ratio of the radiation efficiency coefficients of all orders to the maximum value of the radiation efficiency coefficients, setting a threshold, and primarily selecting the sound radiation modes of all orders as the possible dominant sound radiation modes when the ratio of a certain order is larger than the threshold;
during wide frequency analysis, drawing a radiation efficiency coefficient-frequency curve of the former M-order sound radiation mode, and taking the highest modal order with a peak value in an analysis frequency band as a possible primary selection order j of a dominant sound radiation mode;
2) amplifying the initial selection order by using a formula J ═ mu × J to reserve a margin, and determining a possible leading acoustic radiation modal order J after the margin is reserved;
wherein j is the initial selection order, and mu is an amplification factor; the preferred amplification factor mu is 2-5;
3) arranging a sensor array on a structural vibration surface, measuring vibration speed data, and acquiring possible leading acoustic radiation modal amplitude y of the previous J orderi，i＝1,2,…,J；
The sensor array is arranged by designing a front J-order modal amplitude sensing strategy by utilizing the mode shape consistency among standard acoustic radiation modes under different degrees of freedom, namely
Y 'in the formula'lIs a degree of freedom MlAmplitude vector of lower standard sound radiation mode, J < Ml＜＜M，
D′lAnd DlRespectively a degree of freedom MlA standard acoustic radiation mode matrix and an acoustic radiation mode matrix without conversion processing,
vlis a degree of freedom MlThe normal velocity vectors of the centers of all the units on the vibration surface of the lower structure are measured by the sensor array,
sl、shrespectively representing degrees of freedom MlThe area of the uniformly discrete surface elements of the vibrating surface of the structure at the lower and the degree of freedom M,
s is the structural vibration surface area, and y is the amplitude vector of the front J-order acoustic radiation mode under the degree of freedom M;
4) calculating the front J order acoustic potential energy Ep of the respective contribution of the front J order possible main sound conduction radiation modesi＝λi|yi|2I is 1,2, …, J, comparing the previous J-th order sound potential to finally determine the leading sound radiation mode;
when the main sound-guide radiation mode is determined, and single-frequency analysis is carried out, Ep is directly observediFinally determining a main sound conduction radiation mode along with the change of the order; the method for finally determining the main sound conduction radiation mode by comparing the former J-order sound potential energy in the process of broadband analysis comprises the following steps:
(1) drawing the sound potential energy Ep of the independent contribution of the J-order sound radiation modality beforeiA curve that varies with frequency;
(2) sequentially observing and analyzing the sound radiation mode with the maximum sound potential energy independently contributing under each frequency in the frequency band, and recording the order of the sound radiation mode;
(3) and (3) combining the repeated sound radiation modal orders in the result recorded in the step (2), namely the finally determined dominant sound radiation modal order in the analysis frequency band.
The invention comprehensively considers two factors of radiation efficiency and modal amplitude, can accurately identify the dominant acoustic radiation mode, realizes the mode order truncation through the 'primary selection' link, greatly reduces the workload, does not need the structural mode information of the radiator in the whole determination process, and is convenient for engineering realization.
Drawings
FIG. 1 is a flow chart of the steps embodied in the present invention;
FIG. 2 is a graph of radiation efficiency coefficient versus frequency for the first 6 th order acoustic radiation modes;
3a, b, c, d, e, f are graphs of amplitude of the first 6 th order acoustic radiation modes as a function of frequency;
4a, b, c, d, e, f are graphs of the potential energy of the first 6 th order acoustic radiation modes contributing individually as a function of frequency;
fig. 5 is a comparison graph of reconstructed and measured values of sound potential energy of a closed acoustic cavity.
Detailed Description
The invention is described in detail below with reference to fig. 1.
1) Calculating and comparing radiation efficiency coefficients lambda of all orders of acoustic radiation modes of the coupled closed acoustic cavitymM is 1,2, …, M; the former j-order acoustic radiation mode is initially selected as a possible main sound conduction radiation mode, and M is the number of discrete surface elements of the structural vibration surface, which is also called the degree of freedom of the acoustic radiation mode.
The method comprises the steps of initially selecting possible dominant sound radiation modes, calculating radiation efficiency coefficients corresponding to the sound radiation modes of all orders during single-frequency analysis, then calculating the ratio of the radiation efficiency coefficients of all orders to the maximum value of the radiation efficiency coefficients, setting a threshold, initially selecting the sound radiation modes of all orders as the possible dominant sound radiation modes when the ratio of a certain order is larger than the threshold, wherein the value range of the threshold is preferably 1% o-1%.
And during wide frequency analysis, drawing a radiation efficiency coefficient-frequency curve of the former M-order sound radiation mode, and taking the highest modal order with a peak value in an analysis frequency band as a possible primary selection order j of the leading sound radiation mode. Because the radiation efficiency coefficient corresponding to each order of acoustic radiation mode has a peak value at the mode frequency of the acoustic cavity coupled with the acoustic radiation mode, the radiation efficiency of each order of acoustic radiation mode near the mode frequency of the acoustic cavity coupled with the acoustic radiation mode is far higher than that of other acoustic radiation modes, and the radiation efficiency coefficient needs to be regarded as a possible dominant acoustic radiation mode to be further screened in the step 4).
The primary selection technical scheme of the step 1) can effectively select possible main sound radiation modes on one hand; on the other hand, modal order truncation can be realized, and the workload is reduced to a greater extent.
However, the sound potential energy contributed by each order of sound radiation mode is not only related to the radiation efficiency coefficient, but also affected by the amplitude of the sound radiation mode. If the modal amplitude of a certain order of acoustic radiation mode is small, even if the radiation efficiency coefficient of the order of mode is large, the radiation acoustic potential energy of the order of mode may still be small, and the order of mode cannot be used as the dominant acoustic radiation mode. Conversely, if the radiation efficiency coefficient of a certain order of acoustic radiation mode is small, but the mode amplitude of the order of acoustic radiation mode is large, the individual contribution of the order of acoustic radiation mode can be large, and the individual contribution of the order of acoustic radiation mode becomes the dominant acoustic radiation mode which has a main effect on the overall acoustic potential energy. Therefore, the first j-order acoustic radiation mode is initially selected in step 1) according to the radiation efficiency coefficient of the acoustic radiation mode, and can only be used as a possible dominant acoustic radiation mode. On the other hand, due to the influence of the modal amplitude, the individual contribution potential energy of certain orders of acoustic radiation modalities other than the initially selected order in step 1) may exceed the acoustic potential energy of the initially selected order in step 1), so it is necessary to further expand the initially selected order of the possible dominant acoustic radiation modality, and reserve a margin for further screening in step 4).
So the invention adopts the step 2).
2) Amplifying the initial selection order by using a formula J ═ mu × J to reserve a margin, and determining a possible leading acoustic radiation modal order J after the margin is reserved;
in the formula, j is the initial selection order, and mu is an amplification factor; the value range of the amplification factor mu is more than 1 and less than M/j, and the amplification factor mu can be preferably selected to be 2-5 according to experience.
3) Arranging a sensor array on a structural vibration surface, measuring vibration speed data, and acquiring possible leading acoustic radiation modal amplitude y of the previous J orderi，i＝1,2,…,J；
The sensor array is arranged by designing a front J-order modal amplitude sensing strategy by utilizing the mode shape consistency among standard acoustic radiation modes under different degrees of freedom, namely
Y 'in the formula'lIs a degree of freedom MlAmplitude vector of lower standard sound radiation mode, J < Ml＜＜M，D′lAnd DlRespectively a degree of freedom MlStandard acoustic radiation mode matrix and acoustic radiation mode matrix without conversion processing, vlIs a degree of freedom MlNormal velocity vectors of all unit centers of the lower structure vibration surface are measured by the sensor array, sl、shRespectively representing degrees of freedom MlThe areas of the uniform discrete surface elements of the structural vibration surface under the lower degree of freedom M are obtained, S is the area of the structural vibration surface, and y is the amplitude vector of the front J-order acoustic radiation mode under the degree of freedom M.
4) Calculating the potential energy Ep of the individual contribution of the possible dominant acoustic radiation modality of the previous J orderi＝λi|yi|21,2, …, J, comparing the former J-order acoustic potential energy, and finally determining the leading acoustic radiation mode;
when the main sound conduction radiation mode is determined and single-frequency analysis is carried out, the front J order Ep is directly observediThe method is characterized in that the leading sound radiation mode is finally determined according to the change condition of the order, and the steps of comparing the former J-order sound potential energy and finally determining the leading sound radiation mode in the process of wide-frequency analysis are as follows:
(1) drawing the sound potential energy Ep of the independent contribution of the J-order sound radiation modality beforeiA curve that varies with frequency;
(2) sequentially observing and analyzing the sound radiation mode with the maximum sound potential energy independently contributing under each frequency in the frequency band, and recording the order of the sound radiation mode;
(3) and (3) combining the repeated sound radiation modal orders in the result recorded in the step (2), namely the finally determined dominant sound radiation modal order in the analysis frequency band.
In the invention, the first-order or several-order sound radiation modes which mainly play a role in the sound potential energy of the closed sound cavity under a certain frequency or within a certain frequency band are defined as the dominant sound radiation modes of the coupled closed sound cavity. In order to realize the technical scheme, M & gt J & gt J should be ensured. In the coupled closed acoustic cavity, the acoustic potential energy which is independently contributed by each order of acoustic radiation mode is the product of the square of the amplitude of the mode amplitude of the order and the radiation efficiency coefficient, namely:
Epm＝λm|ym|2，m＝1,2,…,M (3)
on the premise of uniform and discrete structure surface, the acoustic radiation modal of free space can be analogized, acoustic radiation modal vectors of the coupling closed cavity under different degrees of freedom are all converted into a discrete form of an acoustic radiation modal function so as to ensure the consistency of vibration modes, and the specific conversion formula is as follows:
d 'in the formula'mIs converted acoustic radiation mode, called standard acoustic radiation mode of coupled closed acoustic cavity, lambda'mI.e. the radiation efficiency coefficient corresponding to the standard acoustic radiation mode, and s is the area of the surface element when the structure surface is uniformly dispersed.
After conversion processing, the vibration modes of the standard sound radiation modes under different degrees of freedom have consistency in shape and amplitude. Then, the structure vibrates under the same excitation, and the amplitudes of the first order acoustic radiation modes in different degrees of freedom should be consistent. This provides a way to solve the problem of high degrees of freedom at low degrees of freedom. The front J-order modal amplitude sensing strategy designed based on the characteristic avoids matrix inversion operation, and can accurately measure the front J-order acoustic radiation modal amplitude without modal convergence priori knowledge.
In order to verify the effectiveness and feasibility of the method provided by the invention, the applicant designs and manufactures a clamped elastic plate-rectangular cavity coupling model. The rectangular cavity has the size of 0.65m × 0.50m × 0.45m, the top surface is an elastic steel plate with four fixedly-supported edges, and the other 5 surfaces are rigid wall surfaces. The thickness of the elastic steel plate is 0.0026m, and the sound medium in the cavity is air. And setting the lower left corner of the elastic plate as the origin of coordinates to establish an orthogonal coordinate system. White noise excitation with the bandwidth of 30-300 Hz is applied to the elastic plate by adopting a vibration exciter, and the excitation position is (0.155m,0.05 m). The surface of the elastic plate is uniformly dispersed into 13 multiplied by 11 small area elements.
The method provided by the invention is used for determining the dominant acoustic radiation mode of the coupling plate-cavity model under the excitation, and comprises the following specific steps:
1) observing the radiation efficiency coefficient-frequency curve corresponding to each order of acoustic radiation mode, as shown in fig. 1 (only the first 6 orders are shown here), the first 2 orders should be initially selected as possible dominant acoustic radiation modes, i.e., j is 2.
2) In order to fully consider the effect of modal amplitude, the amplification factor μ is set to 3, and the initial selection order is amplified by 3 times to reserve a margin, i.e., J is set to 6.
3) According to the modal amplitude sensing strategies given by the formulas (1) and (2), assuming that the surface of the elastic plate is uniformly dispersed into 4 x 3 small area elements, measuring the normal speed of the surface of the elastic plate by using 12 acceleration sensors uniformly distributed in the center of the 4 x 3 small area elements, obtaining the front 6-order possible dominant acoustic radiation modal amplitudes of the coupling plate-cavity, and then calculating the acoustic potential energy independently contributed by the front 6-order possible dominant acoustic radiation modalities in the formula (1). The amplitude of the first 6 order acoustic radiation modal amplitudes and the individual contributing potential energies are shown in fig. 3a, b, c, d, e, f and fig. 4a, b, c, d, e, f, respectively. Observing the potential energy-frequency curves of the orders in fig. 4a, b, c, d, e, f, it can be seen that: under different frequencies, sound radiation modes of different orders have a dominant effect on the total sound potential energy of the closed sound cavity, for example, the 1 st order sound radiation mode has a dominant contribution to the sound potential energy when the frequency is 30-100 Hz; from the whole analysis frequency band, the common 1 st order, 2 nd order and 3 rd order acoustic radiation modes play a main role in the acoustic potential energy of the closed acoustic cavity. Therefore, the dominant acoustic radiation mode of the coupled plate-cavity model under the excitation can be finally determined to be the 1 st to 3 rd order acoustic radiation mode. In the subsequent control, if the acoustic potential energy contributed by the 1 st to 3 rd order dominant acoustic radiation modes can be effectively counteracted, a more ideal broadband (30 to 300Hz) control effect can be obtained.
The acoustic potential of the closed acoustic cavity was estimated using 4 reference microphones placed at the four corners of the bottom of the rectangular cavity and recorded as measured values. And meanwhile, reconstructing the acoustic potential energy of the closed acoustic cavity by using the determined dominant acoustic radiation mode (1 st-3 rd order), and recording the acoustic potential energy as a reconstruction value. The two are compared to verify the correctness of the above determination result, and the result is shown in fig. 5. As can be seen from fig. 5, the sound potential energy curves obtained through reconstruction and measurement respectively have good overall coincidence except for slight difference at the wave trough due to low signal-to-noise ratio, and especially, the two curves are basically coincident at the wave crest. This proves the correctness of the determination result, thereby showing that the method for determining the main sound radiation mode of the coupled closed sound cavity is effective and feasible.
In addition, by analyzing the radiation efficiency coefficient, the modal amplitude and the variation curve of the acoustic potential energy of the acoustic radiation mode along with the frequency in fig. 2-4, it can be found that: in the frequency band of 162-186 Hz, compared with the 1 st and 2 nd order modes, although the radiation efficiency of the 3 rd order mode is lower, the amplitude of the mode amplitude is larger, so that the ratio of the sound potential energy radiated by the 3 rd order mode in the total sound potential energy is obviously larger than that of the 1 st and 2 nd order modes, and the mode becomes the dominant sound radiation mode in the frequency band. It is necessary to comprehensively consider two factors of radiation efficiency coefficient and modal amplitude when determining the main sound guide radiation mode, which is the advantage and significance of the method for determining the main sound guide radiation mode of the coupled closed sound cavity provided by the invention.
Claims (4)
1. A method of determining a coupled closed acoustic cavity dominant acoustic radiation mode, comprising: the specific steps of the determination are as follows:
1) calculating and comparing radiation efficiency coefficients lambda of all orders of acoustic radiation modes of the coupled closed acoustic cavitymThe order M is 1,2, ·, M, and j order acoustic radiation mode before initial selection is used as possible main acoustic radiation mode; m is the number of discrete surface elements of the structural vibration surface, which is also called the degree of freedom of an acoustic radiation mode;
primarily selecting possible dominant sound radiation modes, calculating radiation efficiency coefficients corresponding to the sound radiation modes of all orders during single-frequency analysis, then calculating the ratio of the radiation efficiency coefficients of all orders to the maximum value of the radiation efficiency coefficients, setting a threshold, and primarily selecting the sound radiation modes of all orders as the possible dominant sound radiation modes when the ratio of a certain order is larger than the threshold;
during wide frequency analysis, drawing a radiation efficiency coefficient-frequency curve of the former M-order sound radiation mode, and taking the highest modal order with a peak value in an analysis frequency band as a possible primary selection order j of a dominant sound radiation mode;
2) amplifying the initial selection order by using a formula J ═ mu × J to reserve a margin, and determining a possible leading acoustic radiation modal order J after the margin is reserved;
wherein j is the initial selection order, and mu is an amplification factor; the amplification factor mu is 2-5;
3) arranging a sensor array on a structural vibration surface, measuring vibration speed data, and acquiring possible leading acoustic radiation modal amplitude y of the previous J orderi，i＝1,2,···,J；
The sensor array is arranged by designing a front J-order modal amplitude sensing strategy by utilizing the mode shape consistency among standard acoustic radiation modes under different degrees of freedom, namely
Y 'in the formula'lIs a degree of freedom MlAmplitude vector of lower standard sound radiation mode, J < Ml＜＜M，
D′lAnd DlRespectively a degree of freedom MlA standard acoustic radiation mode matrix and an acoustic radiation mode matrix without conversion processing,
vlis a degree of freedom MlThe normal velocity vectors of the centers of all the units on the vibration surface of the lower structure are measured by the sensor array,
sl、shrespectively representing degrees of freedom MlThe area of the uniformly discrete surface elements of the vibrating surface of the structure at the lower and the degree of freedom M,
s is the structural vibration surface area, and y is the amplitude vector of the front J-order acoustic radiation mode under the degree of freedom M;
4) calculating the front J order acoustic potential energy Ep of the respective contribution of the front J order possible main sound conduction radiation modesi＝λi|yi|2I is 1,2, J, and finally determining the main sound conduction radiation mode by comparing the former J-order sound potential energy;
when the main sound-guide radiation mode is determined, and single-frequency analysis is carried out, Ep is directly observediFinally determining a main sound conduction radiation mode along with the change of the order; the method for finally determining the main sound conduction radiation mode by comparing the former J-order sound potential energy in the process of broadband analysis comprises the following steps:
(1) drawing the sound potential energy Ep of the independent contribution of the J-order sound radiation modality beforeiA curve that varies with frequency;
(2) sequentially observing and analyzing the sound radiation mode with the maximum sound potential energy independently contributing under each frequency in the frequency band, and recording the order of the sound radiation mode;
(3) and (3) combining the repeated sound radiation modal orders in the result recorded in the step (2), namely the finally determined dominant sound radiation modal order in the analysis frequency band.
2. A method of determining a coupled closed acoustic cavity dominant acoustic radiation mode according to claim 1, wherein: in the step 1), during single-frequency analysis, the value range of the threshold is 1 per thousand-1%; when the frequency spectrum is analyzed, the radiation efficiency coefficient corresponding to each order of acoustic radiation mode has a peak value at the mode frequency of the acoustic cavity coupled with the radiation efficiency coefficient.
3. A method of determining a coupled closed acoustic cavity dominant acoustic radiation mode according to claim 1, wherein: in step 4), the acoustic potential energy of each order, which is independently contributed by each order of acoustic radiation mode, is the product of the square of the amplitude of the mode amplitude of the order and the radiation efficiency coefficient, namely
Epm＝λm|ym|2，m＝1,2,…,M (3)
Here, M > J > J.
4. A method of determining a coupled closed acoustic cavity dominant acoustic radiation mode according to claim 1, wherein: in step 3), on the premise that the structure surface is uniformly dispersed, the acoustic radiation mode of the free space can be analogized, acoustic radiation mode vectors of the coupling closed cavity under different degrees of freedom are all converted into a discrete form of an acoustic radiation mode function to ensure the mode shape consistency, and the specific conversion formula is as follows:
d 'in the formula'mIs converted acoustic radiation mode, called standard acoustic radiation mode of coupled closed acoustic cavity, lambda'mI.e. the radiation efficiency coefficient corresponding to the standard acoustic radiation mode, and s is the area of the surface element when the structure surface is uniformly dispersed.
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