CN104764518A - Method for recognizing mechanical surface vibrating strength based on inverse boundary element method - Google Patents

Abstract

The invention aims at providing a method for recognizing mechanical surface vibrating strength based on an inverse boundary element method. Vibrating mechanical boundary sound pressure and a transfer matrix of a boundary normal direction vibrating speed and field point sound pressure are established. A singular integral which appears during a relation matrix of the boundary sound pressure and the boundary normal direction vibrating speed is solved, and the singular integral is eliminated by adopting a generalized polar coordinate transformation. By utilizing a microphone array, mechanical vibrating radiated sound field complex sound pressure is measured and is regarded as known. According to the mechanical vibrating boundary sound pressure, the transfer matrix of the boundary normal direction vibrating speed and field point sound pressure, the boundary normal direction vibrating speed is reestablished, and therefore the boundary sound pressure is obtained; by utilizing the boundary sound pressure and the boundary normal direction vibrating speed, mechanical vibrating radiated sound power is calculated, and the prediction on the mechanical surface vibrating strength is achieved. By utilizing the mechanical radiated sound field complex sound pressure as the known quantity for calculation, the direct contact with the measured surface vibrating speed is avoided, vibrating mechanical shape is free of restriction, and the calculation can be carried out on mechanical vibrating strength with any shapes.

Description

Based on the method for inverse boundary element method identification machinery surface vibration intensity

Technical field

What the present invention relates to is a kind of oscillation intensity Forecasting Methodology.

Background technology

At present, to convert based on space Fourier and the identification of sound source of near field acoustic holography of inverse transformation method has implementation procedure simple, application facilitate feature, but due to space Fourier convert and inverse transformation method be only applicable to simpler construction, cannot implement the vibrational structure of arbitrary shape.

System decomposition is multiple subsystem by statistical pattern recognize, use energy flow relational expression to compound, the package assembly of resonance carries out the theoretical appraisal of kinematic behavior, vibratory response level and sound radiation, but its analysis frequency scope is limited in high frequency, poor to low-frequency effect.

Summary of the invention

The object of the present invention is to provide the method based on inverse boundary element method identification machinery surface vibration intensity being applicable to arbitrary shape, the prediction of medium and low frequency vibrating machine body structure surface oscillation intensity.

The object of the present invention is achieved like this:

The present invention is based on the method for inverse boundary element method identification machinery surface vibration intensity, it is characterized in that:

(1) arrange at vibration sound source radiated sound field the field point acoustic pressure carrying out measuring radiation sound field with reference to microphone and microphone array, the two distance to vibration sound source is less than analyzes wavelength corresponding to highest frequency, with reference to microphone number 1-2, the measurement field point number of microphone array meets containing 3-5 measuring point in a wave length of sound, measures area and is greater than vibration sound source frontal plane of projection;

(2) with reference to the multiple acoustic pressure that microphone and the acoustic pressure that Microphone array measurement obtains utilize Mutual spectrum to obtain on measurement field point place frequency domain corresponding to microphone array, this multiple acoustic pressure is as the known parameters solving mechanical surface oscillation intensity and input;

(3) vibration surface normal vibration speed is calculated based on inverse boundary element method:

Setting up dynamic surface with measurement point integral equation is

$c\left(P\right)p\left(P\right)=-{\∫}_s(p\left(Q\right)\frac{\∂\mathrm{\Ψ}}{\∂n}+\mathrm{i\ρ\ωv}{\left(Q\right)}_n\mathrm{\Ψ})\mathrm{ds}$

Wherein: c (P) is the multiple acoustic pressure coefficient of field point, and in c (P) bracket, P represents radiated sound field field point, p (P) is the multiple acoustic pressure of field point, p (Q), v (Q) _nacoustic pressure and boundary method are to vibration velocity to be again respectively vibration sound source border, and Q is vibration sound source frontier point, elementary solution for the normal derivative of elementary solution, k is field point acoustic pressure coefficient, and r is radiated sound field field point P and the distance vibrating sound source frontier point Q, ρ is atmospheric density, ω=2 π f, and vibration sound source border is that S, c (P) can be expressed as

$c\left(p\right)=\left\{\begin{array}{cc}1& p\∈V\\ 1-{\∫}_{s_{\mathrm{\ϵ}}}\frac{\∂}{\∂n}\left(\frac{1}{4\mathrm{\πr}}\right)\mathrm{ds}& p\∈S\\ 0& p\∉(v\∪s)\end{array}\right.s$

Wherein: V vibrates sound source radiated sound field, will vibrate sound source border s discrete

$\begin{array}{c}{\∫}_{s}p\left(Q\right)\frac{\∂\mathrm{\Ψ}}{\∂n}\mathrm{ds}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\∫}_{s_j}\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_k\mathrm{ds}\\ =\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\frac{\∂\mathrm{\Ψ}}{\∂n}{\∫}_{-1}^1{\∫}_{-1}^1{N}_k\mathrm{Jd}{\mathrm{\ξ}}_{1}d{\mathrm{\ξ}}_2=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\underset{m=1}{\overset{l}{\mathrm{\Σ}}}\underset{k=1}{\overset{l}{\mathrm{\Σ}}}{w}_m{w}_k\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_{k}J\end{array},$

$\begin{array}{c}{\∫}_s\mathrm{i\ρ\ωv}{\left(Q\right)}_n\mathrm{\Ψds}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{i\ρ\ω}{\∫}_{s_j}\mathrm{\Ψ}{N}_k\mathrm{ds}\\ =\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{i\ρ\ω\Ψ}{\∫}_{-1}^1{\∫}_{-1}^1{N}_k\mathrm{Jd}{\mathrm{\ξ}}_{1}d{\mathrm{\ξ}}_2=\mathrm{i\ρ\ω}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\underset{m=1}{\overset{l}{\mathrm{\Σ}}}\underset{k=1}{\overset{l}{\mathrm{\Σ}}}{w}_n{w}_k\mathrm{\Ψ}{N}_{k}J\end{array},$

Wherein n is the discrete rear unit number of vibration sound source border S, ξ ₁, ξ ₂for Gauss integration point, N _kξ ₁, ξ ₂function, footmark k is cell node number, and l is counting of getting of Gauss integration, and J is Jacobi;

Must be shown up a little multiple acoustic pressure matrix P thus _facoustic pressure matrix P multiple with vibration sound source border _sand boundary method is to vibration velocity matrix V _nrelation:

CP _f＝HP _s+GV _n，

Wherein Matrix C, H, G are matrix of coefficients;

For obtaining the multiple acoustic pressure p (Q) in vibration sound source border and boundary method to vibration velocity v (Q) _nrelation, P point in field is moved on to vibration sound source border S on, due to Ψ with occur unusual, adopt CENERALIZED POLAR coordinate transform to eliminate unusual; If S is discrete is triangular element, using the P point that moves on on boundary element as vertex of a triangle, utilize polar coordinate transform

${\mathrm{\ξ}}_1={\mathrm{\ξ}}_1^3+\mathrm{\ρ}[{\mathrm{\ξ}}_1^1-{\mathrm{\ξ}}_1^3+\mathrm{\θ}({\mathrm{\ξ}}_1^2-{\mathrm{\ξ}}_1^1)],$

${\mathrm{\ξ}}_2={\mathrm{\ξ}}_2^3+\mathrm{\ρ}[{\mathrm{\ξ}}_2^1-{\mathrm{\ξ}}_2^3+\mathrm{\θ}({\mathrm{\ξ}}_2^2-{\mathrm{\ξ}}_2^1)],$

Wherein subscript 1,2,3 represents to be that the triangle on summit is numbered by counterclockwise each point with P, and the point at P place is designated as 1, and two coordinates of subscript 1,2 triangle each point, now have

$\begin{array}{c}{\∫}_s\frac{\∂\mathrm{\Ψ}}{\∂n}\mathrm{ds}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\∫}_{s_j}\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_k\mathrm{ds}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\∫}_0^1{\∫}_0^{1-{\mathrm{\ξ}}_2}\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_k\mathrm{Jd}{\mathrm{\ξ}}_{1}d{\mathrm{\ξ}}_2=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\∫}_0^1{\∫}_0^1\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_k\mathrm{J\ρd}{\mathrm{\ρ}}_{1}d{\mathrm{\θ}}_2\\ =\frac{1}{4}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\∫}_{-1}^1{\∫}_{-1}^1\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_k\mathrm{J\ρd}{\mathrm{\η}}_{1}d{\mathrm{\η}}_2=\frac{1}{4}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\underset{m=1}{\overset{l}{\mathrm{\Σ}}}\underset{k=1}{\overset{l}{\mathrm{\Σ}}}{w}_m{w}_k\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_k\mathrm{J\ρ}\end{array},$

$\begin{array}{c}{\∫}_s\mathrm{i\ρ\ωv}{\left(Q\right)}_n\mathrm{\Ψds}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{i\ρ\ω}{\∫}_{s_j}\mathrm{\Ψ}{N}_k\mathrm{ds}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{i\ρ\ω}{\∫}_0^1{\∫}_0^{1-{\mathrm{\ξ}}_2}\mathrm{\Ψ}{N}_k\mathrm{Jd}{\mathrm{\ξ}}_{1}d{\mathrm{\ξ}}_2\\ =\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\∫}_0^1{\∫}_0^1\mathrm{\Ψ}{N}_k\mathrm{J\ρd}{\mathrm{\ρ}}_{1}d{\mathrm{\θ}}_2=\frac{1}{4}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{i\ρ\ω}{\∫}_{-1}^1{\∫}_{-1}^1\mathrm{\Ψ}{N}_k\mathrm{J\ρd}{\mathrm{\η}}_{1}d{\mathrm{\η}}_2=\frac{1}{4}\mathrm{i\ρ\ω}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\underset{m=1}{\overset{l}{\mathrm{\Σ}}}\underset{k=1}{\overset{l}{\mathrm{\Σ}}}{w}_m{w}_k\mathrm{\Ψ}{N}_k\mathrm{J\ρ}\end{array},$

Wherein now η ₁, η ₂for Gauss integration point; By obtaining the multiple acoustic pressure of sound field and boundary method with co-relation to vibration velocity relation

P _s＝ATM _s·V _n，

Wherein ATM _sfor the multiple acoustic pressure in vibration sound source border and boundary method are to the transfer matrix of vibration velocity acoustics, by formula CP _f=HP _s+ GV _nand P _s=ATM _sv _nmust show up and a little answer acoustic pressure and Oscillating boundary normal vibration length velocity relation

P _f＝ATM _f·V _n，

Be wherein P _fthe multiple acoustic pressure matrix of field point, ATM _ffor the multiple acoustic pressure of field point and boundary method are to vibration velocity acoustics transfer matrix, obtain boundary method thus to vibration velocity

$V_n={\mathrm{ATM}}_f^{-}\·P_f,$

Wherein for the inverse matrix of transfer matrix, according to formula P _s=ATM _sv _n, utilize point multiple acoustic pressure in field to calculate surface normal vibration velocity; According to equation $\begin{array}{c}{\∫}_s\frac{\∂\mathrm{\Ψ}}{\∂n}\mathrm{ds}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\∫}_{s_j}\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_k\mathrm{ds}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\∫}_0^1{\∫}_0^{1-{\mathrm{\ξ}}_2}\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_k\mathrm{Jd}{\mathrm{\ξ}}_{1}d{\mathrm{\ξ}}_2=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\∫}_0^1{\∫}_0^1\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_k\mathrm{J\ρd}{\mathrm{\ρ}}_{1}d{\mathrm{\θ}}_2\\ =\frac{1}{4}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\∫}_{-1}^1{\∫}_{-1}^1\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_k\mathrm{J\ρd}{\mathrm{\η}}_{1}d{\mathrm{\η}}_2=\frac{1}{4}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\underset{m=1}{\overset{l}{\mathrm{\Σ}}}\underset{k=1}{\overset{l}{\mathrm{\Σ}}}{w}_m{w}_k\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_k\mathrm{J\ρ}\end{array}$ The vibration sound source normal vibration speed obtained and border acoustic pressure relation calculate border acoustic pressure p _s;

(4) vibrating mass radiated is calculated according to surface normal vibration velocity

w＝∫ _s0.5re(p(Q) _sv(Q) _n)ds，

Wherein re represents border acoustic pressure and boundary method phase vibration velocity real part, passes judgment on oscillation intensity size according to vibrating machine radiated.

Advantage of the present invention is:

1. utilize the multiple acoustic pressure of mechanical radiative sound field as the known quantity calculated, avoid direct contact measurement surface vibration velocity.

2. vibrating machine shape does not limit, can to arbitrary shape mechanical vibration Strength co-mputation.

Accompanying drawing explanation

Fig. 1 is arrangenent diagram of the present invention;

Fig. 2 is process flow diagram of the present invention.

Embodiment

Below in conjunction with accompanying drawing citing, the present invention is described in more detail:

Composition graphs 1 ~ 2, the technical solution adopted for the present invention to solve the technical problems is:

The first step: arrange the field point acoustic pressure carrying out measuring radiation sound field with reference to microphone and microphone array at vibration sound source radiated sound field, the two distance to vibration sound source is less than analyzes wavelength corresponding to highest frequency, with reference to microphone number 1-2, the measurement field point number of microphone array meets containing 3-5 measuring point in a wave length of sound, measures area and is greater than vibration sound source frontal plane of projection.

Second step: the multiple acoustic pressure utilizing Mutual spectrum to obtain on measurement field point place frequency domain corresponding to microphone array with reference to microphone and the acoustic pressure that Microphone array measurement obtains, this multiple acoustic pressure is as the known parameters solving mechanical surface oscillation intensity and input.

3rd step: calculate vibration surface normal vibration speed based on inverse boundary element method, its Computational Methods is as follows:

Setting up dynamic surface with measurement point integral equation is

$c\left(P\right)p\left(P\right)=-{\∫}_s(p\left(Q\right)\frac{\∂\mathrm{\Ψ}}{\∂n}+\mathrm{i\ρ\ωv}{\left(Q\right)}_n\mathrm{\Ψ})\mathrm{ds}---\left(1\right)$

Wherein: c (P) is the multiple acoustic pressure coefficient of field point, and in c (P) bracket, P represents radiated sound field field point, p (P) is the multiple acoustic pressure of field point, p (Q), v (Q) _nacoustic pressure and boundary method are to vibration velocity to be again respectively vibration sound source border, and Q is vibration sound source frontier point, elementary solution for the normal derivative of elementary solution, k is field point acoustic pressure coefficient, and r is radiated sound field field point P and the distance vibrating sound source frontier point Q, ρ is atmospheric density, ω=2 π f, and vibration sound source border is that S, c (P) can be expressed as

$c\left(p\right)=\left\{\begin{array}{cc}1& p\∈V\\ 1-{\∫}_{s_{\mathrm{\ϵ}}}\frac{\∂}{\∂n}\left(\frac{1}{4\mathrm{\πr}}\right)\mathrm{ds}& p\∈S\\ 0& p\∉(v\∪s)\end{array}\right.s---\left(2\right)$

Wherein: V vibrates sound source radiated sound field, will vibrate sound source border s discrete

$\begin{array}{c}{\∫}_{s}p\left(Q\right)\frac{\∂\mathrm{\Ψ}}{\∂n}\mathrm{ds}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\∫}_{s_j}\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_k\mathrm{ds}\\ =\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\frac{\∂\mathrm{\Ψ}}{\∂n}{\∫}_{-1}^1{\∫}_{-1}^1{N}_k\mathrm{Jd}{\mathrm{\ξ}}_{1}d{\mathrm{\ξ}}_2=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\underset{m=1}{\overset{l}{\mathrm{\Σ}}}\underset{k=1}{\overset{l}{\mathrm{\Σ}}}{w}_m{w}_k\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_{k}J\end{array}---\left(3\right)$

$\begin{array}{c}{\∫}_s\mathrm{i\ρ\ωv}{\left(Q\right)}_n\mathrm{\Ψds}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{i\ρ\ω}{\∫}_{s_j}\mathrm{\Ψ}{N}_k\mathrm{ds}\\ =\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{i\ρ\ω\Ψ}{\∫}_{-1}^1{\∫}_{-1}^1{N}_k\mathrm{Jd}{\mathrm{\ξ}}_{1}d{\mathrm{\ξ}}_2=\mathrm{i\ρ\ω}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\underset{m=1}{\overset{l}{\mathrm{\Σ}}}\underset{k=1}{\overset{l}{\mathrm{\Σ}}}{w}_n{w}_k\mathrm{\Ψ}{N}_{k}J\end{array}---\left(4\right)$

Wherein n is the discrete rear unit number of vibration sound source border S, ξ ₁, ξ ₂for Gauss integration point, N _kξ ₁, ξ ₂function, footmark k is cell node number, and l is counting of getting of Gauss integration, and J is Jacobi.

The multiple acoustic pressure matrix P of field point can be obtained thus _facoustic pressure matrix P multiple with vibration sound source border _sand boundary method is to vibration velocity matrix V _nrelation, obtains

CP _f＝HP _s+GV _n(5)

Wherein Matrix C, H, G are matrix of coefficients, can calculate according to (2), (3), (4).

For obtaining the multiple acoustic pressure p (Q) in vibration sound source border and boundary method to vibration velocity v (Q) _nrelation, P point in field is moved on to vibration sound source border S on, due to Ψ with occur unusual, adopt CENERALIZED POLAR coordinate transform to eliminate unusual.If S is discrete is triangular element, using the P point that moves on on boundary element as vertex of a triangle, utilize polar coordinate transform

${\mathrm{\ξ}}_1={\mathrm{\ξ}}_1^3+\mathrm{\ρ}[{\mathrm{\ξ}}_1^1-{\mathrm{\ξ}}_1^3+\mathrm{\θ}({\mathrm{\ξ}}_1^2-{\mathrm{\ξ}}_1^1)]---\left(6\right)$

${\mathrm{\ξ}}_2={\mathrm{\ξ}}_2^3+\mathrm{\ρ}[{\mathrm{\ξ}}_2^1-{\mathrm{\ξ}}_2^3+\mathrm{\θ}({\mathrm{\ξ}}_2^2-{\mathrm{\ξ}}_2^1)]---\left(7\right)$

Wherein subscript 1,2,3 represents to be that the triangle on summit is numbered by counterclockwise each point with P, and the point at P place is designated as 1, and two coordinates of subscript 1,2 triangle each point, now have

$\begin{array}{c}{\∫}_s\frac{\∂\mathrm{\Ψ}}{\∂n}\mathrm{ds}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\∫}_{s_j}\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_k\mathrm{ds}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\∫}_0^1{\∫}_0^{1-{\mathrm{\ξ}}_2}\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_k\mathrm{Jd}{\mathrm{\ξ}}_{1}d{\mathrm{\ξ}}_2=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\∫}_0^1{\∫}_0^1\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_k\mathrm{J\ρd}{\mathrm{\ρ}}_{1}d{\mathrm{\θ}}_2\\ =\frac{1}{4}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\∫}_{-1}^1{\∫}_{-1}^1\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_k\mathrm{J\ρd}{\mathrm{\η}}_{1}d{\mathrm{\η}}_2=\frac{1}{4}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\underset{m=1}{\overset{l}{\mathrm{\Σ}}}\underset{k=1}{\overset{l}{\mathrm{\Σ}}}{w}_m{w}_k\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_k\mathrm{J\ρ}\end{array}---\left(8\right)$

$\begin{array}{c}{\∫}_s\mathrm{i\ρ\ωv}{\left(Q\right)}_n\mathrm{\Ψds}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{i\ρ\ω}{\∫}_{s_j}\mathrm{\Ψ}{N}_k\mathrm{ds}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{i\ρ\ω}{\∫}_0^1{\∫}_0^{1-{\mathrm{\ξ}}_2}\mathrm{\Ψ}{N}_k\mathrm{Jd}{\mathrm{\ξ}}_{1}d{\mathrm{\ξ}}_2\\ =\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\∫}_0^1{\∫}_0^1\mathrm{\Ψ}{N}_k\mathrm{J\ρd}{\mathrm{\ρ}}_{1}d{\mathrm{\θ}}_2=\frac{1}{4}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{i\ρ\ω}{\∫}_{-1}^1{\∫}_{-1}^1\mathrm{\Ψ}{N}_k\mathrm{J\ρd}{\mathrm{\η}}_{1}d{\mathrm{\η}}_2=\frac{1}{4}\mathrm{i\ρ\ω}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\underset{m=1}{\overset{l}{\mathrm{\Σ}}}\underset{k=1}{\overset{l}{\mathrm{\Σ}}}{w}_m{w}_k\mathrm{\Ψ}{N}_k\mathrm{J\ρ}\end{array}---\left(9\right)$

Wherein now η ₁, η ₂for Gauss integration point.By obtaining the multiple acoustic pressure of sound field and boundary method with co-relation to vibration velocity relation

P _s＝ATM _s·V _n(10)

Wherein ATM _sfor the multiple acoustic pressure in vibration sound source border and boundary method are to the transfer matrix of vibration velocity acoustics, the multiple acoustic pressure of field point and Oscillating boundary normal vibration length velocity relation can be obtained by (5), (10)

P _f＝ATM _f·V _n(11)

Be wherein P _fthe multiple acoustic pressure matrix of field point, ATM _ffor the multiple acoustic pressure of field point and boundary method are to vibration velocity acoustics transfer matrix.Obtain boundary method thus to vibration velocity

$V_n={\mathrm{ATM}}_f^{-}\·P_f---\left(12\right)$

Wherein for the inverse matrix of transfer matrix.According to equation (10), point multiple acoustic pressure in field is utilized to calculate surface normal vibration velocity.The vibration sound source normal vibration speed obtained according to equation (8) and border acoustic pressure relation calculate border acoustic pressure p _s.

4th step: calculate vibrating mass radiated according to surface normal vibration velocity

w＝∫ _s0.5re(p(Q) _sv(Q) _n)ds (13)

Wherein re represents border acoustic pressure and boundary method phase vibration velocity real part.Oscillation intensity size can be passed judgment on according to vibrating machine radiated.

The main hardware equipment that the present invention relates to: testee 1, reference microphone 2, scanning stand 3, microphone array 4, data collecting instrument 5 and computing machine 6.

With reference to Fig. 1, under tested vibration sound source 1 is in running order, be fixed on distance with reference to microphone, microphone array to be less than vibration sound source best result and to analyse in the position of wavelength corresponding to frequency, microphone array is arranged on scanning support 3, data collecting instrument 5 is connected to by signal wire with reference to microphone and microphone array, data collecting instrument connects computing machine 6, computing machine is equipped with Pulse data processing software, can the acoustic pressure of real-time recorded data Acquisition Instrument transmission during its function, and according to the multiple acoustic pressure of the field point providing Microphone array measurement with reference to microphone acoustic pressure.

Tested vibration sound source 1 boundary method is built to vibration velocity and the multiple acoustic pressure relation of field point according to vibration sound source boundary integral equation

$c\left(P\right)p\left(P\right)=-{\∫}_s(p\left(Q\right)\frac{\∂\mathrm{\Ψ}}{\∂n}+\mathrm{i\ρ\ωv}{\left(Q\right)}_n\mathrm{\Ψ})\mathrm{ds}$

Acoustic pressure coefficient

$c\left(p\right)=\left\{\begin{array}{cc}1& p\∈V\\ 1-{\∫}_{s_{\mathrm{\ϵ}}}\frac{\∂}{\∂n}\left(\frac{1}{4\mathrm{\πr}}\right)\mathrm{ds}& p\∈S\\ 0& p\∉(v\∪s)\end{array}\right.$

By boundary discrete method

$\begin{array}{c}{\∫}_{s}p\left(Q\right)\frac{\∂\mathrm{\Ψ}}{\∂n}\mathrm{ds}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\∫}_{s_j}\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_k\mathrm{ds}\\ =\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\frac{\∂\mathrm{\Ψ}}{\∂n}{\∫}_{-1}^1{\∫}_{-1}^1{N}_k\mathrm{Jd}{\mathrm{\ξ}}_{1}d{\mathrm{\ξ}}_2=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\underset{m=1}{\overset{l}{\mathrm{\Σ}}}\underset{k=1}{\overset{l}{\mathrm{\Σ}}}{w}_m{w}_k\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_{k}J\end{array}$

$\begin{array}{c}{\∫}_s\mathrm{i\ρ\ωv}{\left(Q\right)}_n\mathrm{\Ψds}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{i\ρ\ω}{\∫}_{s_j}\mathrm{\Ψ}{N}_k\mathrm{ds}\\ =\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{i\ρ\ω\Ψ}{\∫}_{-1}^1{\∫}_{-1}^1{N}_k\mathrm{Jd}{\mathrm{\ξ}}_{1}d{\mathrm{\ξ}}_2=\mathrm{i\ρ\ω}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\underset{m=1}{\overset{l}{\mathrm{\Σ}}}\underset{k=1}{\overset{l}{\mathrm{\Σ}}}{w}_n{w}_k\mathrm{\Ψ}{N}_{k}J\end{array}$

P is put in field to be moved on on border, adopts Polar Coordinate Transformation Approach to eliminate singular integral.Obtain the multiple acoustic pressure in vibration sound source border and boundary method thus to vibration velocity relation

P _s＝ATM _s·V _n

The multiple acoustic pressure of field point and Oscillating boundary normal vibration length velocity relation is set up according to boundary integral equation

P _f＝ATM _f·V _n

Be wherein P _fthe multiple acoustic pressure of field point, V _nfor vibrational structure normal vibration speed, the multiple acoustic pressure of field point and boundary method are to vibration velocity acoustics transfer matrix.Application matrix inverse operation obtains boundary method to vibration velocity

$V_n={\mathrm{ATM}}_f^{-}\·P_f$

Wherein for the multiple acoustic pressure of field point and boundary method are to the inverse matrix of vibration velocity acoustics transfer matrix.Obtaining acoustic pressure with reference to microphone and Microphone array measurement utilizes Mutual spectrum to obtain the multiple acoustic pressure of field point at some place, Microphone array measurement field, exports the multiple acoustic pressure under each measurement point different frequency, utilizes the multiple acoustic pressure of each measurement point as input, according to formula calculate surface normal vibration velocity v _n, according to integral equation P _s=ATM _sv _nthe vibration sound source normal vibration speed set up and border acoustic pressure relation calculate border acoustic pressure p _s.

Utilize border to vibrate normal velocity, border acoustic pressure calculating vibrating mass radiated is

w＝∫ _s0.5re(p(Q) _sv(Q) _n)ds

Vibration sound source oscillation intensity size can be evaluated according to vibrating machine radiated.A kind of advantage of the method based on inverse boundary element method calculating machine surface vibration intensity is, utilizes mechanical radiative sound field acoustic pressure as the known quantity calculated, avoids the restriction of direct contact measurement surface vibration velocity.Vibrating machine shape based on inverse boundary element method does not limit, can to arbitrary shape mechanical oscillatory structure Strength co-mputation.

Claims (1)

1., based on the method for inverse boundary element method identification machinery surface vibration intensity, it is characterized in that:

(1) arrange at vibration sound source radiated sound field the field point acoustic pressure carrying out measuring radiation sound field with reference to microphone and microphone array, the two distance to vibration sound source is less than analyzes wavelength corresponding to highest frequency, with reference to microphone number 1-2, the measurement field point number of microphone array meets containing 3-5 measuring point in a wave length of sound, measures area and is greater than vibration sound source frontal plane of projection;

(2) with reference to the multiple acoustic pressure that microphone and the acoustic pressure that Microphone array measurement obtains utilize Mutual spectrum to obtain on measurement field point place frequency domain corresponding to microphone array, this multiple acoustic pressure is as the known parameters solving mechanical surface oscillation intensity and input;

(3) vibration surface normal vibration speed is calculated based on inverse boundary element method:

Setting up dynamic surface with measurement point integral equation is

$c\left(P\right)p\left(P\right)=-{\∫}_s(p\left(Q\right)\frac{\∂\mathrm{\Ψ}}{\∂n}+\mathrm{i\ρ\ωv}{\left(Q\right)}_n\mathrm{\Ψ})\mathrm{ds}$

Wherein: c (P) is the multiple acoustic pressure coefficient of field point, and in c (P) bracket, P represents radiated sound field field point, p (P) is the multiple acoustic pressure of field point, p (Q), v (Q) _nacoustic pressure and boundary method are to vibration velocity to be again respectively vibration sound source border, and Q is vibration sound source frontier point, elementary solution for the normal derivative of elementary solution, k is field point acoustic pressure coefficient, and r is radiated sound field field point P and the distance vibrating sound source frontier point Q, ρ is atmospheric density, ω=2 π f, and vibration sound source border is that S, c (P) can be expressed as

$c\left(p\right)=\left\{\begin{array}{ccc}1& p\∈V& \\ 1-{\∫}_{s_{\mathrm{\ϵ}}}\frac{\∂}{\∂n}\left(\frac{1}{4\mathrm{\πr}}\right)\mathrm{ds}& p\∈S& s\\ 0& p\∉(v\∪s)& \end{array}\right.$

Wherein: V vibrates sound source radiated sound field, will vibrate sound source border s discrete

$\begin{array}{c}{\∫}_{s}p\left(Q\right)\frac{\∂\mathrm{\Ψ}}{\∂n}\mathrm{ds}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\∫}_{s_j}\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_k\mathrm{ds}\\ =\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\frac{\∂\mathrm{\Ψ}}{\∂n}{\∫}_{-1}^1{\∫}_{-1}^1{N}_k\mathrm{Jd}{\mathrm{\ξ}}_{1}d{\mathrm{\ξ}}_2=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\underset{m=1}{\overset{l}{\mathrm{\Σ}}}\underset{k=1}{\overset{l}{\mathrm{\Σ}}}{w}_m{w}_k\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_{k}J\end{array},$

$\begin{array}{c}{\∫}_s\mathrm{i\ρ\ωv}{\left(Q\right)}_n\mathrm{\Ψds}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{i\ρ\ω}{\∫}_{s_j}{N}_k\mathrm{ds}\\ =\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{i\ρ\ω\Ψ}{\∫}_{-1}^1{\∫}_{-1}^1{N}_k\mathrm{Jd}{\mathrm{\ξ}}_{1}d{\mathrm{\ξ}}_2=\mathrm{i\ρ\ω}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\underset{m=1}{\overset{l}{\mathrm{\Σ}}}\underset{k=1}{\overset{l}{\mathrm{\Σ}}}{w}_m{w}_k{\mathrm{\ψN}}_{k}J\end{array},$

Wherein n is the discrete rear unit number of vibration sound source border S, ξ ₁, ξ ₂for Gauss integration point, N _kξ ₁, ξ ₂function, footmark k is cell node number, and l is counting of getting of Gauss integration, and J is Jacobi;

Must be shown up a little multiple acoustic pressure matrix P thus _facoustic pressure matrix P multiple with vibration sound source border _sand boundary method is to vibration velocity matrix V _nrelation:

CP _f＝HP _s+GV _n，

Wherein Matrix C, H, G are matrix of coefficients;

For obtaining the multiple acoustic pressure p (Q) in vibration sound source border and boundary method to vibration velocity v (Q) _nrelation, P point in field is moved on to vibration sound source border S on, due to Ψ with occur unusual, adopt CENERALIZED POLAR coordinate transform to eliminate unusual; If S is discrete is triangular element, using the P point that moves on on boundary element as vertex of a triangle, utilize polar coordinate transform

${\mathrm{\ξ}}_1={\mathrm{\ξ}}_1^3+\mathrm{\ρ}[{\mathrm{\ξ}}_1^1-{\mathrm{\ξ}}_1^3+\mathrm{\θ}({\mathrm{\ξ}}_1^2-{\mathrm{\ξ}}_1^1)],$

${\mathrm{\ξ}}_2={\mathrm{\ξ}}_2^3+\mathrm{\ρ}[{\mathrm{\ξ}}_2^1-{\mathrm{\ξ}}_2^3+\mathrm{\θ}({\mathrm{\ξ}}_2^2-{\mathrm{\ξ}}_2^1)],$

Wherein subscript 1,2,3 represents to be that the triangle on summit is numbered by counterclockwise each point with P, and the point at P place is designated as 1, and two coordinates of subscript 1,2 triangle each point, now have

$\begin{array}{c}{\∫}_s\frac{\∂\mathrm{\Ψ}}{\∂n}\mathrm{ds}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\∫}_{s_j}\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_k\mathrm{ds}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\∫}_0^1{\∫}_0^{1-{\mathrm{\ξ}}_2}\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_k\mathrm{Jd}{\mathrm{\ξ}}_{1}d{\mathrm{\ξ}}_2=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\∫}_0^1{\∫}_0^1\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_k\mathrm{J\ρd}{\mathrm{\ρ}}_{1}d{\mathrm{\θ}}_2\\ =\frac{1}{4}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\∫}_{-1}^1{\∫}_{-1}^1\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_k\mathrm{J\ρd}{\mathrm{\η}}_{1}d{\mathrm{\η}}_2=\frac{1}{4}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\underset{m=1}{\overset{l}{\mathrm{\Σ}}}\underset{k=1}{\overset{l}{\mathrm{\Σ}}}{w}_m{w}_k\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_k\mathrm{J\ρ}\end{array},$

$\begin{array}{c}{\∫}_s\mathrm{i\ρ\ωv}{\left(Q\right)}_n\mathrm{\Ψds}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{i\ρ\ω}{\∫}_{s_j}\mathrm{\Ψ}{N}_k\mathrm{ds}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{i\ρ\ω}{\∫}_0^1{\∫}_0^{1-{\mathrm{\ξ}}_2}{\mathrm{\ΨN}}_k\mathrm{Jd}{\mathrm{\ξ}}_{1}d{\mathrm{\ξ}}_2\\ =\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\∫}_0^1{\∫}_0^1{\mathrm{\ΨN}}_k\mathrm{J\ρd}{\mathrm{\ρ}}_{1}d{\mathrm{\θ}}_2=\frac{1}{4}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{i\ρ\ω}{\∫}_{-1}^1{\∫}_{-1}^1{\mathrm{\ΨN}}_k\mathrm{J\ρd}{\mathrm{\η}}_{1}d{\mathrm{\η}}_2=\frac{1}{4}\mathrm{i\ρ\ω}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\underset{m=1}{\overset{l}{\mathrm{\Σ}}}\underset{k=1}{\overset{l}{\mathrm{\Σ}}}{w}_m{w}_k{\mathrm{\ΨN}}_k\mathrm{J\ρ}\end{array},$

Wherein now η ₁, η ₂for Gauss integration point; By obtaining the multiple acoustic pressure of sound field and boundary method with co-relation to vibration velocity relation

P _s＝ATM _s·V _n，

Wherein ATM _sfor the multiple acoustic pressure in vibration sound source border and boundary method are to the transfer matrix of vibration velocity acoustics, by formula CP _f=HP _s+ GV _nand P _s=ATM _sv _nmust show up and a little answer acoustic pressure and Oscillating boundary normal vibration length velocity relation

P _f＝ATM _f·V _n，

Be wherein P _fthe multiple acoustic pressure matrix of field point, ATM _ffor the multiple acoustic pressure of field point and boundary method are to vibration velocity acoustics transfer matrix, obtain boundary method thus to vibration velocity

$V_n={\mathrm{ATM}}_f^{-}\·P_f,$

Wherein for the inverse matrix of transfer matrix, according to formula P _s=ATM _sv _n, utilize point multiple acoustic pressure in field to calculate surface normal vibration velocity; According to equation $\begin{array}{c}{\∫}_s\frac{\∂\mathrm{\Ψ}}{\∂n}\mathrm{ds}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\∫}_{s_j}\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_k\mathrm{ds}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\∫}_0^1{\∫}_0^{1-{\mathrm{\ξ}}_2}\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_k\mathrm{Jd}{\mathrm{\ξ}}_{1}d{\mathrm{\ξ}}_2=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\∫}_0^1{\∫}_0^1\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_k\mathrm{J\ρd}{\mathrm{\ρ}}_{1}d{\mathrm{\θ}}_2\\ =\frac{1}{4}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\∫}_{-1}^1{\∫}_{-1}^1\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_k\mathrm{J\ρd}{\mathrm{\η}}_{1}d{\mathrm{\η}}_2=\frac{1}{4}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\underset{m=1}{\overset{l}{\mathrm{\Σ}}}\underset{k=1}{\overset{l}{\mathrm{\Σ}}}{w}_m{w}_k\frac{\∂\mathrm{\Ψ}}{\∂n}{N}_k\mathrm{J\ρ}\end{array}$ The vibration sound source normal vibration speed obtained and border acoustic pressure relation calculate border acoustic pressure p _s;

(4) vibrating mass radiated is calculated according to surface normal vibration velocity

w＝∫ _s0.5re(p(Q) _sv(Q) _n)ds，

Wherein re represents border acoustic pressure and boundary method phase vibration velocity real part, passes judgment on oscillation intensity size according to vibrating machine radiated.