CN104951596A - Plate structure-sound field coupling analysis method and device and computing device - Google Patents

Abstract

The invention discloses a plate structure-sound field coupling analysis method. The method includes the steps that a finite element method and a radial point interpolation method are combined, and dispersing is conducted on a system kinetic equation of a plate structure; a boundary integral equation of a sound field domain is established according to a boundary element method; a structure-sound field coupling equation is established according to a dispersed system kinetic equation, the boundary integral equation and the structure-sound field coupling boundary condition. The invention further discloses a plate structure-sound field coupling analysis device corresponding to the plate structure-sound field coupling analysis method and a computing device with the plate structure-sound field coupling analysis device.

Description

A kind of plate structure-sound field coupling analytical method, device and computing equipment

Technical field

The present invention relates to the numerical arts of sound field prediction, be specifically related to a kind of plate structure-sound field coupling analytical method, device and computing equipment.

Background technology

Coupled structure-acoustic systems comprises the coupling between domain, sound field territory and two territories, usually, in the state of domain with displacement description scheme, describes the state of sound field in sound field territory acoustic pressure.Nearly all acoustic problems is all relevant with coupled structure-acoustic systems, the analysis of coupled structure-acoustic systems can provide important information for the optimization of structural member, particularly easily be subject to acoustic pressure to encourage and vibrative elastic thin-walled structures part, the research therefore for coupled structure-acoustic systems has important engineering significance; In the vehicle structure operatic tunes, predict that the outer sound field noise that pilothouse acoustic pressure and car outer air etc. cause also has certain using value simultaneously.

At present, the main method of coupled structure-acoustic system analysis has analytical method and numerical method, wherein numerical method mainly finite element method (Finite Element Method, FEM).FEM is a kind of normal scatter equation computational tool, needs to carry out discrete to time (transient problem) and space when solving sound field or structure.It becomes many unit considered sound field or structural separation based on variational principle and local interpolation, supposes acoustic pressure and velocity pattern in each unit, and the shape function that the field point acoustic pressure in each unit is made up of polynomial function is approximate to be obtained.The precision of approximate value is improved by subdivision unit or application shape function that is more complicated or high-order.Be connected by node the transmission realizing speed between each unit, and meet sound pressure level or displacement coordination condition in its connection place, finally set up a set of system of linear equations and obtain the unknown quantity such as acoustic pressure, particle velocity of each unit and node by solving these system of equations.

Theoretically, finite element method is applicable to and solves any acoustic problems.But according to the requirement of wavelength and unit size relation, in order to obtain good precision, acoustics finite element method needs a large amount of unit.And along with the increase of calculated rate, the Contamination Error that numerical dispersion causes also sharply increases, so mesh-density and iterations (in order to meet the requirements of precision) also increase along with the increase of wave number, the internal memory causing calculating to consume and time sharply rise, and counting yield declines.Therefore, finite element analysis is only applied in the acoustics calculating of low-frequency range usually.To medium-high frequency problem, the error of calculation of finite element method is comparatively large, needs to consider the discrete numerical dispersion effect caused.

Boundary element method (Boundary Element Method, BEM) be the more accurate effective method of one grown up after finite element method, also known as boundary integral equation-boundary element method, it is to be defined in borderline boundary integral equation for governing equation, by dividing border first interpolation discrete, turning to Algebraic Equation set and solving.

Finite element-radial point interpolation method (Finite Element-Radial Point Interpolation Method, FE-RPIM) be a kind of mixed method combined with the radial point interpolation method in gridless routing by finite element method, mainly finite element shape function and radial point interpolation method shape function are combined, finite element shape function interpolation is adopted in global scope, radial point interpolation method shape function interpolation is applied in subrange, by synthetic finite unit and radial point interpolation method advantage separately, finite element-radial point interpolation method the shape function of structure compound, this shape function has Kronecker that character and cell compatibilty.

How numerical evaluation FE-RPIM/BEM method is applied to coupled structure-acoustic system analysis field, prior art not yet proposes effective solution.

Summary of the invention

In view of the above problems, the present invention is proposed to provide a kind of plate structure-sound field coupling analytical method, device and computing equipment overcoming the problems referred to above or solve the problem at least in part.

According to an aspect of the present invention, provide a kind of plate structure-sound field coupling analytical method, be suitable for running in computing equipment, and comprise the steps:

In conjunction with finite element method and radial point interpolation method, carry out discrete to the system dynamics equation of plate structure;

According to the boundary integral equation in boundary element method structure sound field territory; And

According to the coupled boundary condition of system dynamics equation, boundary integral equation and the structure-sound field after discrete, structural texture-sound field coupled wave equation.

Alternatively, according to plate structure of the present invention-sound field coupling analytical method, wherein, described in conjunction with finite element method and radial point interpolation method, carry out discrete to the system dynamics equation of plate structure, comprising:

The first displacement equation of location point in unit is set up according to finite element method;

The second displacement equation of unit interior nodes is set up according to radial point interpolation method;

According to the first displacement equation and the second displacement equation, obtain the form function matrix of finite element method-radial point interpolation method, and to form function matrix differentiate;

According to form function matrix and its differentiate result, carry out discrete to the system dynamics equation of plate structure.

Alternatively, according to plate structure of the present invention-sound field coupling analytical method, wherein, described according to form function matrix and its differentiate result, carry out discrete to the system dynamics equation of plate structure, comprise

The parameter of definition plate structure;

According to the differentiate result of described parameter, form function matrix and form function matrix, determine Slab element stiffness matrix, Slab element mass matrix, surface load array and body force array;

According to Slab element stiffness matrix, Slab element mass matrix, surface load array and body force array, carry out discrete to the system dynamics equation of plate structure;

Alternatively, according to plate structure of the present invention-sound field coupling analytical method, wherein, the described boundary integral equation according to boundary element method structure sound field territory, comprising:

The Helmholtz setting up sound field territory is fluctuated equation;

Set up sound field boundary condition;

To fluctuate equation and boundary condition according to Helmholtz, set up boundary integral equation;

Alternatively, according to plate structure of the present invention-sound field coupling analytical method, wherein, the described coupled boundary condition according to system dynamics equation, boundary integral equation and the structure-sound field after discrete, structural texture-sound field coupled wave equation, comprising:

Set up the coupled boundary condition of structure-sound field;

According to coupled boundary condition, determine bonding force;

According to bonding force, simultaneous is carried out to the system dynamics equation after discrete and boundary integral equation, obtains coupled structure-acoustic system equation.

According to a further aspect in the invention, provide a kind of plate structure-sound field coupling analysis device, reside in computing equipment, and comprise:

Domain model sets up unit, is suitable in conjunction with finite element method and radial point interpolation method, carries out discrete to the system dynamics equation of plate structure;

Sound field domain model sets up unit, is suitable for the boundary integral equation according to boundary element method structure sound field territory; And

Coupling model sets up unit, is suitable for the coupled boundary condition according to system dynamics equation, boundary integral equation and the structure-sound field after discrete, structural texture-sound field coupled wave equation.

Alternatively, according to plate structure of the present invention-sound field coupling analysis device, wherein, described domain model is set up unit and is further adapted for:

The first displacement equation of location point in unit is set up according to finite element method;

The second displacement equation of unit interior nodes is set up according to radial point interpolation method;

According to the first displacement equation and the second displacement equation, obtain the form function matrix of finite element method-radial point interpolation method, and to form function matrix differentiate;

The parameter of definition plate structure;

According to the differentiate result of described parameter, form function matrix and form function matrix, determine Slab element stiffness matrix, Slab element mass matrix, surface load array and body force array;

According to Slab element stiffness matrix, Slab element mass matrix, surface load array and body force array, carry out discrete to the system dynamics equation of plate structure;

Alternatively, according to plate structure of the present invention-sound field coupling analysis device, wherein, described sound field domain model is set up unit and is further adapted for:

The Helmholtz setting up sound field territory is fluctuated equation;

Set up sound field boundary condition;

To fluctuate equation and boundary condition according to Helmholtz, set up boundary integral equation;

Alternatively, according to plate structure of the present invention-sound field coupling analysis device, wherein, described coupling model is set up unit and is further adapted for:

Set up the coupled boundary condition of structure-sound field;

According to coupled boundary condition, determine bonding force;

According to bonding force, simultaneous is carried out to the system dynamics equation after discrete and boundary integral equation, obtains coupled structure-acoustic system equation.

According to another aspect of the invention, provide a kind of computing equipment, resident with good grounds plate structure of the present invention-sound field coupling analysis device in this computing equipment.

In plate structure according to the present invention-sound field coupling analysis scheme, FE-RPIM model is adopted at domain, what adopt in sound field territory is BEM model, and what intercouple that the system that acts on adopts by structure and sound field is FE-RPIM/BEM model, thus has following beneficial effect:

1, FE-RPIM requires very low to the element quality of computation model, such as very low to the requirement of the size of the roughness of grid, degreeof tortuosity, grid cell.

2, the shape function of FE-RPIM inherits the Crow Nellie character of the RPIM shape function of improvement and the compatibility of finite element shape function, and possess polynomial high-order completeness, make computing relatively simple, compatibility is also improved, and high-order process computation complexity also has reduction.

3, FE-RPIM/BEM is in structure sound field or extend to the acoustic pressure prediction etc. that fluid domain etc. can solve medium and low frequency construct noise, and that is particularly correlated with at structure thin-wall part has certain reference value as the operatic tunes in automobile and the outer sound field noise prediction of car etc.

Above-mentioned explanation is only the general introduction of technical solution of the present invention, in order to technological means of the present invention can be better understood, and can be implemented according to the content of instructions, and can become apparent, below especially exemplified by the specific embodiment of the present invention to allow above and other objects of the present invention, feature and advantage.

Accompanying drawing explanation

By reading hereafter detailed description of the preferred embodiment, various other advantage and benefit will become cheer and bright for those of ordinary skill in the art.Accompanying drawing only for illustrating the object of preferred implementation, and does not think limitation of the present invention.And in whole accompanying drawing, represent identical parts by identical reference symbol.In the accompanying drawings:

Fig. 1 shows the process flow diagram of plate structure-sound field coupling analytical method according to an embodiment of the invention;

Fig. 2 shows the structural drawing of plate structure-sound field coupling analysis device according to an embodiment of the invention; And

Fig. 3 is arranged as the block diagram realized according to the Example Computing Device of plate structure of the present invention-sound field coupling analysis device.

Embodiment

Below with reference to accompanying drawings exemplary embodiment of the present disclosure is described in more detail.Although show exemplary embodiment of the present disclosure in accompanying drawing, however should be appreciated that can realize the disclosure in a variety of manners and not should limit by the embodiment set forth here.On the contrary, provide these embodiments to be in order to more thoroughly the disclosure can be understood, and complete for the scope of the present disclosure can be conveyed to those skilled in the art.

Fig. 1 shows the process flow diagram of plate structure-sound field coupling analytical method according to an embodiment of the invention, and the method is suitable for running in computing equipment.

With reference to Fig. 1, the method starts from step S102, in step s 102, sets up the FE-RPIM model in plate structure territory.Specifically comprise:

(1) displacement of any point (being called location point) in definition unit: according to plate structure standard finite meta-model, by discrete for plate structure territory be several quadrilateral units (according to actual needs), can be expressed as the displacement of unit any point:

u(x,y)＝Nu ^e(1)

In formula, N=[N ₁n ₂n ₃n ₄], wherein N _i(i=1,2,3,4) are isoparametric elements shape functions in finite element.

u ^e＝{u ₁(x,y) u ₂(x,y) u ₃(x,y) u ₄(x,y)} ^T(2)

(2) Displacement of elemental node is solved according to radial point interpolation method (RPIM): u _i(x, y) (i=1,2,3,4), these nodal displacement functions are unknown, can be obtained by radial point interpolation method,

u _i(x,y)＝Φ _iu _i,i＝1,2,3,4, (3)

${\mathrm{\Φ}}_i=\begin{array}{c}\left[\begin{array}{ccccc}{\mathrm{\Φ}}_1^i& {\mathrm{\Φ}}_2^i& {\mathrm{\Φ}}_3^i& ...& {\mathrm{\Φ}}_M^i\end{array}\right]---\left(4\right)\end{array}$

$u_i={\left[\begin{array}{ccccc}{u}_1^i& u_2^i& u_3^i& ...& u_M^i\end{array}\right]}^T---\left(5\right)$

Φ in formula _ifor the RPIM shape function of cell node i, it is consisted of RPIM the supporting domain point of i; u _ifor the displacement parameter vector of the supporting domain point of cell node i; M represents the number of the supporting domain point of cell node i.

(3) FE-RPIM form function matrix is solved: formula (3) is substituted into formula (1) and is write as:

$u(x,y)=\underset{1\×4}{N}\left(\underset{4\×M}{\mathrm{\Φ}}\underset{M\×1}{u}\right)=\left(\underset{1\×M}{\mathrm{N\Φ}}\right)\underset{M\×1}{u}=\underset{1\×M}{\mathrm{\Ψ}}\underset{M\×1}{u}---\left(6\right)$

Wherein FE-RPIM form function matrix Ψ is write as:

$\underset{1\×M}{\mathrm{\Ψ}}=\left[\begin{array}{ccccc}{\mathrm{\Ψ}}_1& {\mathrm{\Ψ}}_2& {\mathrm{\Ψ}}_3,& ...& {\mathrm{\Ψ}}_M\end{array}\right]=\underset{1\×4}{N}\underset{4\×M}{\mathrm{\Φ}}---\left(7\right)$

Matrix Φ in formula _{4 × M}by Φ _i(i=1,2,3,4) obtain, and columns M equals the nodes in unit supports territory.Φ _{4 × M}four nodes of front four row respectively corresponding quadrilateral units; All the other row correspond to the node in other supporting domain of unit.

(4) FE-RPIM shape function differentiate: when solving plate structure problem by the Galerkin method of standard, needs the derivative solving shape function to calculate the stiffness matrix of FE-RPIM, to need formula (7), to x, y differentiate, can obtain for this reason

Ψ _,x＝[Ψ _1,xΨ _2,xΨ _3,x,…Ψ _M,x]≡N _,xΦ+NΦ _,x(8)

Ψ _,y＝[Ψ _1,yΨ _2,yΨ _3,y,…Ψ _M,y]≡N _,yΦ+NΦ _,y

(5) parameter of definition structure problem: if E is elastic modulus, v is Bai Song ratio, and t is element thickness, and ρ is density of material, t _sfor plate structure surface load, b _sfor body force, represent acceleration, κ is bending strain, and γ is shear strain etc., D ^bfor the bending stiffness constitutive matrix of plate structure, D ^sfor transverse shear stiffness constitutive matrix, θ _xfor the corner around x-axis, θ _yfor the corner around y-axis, w is amount of deflection;

$\mathrm{\κ}={\left[\begin{array}{ccc}-\frac{\∂{\mathrm{\θ}}_x}{\∂x}& -\frac{\∂{\mathrm{\θ}}_y}{\∂y}& -(\frac{{\∂\mathrm{\θ}}_x}{\∂y}+\frac{{\∂\mathrm{\θ}}_y}{\∂x})\end{array}\right]}^T$ (9)

$\mathrm{\γ}={\left[\begin{array}{cc}\frac{\∂w}{\∂x}-{\mathrm{\θ}}_x& \frac{\∂w}{\∂y}-{\mathrm{\θ}}_y\end{array}\right]}^T$

$D_b=\frac{{\mathrm{Et}}^3}{12(1-v^2)}\left[\begin{array}{ccc}1& v& 0\\ v& 1& 0\\ 0& 0& \frac{1-v}{2}\end{array}\right]D_s=\frac{\mathrm{Et\υ}}{2(1+v)}\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]---\left(10\right)$

(6) FE-RPIM mould plate dynamics equations solves: according to above-mentioned parameter, carries out discrete to the Galerkin weak form of dynamics equations

$\begin{array}{c}{\∫}_{\mathrm{\Ω}}{\mathrm{\δ\κ}}^T{D}_b\mathrm{\κd\Ω}+{\∫}_{\mathrm{\Ω}}{\mathrm{\δ\γ}}^T{D}_s\mathrm{\γd\Ω}+{\∫}_{\mathrm{\Ω}}{\mathrm{\δu}}^T\mathrm{\ρt}{\mathrm{\ω}}^2\stackrel{\·\·}{u}\mathrm{d\Ω}\\ +{\∫}_{\∂\mathrm{\Ω}}{\mathrm{\δu}}^T{t}_s\mathrm{dS}-{\∫}_{\mathrm{\Ω}}{\mathrm{\δu}}^T{b}_s\mathrm{d\Ω}=0\end{array}---\left(11\right)$

In formula, Ω is studied a question domain.

Kinetics equation after plate structure is discrete is

$\mathrm{Ku}-M\stackrel{\·\·}{u}=F_f+F_b---\left(12\right)$

K=K in formula ^b+ K ^sfor Slab element stiffness matrix; K ^bfor bending stiffness matrix, K ^sfor shearing rigidity matrix, M is Slab element mass matrix, F _ffor surface load array, F _bfor body force array.

Stiffness matrix K can be expressed as

K＝K _b+K _s＝∫ _Ω(B _b) ^TD _bB _bdΩ+∫ _Ω(B _s) ^TD _sB _sdΩ (13)

$B_b=\left[\begin{array}{cccccccccc}-{\mathrm{\Ψ}}_{1,x}& 0& 0& -{\mathrm{\Ψ}}_{2,x}& 0& 0& ...& -{\mathrm{\Ψ}}_{M,x}& 0& 0\\ 0& -{\mathrm{\Ψ}}_{1,y}& 0& 0& -{\mathrm{\Ψ}}_{2,y}& 0& ...& 0& -{\mathrm{\Ψ}}_{M,y}& 0\\ -{\mathrm{\Ψ}}_{1,y}& -{\mathrm{\Ψ}}_{1,x}& 0& -{\mathrm{\Ψ}}_{2,y}& -{\mathrm{\Ψ}}_{2,x}& 0& ...& -{\mathrm{\Ψ}}_{M,y}& -{\mathrm{\Ψ}}_{M,x}& 0\end{array}\right]$ (14)

$B_s=\left[\begin{array}{cccccccccc}-{\mathrm{\Ψ}}_1& 0& {\mathrm{\Ψ}}_{1,x}& -{\mathrm{\Ψ}}_2& 0& {\mathrm{\Ψ}}_{2,x}& ...& -{\mathrm{\Ψ}}_M& 0& {\mathrm{\Ψ}}_{M,x}\\ 0& -{\mathrm{\Ψ}}_1& {\mathrm{\Ψ}}_{1,y}& 0& -{\mathrm{\Ψ}}_2& {\mathrm{\Ψ}}_{2,y}& ...& 0& -{\mathrm{\Ψ}}_M& {\mathrm{\Ψ}}_{M,y}\end{array}\right]$

Mass matrix Μ can be expressed as

$Q=\left[\begin{array}{cccccccccc}{\mathrm{\Ψ}}_1& 0& 0& {\mathrm{\Ψ}}_2& 0& 0& ...& {\mathrm{\Ψ}}_M& 0& 0\\ 0& {\mathrm{\Ψ}}_1& 0& 0& {\mathrm{\Ψ}}_2& 0& ...& 0& {\mathrm{\Ψ}}_M& 0\\ 0& 0& {\mathrm{\Ψ}}_1& 0& 0& {\mathrm{\Ψ}}_2& ...& 0& 0& {\mathrm{\Ψ}}_M\end{array}\right]$ (15)

$M={\∫}_{\mathrm{\Ω}}\mathrm{\ρ}{Q}^T\mathrm{diag}\left[\begin{array}{ccc}\frac{t^3}{12}& \frac{t^3}{12}& t\end{array}\right]\mathrm{Qd\Ω}$

The loading of Slab element is

$F_f={\∫}_{\mathrm{d\Ω}}{Q}^T{t}_s\mathrm{dS}$ F _b＝∫ _ΩQ ^Tb _sdΩ (16)

After the FE-RPIM model in plate structure territory has been set up, method has entered step S104.In step S104, set up the BEM model in sound field territory.Specifically comprise:

(1) Helmholtz wave equation is set up: the little amplitude simple harmonic quantity sound wave that structural vibration causes in desirable fluid media (medium), acoustic pressure meet Helmholtz wave equation

▽ ²p+k ²p＝0 (17)

In formula, k is wave number, k=ω/c; ω is circular frequency, and c is the velocity of sound; P is acoustic pressure.

(2) sound field boundary condition: on boundary condition, general consideration rigid boundary condition and Riemann's boundary condition, following formula:

$\frac{\∂p}{\∂n}=0---\left(18\right)$

$\frac{\∂p}{\∂n}=-\mathrm{i\ω}{\mathrm{\ρ}}_f{\mathrm{\υ}}_n---\left(19\right)$

In formula n shows the outer normal vector in sound field territory, ρ in formula _ffor fluid density; υ _nrepresent interface normal velocity.

(3) boundary integral equation is set up: use the elementary solution free space Green function that weighted residual method obtains:

$G(Q,P)=\frac{e^{-\mathrm{ikr}}}{4\mathrm{\πr}}---\left(20\right)$

In formula, r=|Q-P|, Q are arbitrfary point on body structure surface, and P is arbitrfary point in space.

According to the second green theorem, become Line Integral by the Integral Transformation of volume, derive Boundary Integral Equation in Acoustics according to formula (17):

$C\left(Q\right)p\left(Q\right)={\∫}_T(\frac{\∂G(Q,P)}{\∂n}p\left(Q\right)-G(Q,P)\frac{\∂p\left(Q\right)}{\∂n})\mathrm{d\Γ}---\left(21\right)$

In formula, Γ is the border in sound field territory, and C (Q) is constant, can be obtained, the computing formula of C (Q) by Q point position:

Wherein Ω _ffor fluid domain (sound field territory), according to coupled boundary condition formula (19), the normal derivative of acoustic pressure and speed in sound field, formula (21) can be write as:

$C\left(Q\right)p\left(Q\right)=-{\∫}_{\mathrm{\Γ}}(\frac{\∂G(Q,P)}{\∂n}p\left(Q\right)+\mathrm{i\ω}{\mathrm{\ρ}}_f{\mathrm{\υ}}_{n}G(Q,P))\mathrm{d\Γ}---\left(23\right)$

Wherein p (Q), υ _ncan be obtained by sound field territory unit shape function, same to formula (1) is consistent.Can be write as:

$p=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{N}_j{p}_j,v_n=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{N}_j{v}_{\mathrm{nj}}---\left(24\right)$

P in formula _j, v _njrepresent sound pressure level and the normal velocity of cell node j, m is the nodes on each face, N _jit is unit shape function.

(4) discretize of boundary integral equation: consider simultaneously by sound field boundary demarcation be M node, N number of quadrilateral units composition grid model, the all nodes of Q point selection on sound field field surface, the formula drawn (24) is updated to formula (23), obtains by boundary integral equation is discrete:

$C_i{\mathrm{\δ}}_{\mathrm{ij}}{p}_i+\underset{m=1}{\overset{N}{\mathrm{\Σ}}}{\∫}_S\frac{\∂G(Q,P)}{\∂n}{N}_j{p}_j\mathrm{dS}=-\underset{m=1}{\overset{N}{\mathrm{\Σ}}}{\∫}_S\mathrm{i\ω}{\mathrm{\ρ}}_{f}G(Q,P)N_j{v}_{\mathrm{nj}}\mathrm{dS}---\left(25\right)$

In above formula, S is sound field field surface, C _ifor constant, can be obtained by formula (22) according to i position, δ _ijrepresent δ function, namely ${\mathrm{\δ}}_{\mathrm{ij}}=\left\{\begin{array}{cc}1& i=j\\ 0& i\≠j\end{array}\right.,$ Can being obtained by your character of Kronecker, writing as matrix form last time being:

[H][P]＝iρω[G][v _n] (26)

In formula

$H=C_i{\mathrm{\δ}}_{\mathrm{ij}}+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\∫}_S\frac{\∂G(Q,P)}{\∂n}{N}_j\mathrm{dS}---\left(27\right)$

$G=-\underset{m=1}{\overset{N}{\mathrm{\Σ}}}{\∫}_S\mathrm{i\ω}{\mathrm{\ρ}}_{f}G(Q,P)N_j\mathrm{dS}---\left(28\right)$

After the BEM model in sound field territory has been set up, method has entered step S106.In step s 106, the FE-RPIM/BEM model of coupled structure-acoustic system is set up.Specifically comprise:

(1) coupled boundary condition: for the coupled system of structure-sound field, Ω _srepresentative structure territory adopts FE-RPIM model, Ω _frepresent fluid (sound field) territory and adopt BEM model.N _fit is coupled interface sound field normal vector.At coupled interface place, structural unit will meet coupling sound field unit condition.Coupled system should meet displacement and the pressure condition of continuity, introduces interface normal vector n=n _f=-n _s, the displacement condition of continuity and the pressure condition of continuity can be expressed as:

u _sn _s＝u _fn _fσ _s| _n＝-p (29)

Wherein n _ffor the sound field normal vector on coupled interface; n _sfor the plate structure normal vector on coupled interface.

(2) derivation of bonding force: sound field acoustic pressure acts on the load on vibro-acoustical couple system face, can be write as by formula (16):

$F_a=-{\∫}_{{\mathrm{\Ω}}_{\mathrm{sf}}}{N}_S^T{n}_S{\mathrm{\σ}}_S\mathrm{d\Γ}=\left({\∫}_{{\mathrm{\Ω}}_{\mathrm{sf}}}{N}_f^T{n}_f{N}_s\mathrm{d\Γ}\right)P_a---\left(30\right)$

In formula, N _sfor the shape function of domain discrete unit, N _fit is the shape function of sound field discrete unit.

Introduce coupled matrix:

$L={\∫}_{{\mathrm{\Ω}}_{\mathrm{sf}}}{N}_s{n}_f{N}_f\mathrm{dS}---\left(31\right)$

Bonding force can be write as:

F _a＝LP _a(32)

P _arepresent the node acoustic pressure vector of coupling boundary.

(3) foundation of coupled wave equation: under considering sound field reflecting, structural system kinetics equation is drawn by formula (12):

(K-ω ²M)u-Lp _a＝F (33)

For sound field territory, because boundary condition has coupling boundary a and non-coupled border b, boundary element equation is write as:

$\left[\begin{array}{cc}{H}_{11}& H_{12}\\ H_{21}& H_{22}\end{array}\right]\left[\begin{array}{c}{p}_a\\ p_b\end{array}\right]=-{\mathrm{\ρ\ω}}^2\left[\begin{array}{cc}{G}_{11}& G_{12}\\ G_{21}& G_{22}\end{array}\right]\left[\begin{array}{c}n\\ 0\end{array}\right]---\left(34\right)$

H ₁₁, H ₁₂, H ₂₁, H ₂₂for the partitioned matrix of matrix H, G ₁₁, G ₁₂, G ₂₁, G ₂₂for the partitioned matrix of matrix G, p _bthe node acoustic pressure vector on non-coupled border

By the FE-RPIM model of domain and the BEM model of sound field, the FE-RPIM/BEM model that can obtain coupled structure-acoustic systems is:

$\left[\begin{array}{ccc}K-{\mathrm{\ω}}^{2}M& L& 0\\ {\mathrm{\ρ}}_f{\mathrm{\ω}}^2{G}_{11}{n}_a& H_{11}& H_{12}\\ {\mathrm{\ρ}}_f{\mathrm{\ω}}^2{G}_{21}{n}_a& H_{12}& H_{22}\end{array}\right]\left[\begin{array}{c}u\\ p_a\\ p_b\end{array}\right]=\left[\begin{array}{c}F\\ 0\\ 0\end{array}\right]---\left(35\right)$

Formula (35) is solved, just can obtain the result that coupled structure-acoustic system is analyzed, i.e. displacement structure and sound field acoustic pressure.

Fig. 2 shows the structural drawing of plate structure-sound field coupling analysis device according to an embodiment of the invention, and this device resides in computing equipment.With reference to Fig. 2, this device comprises that domain model sets up unit 10, sound field domain model sets up unit 20 and coupling model sets up unit 30.

Domain model is set up unit 10 and is suitable in conjunction with finite element method and radial point interpolation method, carries out discrete to the system dynamics equation of plate structure.Detailed process is: the first displacement equation setting up location point in unit according to finite element method; The second displacement equation of unit interior nodes is set up according to radial point interpolation method; According to the first displacement equation and the second displacement equation, obtain the form function matrix of finite element method-radial point interpolation method, and to form function matrix differentiate; The parameter of definition plate structure; According to the differentiate result of described parameter, form function matrix and form function matrix, determine Slab element stiffness matrix, Slab element mass matrix, surface load array and body force array; According to Slab element stiffness matrix, Slab element mass matrix, surface load array and body force array, carry out discrete to the system dynamics equation of plate structure.

Sound field domain model sets up the boundary integral equation that unit 20 is suitable for constructing according to boundary element method sound field territory.Detailed process is: the Helmholtz setting up sound field territory is fluctuated equation; Set up sound field boundary condition; To fluctuate equation and boundary condition according to Helmholtz, set up boundary integral equation.

Coupling model sets up the coupled boundary condition that unit 30 is suitable for according to system dynamics equation, boundary integral equation and the structure-sound field after discrete, structural texture-sound field coupled wave equation.Detailed process is: the coupled boundary condition setting up structure-sound field; According to coupled boundary condition, determine bonding force; According to bonding force, simultaneous is carried out to the system dynamics equation after discrete and boundary integral equation, obtains coupled structure-acoustic system equation.

It should be noted that, domain model sets up unit 10, sound field domain model sets up unit 20 and coupling model sets up the process that performs in unit 30 and the process of step S102 ~ S106 is similar, and detail can with reference to above-mentioned steps.

Fig. 3 is arranged as the block diagram realized according to the Example Computing Device 900 of plate structure of the present invention-sound field coupling analysis device.In basic configuration 902, computing equipment 900 typically comprises system storage 906 and one or more processor 904.Memory bus 908 may be used for the communication between processor 904 and system storage 906.

Depend on the configuration of expectation, processor 904 can be the process of any type, includes but not limited to: microprocessor (μ P), microcontroller (μ C), digital information processor (DSP) or their any combination.Processor 904 can comprise the high-speed cache of one or more rank of such as on-chip cache 910 and second level cache 912 and so on, processor core 914 and register 916.The processor core 914 of example can comprise arithmetic and logical unit (ALU), floating-point unit (FPU), digital signal processing core (DSP core) or their any combination.The Memory Controller 918 of example can use together with processor 904, or in some implementations, Memory Controller 918 can be an interior section of processor 904.

Depend on the configuration of expectation, system storage 906 can be the storer of any type, includes but not limited to: volatile memory (such as RAM), nonvolatile memory (such as ROM, flash memory etc.) or their any combination.System storage 906 can comprise operating system 920, one or more application 922 and routine data 924.Application 922 can comprise the plate structure-sound field coupling analysis device 926 being configured to realize plate structure-sound field coupling analytical method.Routine data 924 can comprise and can be used for various algorithm model 928 as described here.In some embodiments, application 922 can be arranged as and utilize routine data 924 to operate on an operating system.

Computing equipment 900 can also comprise the interface bus 940 communicated contributed to from various interfacing equipment (such as, output device 942, Peripheral Interface 944 and communication facilities 946) to basic configuration 902 via bus/interface controller 930.The output device 942 of example comprises Graphics Processing Unit 948 and audio treatment unit 950.They can be configured to contribute to communicating with the various external units of such as display or loudspeaker and so on via one or more A/V port 952.Example Peripheral Interface 944 can comprise serial interface controller 954 and parallel interface controller 956, they can be configured to the external unit contributed to via one or more I/O port 958 and such as input equipment (such as, keyboard, mouse, pen, voice-input device, touch input device) or other peripheral hardwares (such as printer, scanner etc.) and so on and communicate.The communication facilities 946 of example can comprise network controller 960, and it can be arranged to is convenient to via one or more communication port 964 and the communication of one or more other computing equipments 962 by network communication link.

Network communication link can be an example of communication media.Communication media can be presented as computer-readable instruction, data structure, program module in the modulated data signal of such as carrier wave or other transmission mechanisms and so on usually, and can comprise any information delivery media." modulated data signal " can be such signal, the change of one or more or it of its data centralization can the mode of coded message in the signal be carried out.As nonrestrictive example, communication media can comprise the wire medium of such as cable network or private line network and so on, and such as sound, radio frequency (RF), microwave, infrared (IR) or other wireless medium are at interior various wireless mediums.Term computer-readable medium used herein can comprise both storage medium and communication media.

Computing equipment 900 can be implemented as a part for small size portable (or mobile) electronic equipment, and these electronic equipments can be such as cell phone, personal digital assistant (PDA), personal media player equipment, wireless network browsing apparatus, individual helmet, application specific equipment or the mixing apparatus that can comprise any function above.Computing equipment 900 can also be embodied as the personal computer comprising desktop computer and notebook computer configuration.

Intrinsic not relevant to any certain computer, virtual system or miscellaneous equipment with display at this algorithm provided.Various general-purpose system also can with use based on together with this teaching.According to description above, the structure constructed required by this type systematic is apparent.In addition, the present invention is not also for any certain programmed language.It should be understood that and various programming language can be utilized to realize content of the present invention described here, and the description done language-specific is above to disclose preferred forms of the present invention.

In instructions provided herein, describe a large amount of detail.But can understand, embodiments of the invention can be put into practice when not having these details.In some instances, be not shown specifically known method, structure and technology, so that not fuzzy understanding of this description.

Similarly, be to be understood that, in order to simplify the disclosure and to help to understand in each inventive aspect one or more, in the description above to exemplary embodiment of the present invention, each feature of the present invention is grouped together in single embodiment, figure or the description to it sometimes.But, the method for the disclosure should be construed to the following intention of reflection: namely the present invention for required protection requires feature more more than the feature clearly recorded in each claim.Or rather, as claims below reflect, all features of disclosed single embodiment before inventive aspect is to be less than.Therefore, the claims following embodiment are incorporated to this embodiment thus clearly, and wherein each claim itself is as independent embodiment of the present invention.

Those skilled in the art are appreciated that and adaptively can change the module in the equipment in embodiment and they are arranged in one or more equipment different from this embodiment.Module in embodiment or unit or assembly can be combined into a module or unit or assembly, and multiple submodule or subelement or sub-component can be put them in addition.Except at least some in such feature and/or process or unit be mutually repel except, any combination can be adopted to combine all processes of all features disclosed in this instructions (comprising adjoint claim, summary and accompanying drawing) and so disclosed any method or equipment or unit.Unless expressly stated otherwise, each feature disclosed in this instructions (comprising adjoint claim, summary and accompanying drawing) can by providing identical, alternative features that is equivalent or similar object replaces.

All parts embodiment of the present invention with hardware implementing, or can realize with the software module run on one or more processor, or realizes with their combination.It will be understood by those of skill in the art that the some or all functions that microprocessor or digital signal processor (DSP) can be used in practice to realize according to the some or all parts in the document protection equipment of the embodiment of the present invention.The present invention can also be embodied as part or all equipment for performing method as described herein or device program (such as, computer program and computer program).Realizing program of the present invention and can store on a computer-readable medium like this, or the form of one or more signal can be had.Such signal can be downloaded from internet website and obtain, or provides on carrier signal, or provides with any other form.

The present invention will be described instead of limit the invention to it should be noted above-described embodiment, and those skilled in the art can design alternative embodiment when not departing from the scope of claims.In the claims, any reference symbol between bracket should be configured to limitations on claims.Word " comprises " not to be got rid of existence and does not arrange element in the claims or step.Word "a" or "an" before being positioned at element is not got rid of and be there is multiple such element.The present invention can by means of including the hardware of some different elements and realizing by means of the computing machine of suitably programming.In the unit claim listing some devices, several in these devices can be carry out imbody by same hardware branch.Word first, second and third-class use do not represent any order.Can be title by these word explanations.

Claims (10)

1. plate structure-sound field coupling analytical method, is suitable for running in computing equipment, and comprises the steps:

In conjunction with finite element method and radial point interpolation method, carry out discrete to the system dynamics equation of plate structure;

According to the boundary integral equation in boundary element method structure sound field territory; And

According to the coupled boundary condition of system dynamics equation, boundary integral equation and the structure-sound field after discrete, structural texture-sound field coupled wave equation.

The method of claim 1, wherein 2. described in conjunction with finite element method and radial point interpolation method, carry out discrete to the system dynamics equation of plate structure, comprising:

The first displacement equation of location point in unit is set up according to finite element method;

The second displacement equation of unit interior nodes is set up according to radial point interpolation method;

According to the first displacement equation and the second displacement equation, obtain the form function matrix of finite element method-radial point interpolation method, and to form function matrix differentiate;

According to form function matrix and its differentiate result, carry out discrete to the system dynamics equation of plate structure.

3. method as claimed in claim 2, wherein, described according to form function matrix and its differentiate result, carries out discrete, comprise the system dynamics equation of plate structure

The parameter of definition plate structure;

According to the differentiate result of described parameter, form function matrix and form function matrix, determine Slab element stiffness matrix, Slab element mass matrix, surface load array and body force array;

According to Slab element stiffness matrix, Slab element mass matrix, surface load array and body force array, carry out discrete to the system dynamics equation of plate structure.

4. the method for claim 1, wherein described according to boundary element method structure sound field territory boundary integral equation, comprising:

The Helmholtz setting up sound field territory is fluctuated equation;

Set up sound field boundary condition;

To fluctuate equation and boundary condition according to Helmholtz, set up boundary integral equation.

5. the method for claim 1, wherein described coupled boundary condition according to system dynamics equation, boundary integral equation and the structure-sound field after discrete, structural texture-sound field coupled wave equation, comprising:

Set up the coupled boundary condition of structure-sound field;

According to coupled boundary condition, determine bonding force;

According to bonding force, simultaneous is carried out to the system dynamics equation after discrete and boundary integral equation, obtains coupled structure-acoustic system equation.

6. plate structure-sound field coupling analysis device, resides in computing equipment, and comprises:

Domain model sets up unit, is suitable in conjunction with finite element method and radial point interpolation method, carries out discrete to the system dynamics equation of plate structure;

Sound field domain model sets up unit, is suitable for the boundary integral equation according to boundary element method structure sound field territory; And

Coupling model sets up unit, is suitable for the coupled boundary condition according to system dynamics equation, boundary integral equation and the structure-sound field after discrete, structural texture-sound field coupled wave equation.

7. device as claimed in claim 6, wherein, described domain model is set up unit and is further adapted for:

The first displacement equation of location point in unit is set up according to finite element method;

The second displacement equation of unit interior nodes is set up according to radial point interpolation method;

According to the first displacement equation and the second displacement equation, obtain the form function matrix of finite element method-radial point interpolation method, and to form function matrix differentiate;

The parameter of definition plate structure;

According to the differentiate result of described parameter, form function matrix and form function matrix, determine Slab element stiffness matrix, Slab element mass matrix, surface load array and body force array;

According to Slab element stiffness matrix, Slab element mass matrix, surface load array and body force array, carry out discrete to the system dynamics equation of plate structure.

8. method as claimed in claim 6, wherein, described sound field domain model is set up unit and is further adapted for:

The Helmholtz setting up sound field territory is fluctuated equation;

Set up sound field boundary condition;

To fluctuate equation and boundary condition according to Helmholtz, set up boundary integral equation.

9. method as claimed in claim 6, wherein, described coupling model is set up unit and is further adapted for:

Set up the coupled boundary condition of structure-sound field;

According to coupled boundary condition, determine bonding force;

According to bonding force, simultaneous is carried out to the system dynamics equation after discrete and boundary integral equation, obtains coupled structure-acoustic system equation.

10. a computing equipment, resident just like the plate structure according to any one of claim 6 to 9-sound field coupling analysis device in this computing equipment.