CN104951596B - A kind of hardened structure-sound field coupling analytical method - Google Patents
A kind of hardened structure-sound field coupling analytical method Download PDFInfo
- Publication number
- CN104951596B CN104951596B CN201510299576.7A CN201510299576A CN104951596B CN 104951596 B CN104951596 B CN 104951596B CN 201510299576 A CN201510299576 A CN 201510299576A CN 104951596 B CN104951596 B CN 104951596B
- Authority
- CN
- China
- Prior art keywords
- sound field
- formula
- boundary
- matrix
- domain
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Landscapes
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
The invention discloses a kind of hardened structure-sound field coupling analytical methods.The described method includes: being carried out to the system dynamics equation of hardened structure discrete in conjunction with FInite Element and radial point interpolation method；The boundary integral equation in sound field domain is constructed according to boundary element method；According to system dynamics equation, boundary integral equation and the structure-sound field coupled boundary condition after discrete, structural texture-sound field coupled wave equation.The invention also discloses a kind of hardened structure-sound field coupling analysis device corresponding with the hardened structure-sound field coupling analytical method and the calculating equipment including the device.
Description
Technical field
The present invention relates to the numerical arts of sound field prediction, and in particular to a kind of hardened structure-sound field coupling analytical method,
Device and calculating equipment.
Background technique
Coupled structure-acoustic systems include the coupling between structural domain, sound field domain and two domains, in general, tying
The structure domain state of displacement description scheme, the state of sound field is described in sound field domain with acoustic pressure.Almost all of acoustic problems all with
Coupled structure-acoustic systems are related, and the analysis of coupled structure-acoustic systems can provide important information for the optimization of structural member,
It is especially susceptible to acoustic pressure excitation and generates the elastic thin-walled structures part vibrated, therefore for coupled structure-acoustic systems
Research has important engineering significance；It is predicted in the vehicle structure operatic tunes simultaneously outer caused by air etc. outside driver's cabin acoustic pressure and vehicle
Sound field noise also has certain application value.
Currently, the main method of coupled structure-acoustic system analysis has analytic method and numerical method, wherein numerical method is mainly limited
First method (Finite Element Method, FEM).FEM is a kind of normal scatter equation calculation tool, solve sound field or
It needs to carry out time (transient problem) and space when structure discrete.It is based on variation principle and local interpolation, being examined
Sound field or structural separation are considered into many units, and acoustic pressure and velocity pattern, the field in each unit are assumed in each unit
The shape function approximation that point acoustic pressure is made of polynomial function obtains.The precision of approximation is more multiple by subdivision unit or application
Miscellaneous or high-order shape function improves.It is connected between each unit by node to realize the transmitting of speed, and full in its connection place
Sufficient sound pressure level or displacement coordination condition, finally establish a set of system of linear equations and by solve these equation groups obtain each unit and
The unknown quantitys such as acoustic pressure, the particle velocity of node.
Theoretically, FInite Element is applicable to solve any acoustic problems.But according to wavelength and unit size relationship
Requirement, preferable precision in order to obtain, acoustics FInite Element needs a large amount of unit.And with calculate frequency increase,
Contamination Error caused by numerical dispersion also sharply increases, then mesh-density and the number of iterations (in order to reach permissible accuracy)
Increase with the increase of wave number, causes to calculate consumed memory and the time steeply rises, computational efficiency decline.Therefore, have
During the acoustics that finite element analysis is usually only applied to low-frequency range calculates.To medium-high frequency problem, the calculating error of FInite Element is larger, needs
Consider discrete caused numerical dispersion effect.
Boundary element method (Boundary Element Method, BEM) be grow up after FInite Element it is a kind of compared with
Accurate effective method, also known as boundary integral equation-boundary element method, it is to be defined on borderline boundary integral equation as control
Equation turns to Algebraic Equation set solution by dividing first interpolation discrete on boundary.
Finite element-radial point interpolation method (Finite Element-Radial Point Interpolation Method,
It FE-RPIM) is a kind of mixed method for combining FInite Element with the radial point interpolation method in gridless routing, it mainly will be limited
First shape function and radial point interpolation method shape function combine, and finite element shape function interpolation are used in global scope, in subrange
Interior application radial point interpolation method shape function interpolation is constructed compound by synthetic finite member and the advantage of radial point interpolation method respectively
Finite element-radial point interpolation method shape function, the shape function have Kronecker that property and cell compatibilty.
How numerical value is calculated into FE-RPIM/BEM method and be applied to coupled structure-acoustic system analysis field, the prior art is not yet
It puts forward effective solutions.
Summary of the invention
In view of the above problems, it proposes on the present invention overcomes the above problem or at least be partially solved in order to provide one kind
State the hardened structure-sound field coupling analytical method, device and calculating equipment of problem.
According to an aspect of the invention, there is provided a kind of hardened structure-sound field coupling analytical method, is suitable for calculating equipment
Middle operation, and include the following steps:
In conjunction with FInite Element and radial point interpolation method, the system dynamics equation of hardened structure is carried out discrete；
The boundary integral equation in sound field domain is constructed according to boundary element method；And
According to system dynamics equation, boundary integral equation and the structure-sound field coupled boundary condition after discrete, construction
Coupled structure-acoustic system equation.
Optionally, hardened structure-sound field coupling analytical method according to the present invention, wherein the combination FInite Element and radial direction
Point interpolation method carries out the system dynamics equation of hardened structure discrete, comprising:
The first displacement equation of location point in unit is established according to FInite Element；
The second displacement equation of unit interior nodes is established according to radial point interpolation method；
According to the first displacement equation and second displacement equation, FInite Element-radial point interpolation method form function matrix is obtained,
And to form function matrix derivation；
According to form function matrix and its derivation as a result, being carried out to the system dynamics equation of hardened structure discrete.
Optionally, hardened structure-sound field coupling analytical method according to the present invention, wherein it is described according to form function matrix and
Its derivation as a result, the system dynamics equation of hardened structure is carried out it is discrete, including
Define the parameter of hardened structure；
According to the derivation of the parameter, form function matrix and form function matrix as a result, determining plate unit stiffness matrix, plate list
First mass matrix, surface load array and body force array；
According to plate unit stiffness matrix, plate unit mass matrix, surface load array and body force array, to hardened structure
System dynamics equation carries out discrete；
Optionally, hardened structure-sound field coupling analytical method according to the present invention, wherein described according to boundary element method construction sound
The boundary integral equation of field domain, comprising:
The Helmholtz for establishing sound field domain fluctuates equation；
Establish sound field boundary condition；
Equation and boundary condition are fluctuated according to Helmholtz, establishes boundary integral equation；
Optionally, hardened structure-sound field coupling analytical method according to the present invention, wherein described dynamic according to the system after discrete
Mechanical equation, boundary integral equation and structure-sound field coupled boundary condition, structural texture-sound field coupled wave equation, comprising:
Establish structure-sound field coupled boundary condition；
According to coupled boundary condition, bonding force is determined；
According to bonding force, to after discrete system dynamics equation and boundary integral equation carry out simultaneous, obtain structure-sound
Field coupled wave equation.
According to another aspect of the present invention, a kind of hardened structure-sound field coupling analysis device is provided, calculating equipment is resided in
In, and include:
Domain model establishes unit, is suitable for combining FInite Element and radial point interpolation method, to the system dynamic of hardened structure
It is discrete to learn equation progress；
Sound field domain model establishes unit, suitable for constructing the boundary integral equation in sound field domain according to boundary element method；And
Coupling model establishes unit, suitable for according to system dynamics equation, boundary integral equation and the structure-sound after discrete
The coupled boundary condition of field, structural texture-sound field coupled wave equation.
Optionally, hardened structure-sound field coupling analysis device according to the present invention, wherein the domain model establishes unit
It is further adapted for:
The first displacement equation of location point in unit is established according to FInite Element；
The second displacement equation of unit interior nodes is established according to radial point interpolation method；
According to the first displacement equation and second displacement equation, FInite Element-radial point interpolation method form function matrix is obtained,
And to form function matrix derivation；
Define the parameter of hardened structure；
According to the derivation of the parameter, form function matrix and form function matrix as a result, determining plate unit stiffness matrix, plate list
First mass matrix, surface load array and body force array；
According to plate unit stiffness matrix, plate unit mass matrix, surface load array and body force array, to hardened structure
System dynamics equation carries out discrete；
Optionally, hardened structure-sound field coupling analysis device according to the present invention, wherein the sound field domain model establishes unit
It is further adapted for:
The Helmholtz for establishing sound field domain fluctuates equation；
Establish sound field boundary condition；
Equation and boundary condition are fluctuated according to Helmholtz, establishes boundary integral equation；
Optionally, hardened structure-sound field coupling analysis device according to the present invention, wherein the coupling model establish unit into
One step is suitable for:
Establish structure-sound field coupled boundary condition；
According to coupled boundary condition, bonding force is determined；
According to bonding force, to after discrete system dynamics equation and boundary integral equation carry out simultaneous, obtain structure-sound
Field coupled wave equation.
According to another aspect of the invention, a kind of calculating equipment is provided, is populated with according to the present invention in the calculating equipment
Hardened structure-sound field coupling analysis device.
In hardened structure according to the present invention-sound field coupling analysis scheme, FE-RPIM model is used in structural domain, in sound
Field domain using BEM model, by structure and sound field intercouple effect system using FE-RPIM/BEM model, from
And it has the following beneficial effects:
1, FE-RPIM requires the element quality of computation model very low, such as the roughness to grid, degreeof tortuosity, net
The requirement of the size of lattice unit is very low.
2, the shape function of FE-RPIM inherits the Crow Nellie property and finite element shape function of improved RPIM shape function
Compatibility, and have polynomial high-order completeness, so that calculation processing is relatively easy, compatibility is also improved, high-order processing
Computation complexity also has reduction.
3, the sound of FE-RPIM/BEM low frequency configuration noise in structure sound field or in extending to fluid domain etc. and can solving
Pressure prediction etc., the operatic tunes and vehicle outer sound field noise prediction have certain especially in the relevant such as automobile of structure thin-wall part
Reference value.
The above description is only an overview of the technical scheme of the present invention, in order to better understand the technical means of the present invention,
And it can be implemented in accordance with the contents of the specification, and in order to allow above and other objects of the present invention, feature and advantage can
It is clearer and more comprehensible, the followings are specific embodiments of the present invention.
Detailed description of the invention
By reading the following detailed description of the preferred embodiment, various other advantages and benefits are common for this field
Technical staff will become clear.The drawings are only for the purpose of illustrating a preferred embodiment, and is not considered as to the present invention
Limitation.And throughout the drawings, the same reference numbers will be used to refer to the same parts.In the accompanying drawings:
Fig. 1 shows the flow chart of hardened structure-sound field coupling analytical method according to an embodiment of the invention；
Fig. 2 shows hardened structure according to an embodiment of the invention-sound field coupling analysis device structure charts；And
Fig. 3 is the frame for being arranged as realizing hardened structure according to the present invention-sound field coupling analysis device Example Computing Device
Figure.
Specific embodiment
Exemplary embodiments of the present disclosure are described in more detail below with reference to accompanying drawings.Although showing the disclosure in attached drawing
Exemplary embodiment, it being understood, however, that may be realized in various forms the disclosure without should be by embodiments set forth here
It is limited.On the contrary, these embodiments are provided to facilitate a more thoroughly understanding of the present invention, and can be by the scope of the present disclosure
It is fully disclosed to those skilled in the art.
Fig. 1 shows the flow chart of hardened structure-sound field coupling analytical method according to an embodiment of the invention, this method
Suitable for being run in calculating equipment.
Referring to Fig.1, this method starts from step S102, in step s 102, establishes the FE-RPIM model of plate structural domain.Tool
Body includes:
(1) in definition unit any point (referred to as location point) displacement:, will be hardened according to hardened structure standard finite meta-model
Discrete structure domain is several quadrilateral units (according to actual needs), and the displacement of unit any point may be expressed as:
U (x, y)=Nue (1)
In formula, N=[N1N2N3N4], wherein Ni(i=1,2,3,4) is isoparametric elements shape function in finite element.
ue={ u1(x, y) u2(x, y) u3(x, y) u4(x, y) }T (2)
(2) Displacement of elemental node: u is solved according to radial point interpolation method (RPIM)i(x, y) (i=1,2,3,4), these sections
Point displacement function be it is unknown, can be obtained by radial point interpolation method,
ui(x, y)=Φiui, i=1,2,3,4, (3)
Φ in formulaiFor the RPIM shape function of cell node i, it is made up of the supporting domain of i point RPIM；uiFor unit section
The displacement parameter vector of the supporting domain point of point i；M indicates the number of the supporting domain point of cell node i.
(3) it solves FE-RPIM form function matrix: formula (3) substitution formula (1) is write as:
Wherein FE-RPIM form function matrix Ψ is write as:
Matrix Φ in formula4×MBy Φi(i=1,2,3,4) is obtained, and columns M is equal to the number of nodes in unit supports domain.Φ4×M's
Preceding four column respectively correspond four nodes of quadrilateral units；Remaining column corresponds to the node in other supporting domains of unit.
(4) it FE-RPIM shape function derivation: when solving plate structure problem with the Galerkin method of standard, needs to solve shape
The derivative of function is needed thus by formula (7) to x, y derivation can obtain with calculating the stiffness matrix of FE-RPIM
(5) parameter of definition structure problem: if E is elasticity modulus, v is Bai Song ratio, and t is element thickness, and ρ is that material is close
Degree, tsFor hardened structure surface load, bsFor body force, ü indicates that acceleration, κ are bending strain, and γ is shear strain etc., DbFor plate
The bending stiffness constitutive matrix of structure, DSFor transverse shear stiffness constitutive matrix, θxFor around the corner of x-axis, θyFor turning around y-axis
Angle, w are amount of deflection；
(6) FE-RPIM mould plate dynamics equations solve: according to above-mentioned parameter, to dynamics equations
Galerkin weak form carries out discrete
In formula, Ω is studied a question structural domain.
Kinetics equation after plate structural separation is
Ku-Z ü=Ff+Fb (12)
K=K in formulab+KsFor plate unit stiffness matrix；KbFor bending stiffness matrix, KSFor shearing rigidity matrix, Z is plate list
First mass matrix, FfFor surface load array, FbFor body force array.
Stiffness matrix K is represented by
K=Kb+Ks=∫Ω(Bb)TDbBbdΩ+∫Ω(Bs)TDsBsdΩ (13)
Mass matrix Z is represented by
The loading of plate unit is
Fb=∫ΩJTbsdΩ (16)
After the completion of the FE-RPIM model foundation of plate structural domain, method enters step S104.In step S104, sound is established
The BEM model of field domain.It specifically includes:
(1) Helmholtz wave equation is established: structural vibration caused small amplitude simple harmonic quantity sound in ideal fluid media (medium)
Wave, acoustic pressure meet Helmholtz wave equation
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 are as follows
Formula:
In formulaThe outer normal vector in n table sound field domain, ρ in formulafFor fluid density；υnIndicate interface normal velocity.
(3) boundary integral equation is established: the elementary solution free space Green's function obtained using weighted residual method:
R=in formula | Q-P |, Q is arbitrary point on body structure surface, and P is arbitrary point in space.
According to the second green theorem, by the Integral Transformation to volume at Line Integral, acoustic boundary is derived according to formula (17)
Integral equation:
Γ is the boundary in sound field domain in formula, and C (Q) is constant, can be obtained by Q point position, the calculation formula of C (Q):
Wherein ΩfFor fluid domain (sound field domain), according to coupled boundary condition formula (19), the method for acoustic pressure and speed in sound field
To derivative, formula (21) can be write as:
Wherein p (Q), υnIt can be obtained by sound field domain unit shape function, same to formula (1) is consistent.It can be write as:
P in formulaj、vnjIndicate the sound pressure level and normal velocity of cell node j, m is the number of nodes on each face, NjIt is
Unit shape function.
(4) discretization of boundary integral equation: while considering sound field boundary demarcation to be a node of M ', a quadrangle list of N '
The grid model of member composition, Q point select all nodes on sound field field surface, the formula (24) obtained are updated to formula
(23), it is obtained by boundary integral equation is discrete:
S is sound field field surface, C in above formulaiFor constant, can be obtained by formula (22) according to the position i, δijIndicate δ letter
Number, i.e.,It your property can be obtained by Kronecker, last time is write as matrix form are as follows:
[H] [P]=i ρ ω [G] [vn] (26)
In formula
After the completion of the BEM model foundation in sound field domain, method enters step S106.In step s 106, structure-sound field is established
The FE-RPIM/BEM model of coupling.It specifically includes:
(1) coupled boundary condition: for structure-sound field coupled system, ΩsRepresentative structure domain using FE-RPIM model,
ΩfFluid (sound field) domain is represented using BEM model.nfIt is coupled interface sound field normal vector.At coupled interface, structural unit is wanted
Meet matching sound field unit condition.Coupled system should meet displacement and the pressure condition of continuity, introduce interface normal vector n=nf
=-ns, being displaced the condition of continuity and the pressure condition of continuity may be expressed as:
usns=ufnf σs|n=-p (29)
Wherein nfFor the sound field normal vector on coupled interface；nsFor the hardened 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 by formula (16)
At:
In formula, NsFor the shape function of structural domain discrete unit, NfIt is the shape function of sound field discrete unit.
Introduce coupling matrix:
Bonding force can be write as:
Fa=LPa (32)
PaIndicate the node acoustic pressure vector of coupling boundary.
(3) foundation of coupled wave equation: consider under sound field reflecting, structural system kinetics equation is obtained by formula (12):
(K-ω2M)u-Lpa=F (33)
For sound field domain, because boundary condition has coupling boundary a and non-coupled boundary b, boundary element equation is write as:
H11、H12、H21、H22For the matrix in block form of matrix H, G11、G12、G21、G22For the matrix in block form of matrix G, pbIt is non-coupled
The node acoustic pressure vector on boundary
By the FE-RPIM model of structural domain and the BEM model of sound field, the FE-RPIM/ of coupled structure-acoustic systems can be obtained
BEM model are as follows:
Formula (35) is solved, can obtain coupled structure-acoustic system analysis as a result, i.e. displacement structure and sound field sound
Pressure.
Fig. 2 shows hardened structure according to an embodiment of the invention-sound field coupling analysis device structure chart, the devices
It resides in and calculates in equipment.Referring to Fig. 2, which includes that domain model establishes unit 10, sound field domain model establishes unit 20
Unit 30 is established with coupling model.
Domain model establishes unit 10 and is suitable for combining FInite Element and radial point interpolation method, to the system dynamic of hardened structure
It is discrete to learn equation progress.Detailed process are as follows: the first displacement equation of location point in unit is established according to FInite Element；According to radial direction
Point interpolation method establishes the second displacement equation of unit interior nodes；According to the first displacement equation and second displacement equation, obtain limited
The form function matrix of first method-radial point interpolation method, and to form function matrix derivation；Define the parameter of hardened structure；According to the ginseng
The derivation of number, form function matrix and form function matrix is as a result, determine that plate unit stiffness matrix, plate unit mass matrix, surface carry
Lotus array and body force array；It is arranged according to plate unit stiffness matrix, plate unit mass matrix, surface load array and body force
Battle array carries out the system dynamics equation of hardened structure discrete.
Sound field domain model establishes the boundary integral equation that unit 20 is suitable for constructing sound field domain according to boundary element method.Detailed process
Are as follows: the Helmholtz for establishing sound field domain fluctuates equation；Establish sound field boundary condition；Equation and perimeter strip are fluctuated according to Helmholtz
Part establishes boundary integral equation.
Coupling model is established unit 30 and is suitable for according to system dynamics equation, boundary integral equation and the structure-after discrete
The coupled boundary condition of sound field, structural texture-sound field coupled wave equation.Detailed process are as follows: establish structure-sound field coupling boundary item
Part；According to coupled boundary condition, bonding force is determined；According to bonding force, to the system dynamics equation and boundary integral after discrete
Equation carries out simultaneous, obtains coupled structure-acoustic system equation.
It should be noted that domain model establishes unit 10, sound field domain model establishes unit 20 and coupling model is established
The processing executed in unit 30 is similar with the processing of step S102~S106, and detail is referred to above-mentioned steps.
Fig. 3 is to be arranged as realizing hardened structure according to the present invention-sound field coupling analysis device Example Computing Device 900
Block diagram.In basic configuration 902, calculates equipment 900 and typically comprise system storage 906 and one or more processor
904.Memory bus 908 can be used for the communication between processor 904 and system storage 906.
Depending on desired configuration, processor 904 can be any kind of processing, including but not limited to: microprocessor
(μ P), microcontroller (μ C), digital information processor (DSP) or any combination of them.Processor 904 may include such as
The cache of one or more rank of on-chip cache 910 and second level cache 912 etc, processor core
914 and register 916.Exemplary processor core 914 may include arithmetic and logical unit (ALU), floating-point unit (FPU),
Digital signal processing core (DSP core) or any combination of them.Exemplary Memory Controller 918 can be with processor
904 are used together, or in some implementations, and Memory Controller 918 can be an interior section of processor 904.
Depending on desired configuration, system storage 906 can be any type of memory, including but not limited to: easily
The property lost memory (RAM), nonvolatile memory (ROM, flash memory etc.) or any combination of them.System storage
Device 906 may include operating system 920, one or more is using 922 and program data 924.Using 922 may include by
It is arranged for carrying out the hardened structure of hardened structure-sound field coupling analytical method-sound field coupling analysis device 926.Program data 924 can be with
Including can be used for various algorithm models 928 as described here.In some embodiments, application 922 may be arranged to grasping
Make to be operated in system using program data 924.
Calculating equipment 900 can also include facilitating from various interface equipments (for example, output equipment 942, Peripheral Interface
944 and communication equipment 946) to basic configuration 902 via the communication of bus/interface controller 930 interface bus 940.Example
Output equipment 942 include graphics processing unit 948 and audio treatment unit 950.They can be configured as facilitate via
One or more port A/V 952 is communicated with the various external equipments of such as display or loudspeaker etc.Outside example
If interface 944 may include serial interface controller 954 and parallel interface controller 956, they, which can be configured as, facilitates
Via one or more port I/O 958 and such as input equipment (for example, keyboard, mouse, pen, voice-input device, touch
Input equipment) or the external equipment of other peripheral hardwares (such as printer, scanner etc.) etc communicated.Exemplary communication is set
Standby 946 may include network controller 960, can be arranged to convenient for via one or more communication port 964 and one
A or multiple other calculate communication of the equipment 962 by network communication link.
Network communication link can be an example of communication media.Communication media can be usually presented as in such as carrier wave
Or computer readable instructions, data structure, program module in the modulated data signal of other transmission mechanisms etc, and can
To include any information delivery media." modulated data signal " can such signal, one in its data set or more
It is a or it change can the mode of encoded information in the signal carry out.As unrestricted example, communication media can be with
Wired medium including such as cable network or private line network etc, and it is such as sound, radio frequency (RF), microwave, infrared
(IR) the various wireless mediums or including other wireless mediums.Term computer-readable medium used herein may include depositing
Both storage media and communication media.
Calculating equipment 900 can be implemented as a part of portable (or mobile) electronic equipment of small size, these electronics are set
The standby such as cellular phone, personal digital assistant (PDA), personal media player device, wireless network browsing apparatus, a of can be
People's helmet, application specific equipment or may include any of the above function mixing apparatus.Calculating equipment 900 can be with
Be embodied as include desktop computer and notebook computer configuration personal computer.
Algorithm and display are not inherently related to any particular computer, virtual system, or other device provided herein.
Various general-purpose systems can also be used together with teachings based herein.As described above, it constructs required by this kind of system
Structure be obvious.In addition, the present invention is also not directed to any particular programming language.It should be understood that can use various
Programming language realizes summary of the invention described herein, and the description done above to language-specific is to disclose this hair
Bright preferred forms.
In the instructions provided here, numerous specific details are set forth.It is to be appreciated, however, that implementation of the invention
Example can be practiced without these specific details.In some instances, well known method, structure is not been shown in detail
And technology, so as not to obscure the understanding of this specification.
Similarly, it should be understood that in order to simplify the disclosure and help to understand one or more of the various inventive aspects,
Above in the description of exemplary embodiment of the present invention, each feature of the invention is grouped together into single implementation sometimes
In example, figure or descriptions thereof.However, the disclosed method should not be interpreted as reflecting the following intention: i.e. required to protect
Shield the present invention claims features more more than feature expressly recited in each claim.More precisely, as following
Claims reflect as, inventive aspect is all features less than single embodiment disclosed above.Therefore,
Thus the claims for following specific embodiment are expressly incorporated in the specific embodiment, wherein each claim itself
All as a separate embodiment of the present invention.
Those skilled in the art will understand that can be carried out adaptively to the module in the equipment in embodiment
Change and they are arranged in one or more devices different from this embodiment.It can be the module or list in embodiment
Member or component are combined into a module or unit or component, and furthermore they can be divided into multiple submodule or subelement or
Sub-component.Other than such feature and/or at least some of process or unit exclude each other, it can use any
Combination is to all features disclosed in this specification (including adjoint claim, abstract and attached drawing) and so disclosed
All process or units of what method or apparatus are combined.Unless expressly stated otherwise, this specification is (including adjoint power
Benefit require, abstract and attached drawing) disclosed in each feature can carry out generation with an alternative feature that provides the same, equivalent, or similar purpose
It replaces.
Various component embodiments of the invention can be implemented in hardware, or to run on one or more processors
Software module realize, or be implemented in a combination thereof.It will be understood by those of skill in the art that can be used in practice
Microprocessor or digital signal processor (DSP) come realize some in document protection equipment according to an embodiment of the present invention or
The some or all functions of person's whole component.The present invention is also implemented as one for executing method as described herein
Point or whole device or device programs (for example, computer program and computer program product).Such this hair of realization
Bright program can store on a computer-readable medium, or may be in the form of one or more signals.It is such
Signal can be downloaded from an internet website to obtain, and is perhaps provided on the carrier signal or is provided in any other form.
It should be noted that the above-mentioned embodiments illustrate rather than limit the invention, and ability
Field technique personnel can be designed alternative embodiment without departing from the scope of the appended claims.In the claims,
Any reference symbol between parentheses should not be configured to limitations on claims.Word "comprising" does not exclude the presence of not
Element or step listed in the claims.Word "a" or "an" located in front of the element does not exclude the presence of multiple such
Element.The present invention can be by means of including the hardware of several different elements and being come by means of properly programmed computer real
It is existing.In the unit claims listing several devices, several in these devices can be through the same hardware branch
To embody.The use of word first, second, and third does not indicate any sequence.These words can be explained and be run after fame
Claim.
Claims (1)
1. a kind of hardened structure-sound field coupling analytical method suitable for running in calculating equipment, and includes the following steps:
Step S102 establishes the FE-RPIM model of plate structural domain, comprising:
The displacement of any point in definition unit: according to hardened structure standard finite meta-model, by plate structural domain it is discrete for several four
Side shape unit is expressed as the displacement of unit any point:
U (x, y)=Nue (1)
In formula, N=[N1 N2 N3 N4], wherein Ni, i=1,2,3,4 be isoparametric elements shape function in finite element；
ue={ u1(x, y) u2(x, y) u3(x, y) u4(x, y) }T (2)
Displacement of elemental node: u is solved according to RPIMi(x, y), i=1,2,3,4, modal displacement function is obtained by radial point interpolation method
It arrives,
ui(x, y)=Φiui, i=1,2,3,4, (3)
Φ in formulaiFor the RPIM shape function of cell node i, it is made up of the supporting domain of i point RPIM；uiFor cell node i's
The displacement parameter vector of supporting domain point；M indicates the number of nodes of the supporting domain of cell node i；
It solves FE-RPIM form function matrix: formula (3) substitution formula (1) is write as:
Wherein FE-RPIM form function matrix Ψ is write as:
Matrix Φ in formula4×MBy Φi, i=1,2,3,4 obtain, and columns M is equal to the number of nodes in unit supports domain, Φ4×MIt is preceding four column
Respectively correspond four nodes of quadrilateral units；Remaining column corresponds to the node in other supporting domains of unit；
FE-RPIM shape function derivation: by formula (7) to x, y derivation can be obtained
The parameter of definition structure problem: E is elasticity modulus, and v is Bai Song ratio, and t is element thickness, and ρ is density of material, tsIt is hardened
Structure surface load, bsFor body force, ü indicates acceleration, and κ is bending strain, and γ is shear strain, DbBending for hardened structure is rigid
Spend constitutive matrix, DsFor transverse shear stiffness constitutive matrix, θxFor around the corner of x-axis, θyFor around the corner of y-axis, w is amount of deflection；
FE-RPIM mould plate dynamics equations solve: weak to the Galerkin of dynamics equations according to above-mentioned parameter
Form carries out discrete
In formula, Ω is studied a question structural domain；
Kinetics equation after plate structural separation is
K=K in formulab+KsFor plate unit stiffness matrix；KbFor bending stiffness matrix, KsFor shearing rigidity matrix, Z is plate unit matter
Moment matrix, FfFor surface load array, FbFor body force array；
Stiffness matrix K is expressed as
K=Kb+Ks=∫Ω(Bb)TDbBbdΩ+∫Ω(Bs)TDsBsdΩ (13)
Mass matrix Z is expressed as
The loading of plate unit is
Fb=∫ΩJTbsdΩ (16)
Step S104 establishes the BEM model in sound field domain, comprising:
Helmholtz wave equation is established: structural vibration caused small amplitude simple harmonic quantity sound wave, acoustic pressure in ideal fluid media (medium) is full
Sufficient Helmholtz wave equation
In formula, k is wave number, k=ω/c；ω is circular frequency, and c is the velocity of sound；P is acoustic pressure；
Sound field boundary condition: on boundary condition, consider rigid boundary condition and Riemann's boundary condition, following formula:
In formulaThe outer normal vector in n table sound field domain, ρ in formulafFor fluid density；υnIndicate interface normal velocity；
Boundary integral equation is established: the elementary solution free space Green's function obtained using weighted residual method:
R=in formula | Q-P |, Q is arbitrary point on body structure surface, and P is arbitrary point in space；
According to the second green theorem, by the Integral Transformation to volume at Line Integral, derive that acoustic boundary integrates according to formula (17)
Equation:
Γ is the boundary in sound field domain in formula, and C (Q) is constant, can be obtained by Q point position, the calculation formula of C (Q):
Wherein ΩfFor sound field domain, according to coupled boundary condition formula (19), the normal derivative of acoustic pressure and speed, formula in sound field
(21) it can be write as:
Wherein p (Q), υnIt is obtained by sound field domain unit shape function, same to formula (1) unanimously, is write as:
P in formulaj、vnjIndicate the sound pressure level and normal velocity of cell node j, m is the number of nodes on each face, NjIt is unit
Shape function；
The discretization of boundary integral equation: consider that by sound field boundary demarcation be a node of M ', the net of a quadrilateral units composition of N '
Lattice model, Q point select all nodes on sound field field surface, the formula (24) obtained are updated to formula (23), by boundary
Integral equation is discrete to be obtained:
S is sound field field surface, C in above formulaiFor constant, obtained according to the position i by formula (22), δijIndicate δ function, i.e.,By Kronecker, your property is obtained, and is write as matrix form are as follows:
[H] [P]=i ρ ω [G] [vn] (26)
In formula
Step S106 establishes the FE-RPIM/BEM model of coupled structure-acoustic system, comprising:
Coupled boundary condition: for structure-sound field coupled system, ΩsRepresentative structure domain uses FE-RPIM model, ΩfIt represents
Sound field domain uses BEM model；nfIt is coupled interface sound field normal vector, at coupled interface, structural unit will meet matching sound field
Unit condition, coupled system should meet displacement and the pressure condition of continuity, introduce interface normal vector n=nf=-ns, displacement is continuously
Condition and the pressure condition of continuity indicate are as follows:
usns=ufnf σs|n=-p (29)
Wherein nfFor the sound field normal vector on coupled interface；nsFor the hardened structure normal vector on coupled interface；
The derivation of bonding force: sound field acoustic pressure acts on the load on vibro-acoustical couple system face, is write as by formula (16):
In formula, NsFor the shape function of structural domain discrete unit, NfIt is the shape function of sound field discrete unit；
Introduce coupling matrix:
Bonding force is write as:
Fa=LPa (32)
PaIndicate the node acoustic pressure vector of coupling boundary；
The foundation of coupled wave equation: consider under sound field reflecting, structural system kinetics equation is obtained by formula (12):
(K-ω2M)u-Lpa=F (33)
For sound field domain, because boundary condition has coupling boundary a and non-coupled boundary b, boundary element equation is write as:
H11、H12、H21、H22For the matrix in block form of matrix H, G11、G12、G21、G22For the matrix in block form of matrix G, pbNon-coupled boundary
Node acoustic pressure vector；
By the FE-RPIM model of structural domain and the BEM model of sound field, the FE-RPIM/BEM mould of coupled structure-acoustic systems can be obtained
Type are as follows:
Formula (35) is solved, obtain coupled structure-acoustic system analysis as a result, i.e. displacement structure and sound field acoustic pressure.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201510299576.7A CN104951596B (en) | 2015-06-03 | 2015-06-03 | A kind of hardened structure-sound field coupling analytical method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201510299576.7A CN104951596B (en) | 2015-06-03 | 2015-06-03 | A kind of hardened structure-sound field coupling analytical method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN104951596A CN104951596A (en) | 2015-09-30 |
| CN104951596B true CN104951596B (en) | 2019-08-02 |
Family
ID=54166253
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201510299576.7A Active CN104951596B (en) | 2015-06-03 | 2015-06-03 | A kind of hardened structure-sound field coupling analytical method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN104951596B (en) |
Families Citing this family (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105760585A (en) * | 2016-02-03 | 2016-07-13 | 北京航空航天大学 | Quick fuzzy sound pressure solving method based on high-order perturbation theory |
| CN112632818B (en) * | 2020-12-17 | 2023-03-14 | 重庆交通大学 | High-order gradient smooth meshless method, system, medium and computer device |
| CN112541294B (en) * | 2020-12-25 | 2023-03-28 | 华东交通大学 | Method for predicting noise in vehicle |
| CN114970224A (en) * | 2021-02-25 | 2022-08-30 | 湖南大学 | Structural sound field coupling analysis method based on GPU parallel computation |
Family Cites Families (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6090147A (en) * | 1997-12-05 | 2000-07-18 | Vibro-Acoustics Sciences, Inc. | Computer program media, method and system for vibration and acoustic analysis of complex structural-acoustic systems |
| US8306793B2 (en) * | 2010-06-04 | 2012-11-06 | Livermore Software Technology Corporation | Systems and methods of performing vibro-acoustic analysis of a structure |
| US10296683B2 (en) * | 2013-11-06 | 2019-05-21 | Thornton Tomasetti, Inc. | Computer implemented apparatus and method for finite element modeling using hybrid absorbing element |
| CN103559366A (en) * | 2013-11-18 | 2014-02-05 | 中国汽车工程研究院股份有限公司 | Forecasting method for vehicle body structure-acoustic coupling based on smoothed finite element boundary element method |
-
2015
- 2015-06-03 CN CN201510299576.7A patent/CN104951596B/en active Active
Non-Patent Citations (2)
| Title |
|---|
| 基于分区光滑与无网格法的声学数值方法研究;姚凌云;《中国博士学位论文全文数据库 工程科技Ⅱ辑》;20130515(第05期);第C028-10页正文第3章第3.1-3.5节，第6章第6.1-6.3节，第109页倒数第2段，图3.2 |
| 板结构-声场耦合分析的FE-LSPIM/FE-LSPIM法;陈宁等;《振动与冲击》;20140815;第33卷(第15期);第131-137页 |
Also Published As
| Publication number | Publication date |
|---|---|
| CN104951596A (en) | 2015-09-30 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN104951596B (en) | A kind of hardened structure-sound field coupling analytical method | |
| Bendsøe | Optimization of structural topology, shape, and material | |
| US8306793B2 (en) | Systems and methods of performing vibro-acoustic analysis of a structure | |
| Brunner et al. | A comparison of FE–BE coupling schemes for large‐scale problems with fluid–structure interaction | |
| Seçgin et al. | Free vibration analysis of symmetrically laminated thin composite plates by using discrete singular convolution (DSC) approach: algorithm and verification | |
| CN102262689B (en) | Hybrid element enabling finite element/smoothed particle hydrodynamics coupling | |
| Tanaka et al. | Fracture mechanics analysis using the wavelet Galerkin method and extended finite element method | |
| Favre et al. | A continuous crystallographic approach to generate cubic lattices and its effect on relative stiffness of architectured materials | |
| Xie et al. | A variational formulation for vibro-acoustic analysis of a panel backed by an irregularly-bounded cavity | |
| CN105808206B (en) | The method and its system of multiplying are realized based on RAM | |
| Jonckheere et al. | A direct hybrid Finite Element–Wave Based Method for the steady-state analysis of acoustic cavities with poro-elastic damping layers using the coupled Helmholtz–Biot equations | |
| Puri et al. | Reduced order fully coupled structural–acoustic analysis via implicit moment matching | |
| CN104850721A (en) | External sound field prediction method and device based on mixing probability and interval | |
| Rodríguez-Tembleque et al. | Partitioned solution strategies for coupled BEM–FEM acoustic fluid–structure interaction problems | |
| Baaiu et al. | Structure-preserving infinite dimensional model reduction: Application to adsorption processes | |
| Court et al. | A fictitious domain approach for the Stokes problem based on the extended finite element method | |
| Vejchodský et al. | Modular hp-FEM system HERMES and its application to Maxwell’s equations | |
| Park et al. | Transverse vibration and waves in a membrane: frequency domain spectral element modeling and analysis | |
| Ibrahimbegović et al. | Shape optimization of two‐phase inelastic material with microstructure | |
| Alia et al. | CMRH method as iterative solver for boundary element acoustic systems | |
| IT202000009358A1 (en) | CORRESPONDING CIRCUIT, DEVICE, SYSTEM AND PROCEDURE | |
| Bergamasco et al. | Direct numerical simulation of complex viscoelastic flows via fast lattice-Boltzmann solution of the Fokker–Planck equation | |
| Pfeifle | Real-time signal processing on field programmable gate array hardware | |
| Attallah et al. | Three-dimensional state space spline finite strip analysis of angle-plied laminates | |
| IT202000009364A1 (en) | PROCEDURE FOR ACCESSING A MEMORY AND CORRESPONDING CIRCUIT |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |