CN108491595B - Gu a kind of high frequency partial of sound-coupled structure responds predicting method - Google Patents
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Abstract
Gu the present invention provides a kind of high frequency partials of sound-coupled structure to respond predicting method, combine FInite Element, Gu mode power flow equilibrium equation and local energy indication are theoretical predictive of the response of sound-coupled structure high frequency partial, structure subsystem is obtained in the displacement modes vibration shape of coupling edge using FInite Element, stress Mode Shape of the operatic tunes subsystem in coupling edge, the intrinsic frequency and modal mass of subsystem, pass through the modal coupling fissipation factor between computing subsystem, it resettles the mode power flow equilibrium equation between subsystem and solves, obtain the mode energy of structure subsystem.Finally indicate that the theoretical structure subsystem local energy that solves responds using local energy, local stress/strain-responsive is solved by isotropic material strain energy and the relationship of ess-strain.Gu this method can accurately indication sound-coupled structure high frequency partial respond, solve the problems, such as that the discretization methods computational efficiency such as conventional finite element method and boundary element method is low, SEA method every assumes to be frequently not to fully meet and be difficult to obtain the local energy of subsystem in engineer application.
Description
Technical field
The present invention relates to a kind of dynamic response analytic approach of high frequency, and in particular to Gu a kind of sound-coupling response method.
Background technique
Gu sound-coupled problem is widely present in aerospace structure, especially for the thin-wall construction under high frequency pumping,
Gu easily generation sound-coupling effect between structure and sound field, causes the vibration of structure and changes the distribution of sound field, and then influences knot
The safety of structure and the functionality of instrument and equipment.Therefore, the level of vibration of structure and the noise level of sound field are structure design ranks
The important indicator that section must be taken into consideration, Gu sound-coupled problem of the research thin-wall construction under high frequency pumping has highly important answer
With value.
Currently, Gu acquisition sound-coupling response method mainly has test method, theoretical method and numerical method.Test side
The real result of method is credible, disadvantage is that expend huge, test period it is longer and be only able to achieve limited experimentation condition and
Operating condition.Theoretical analysis method is more difficult to be suitable for Complex engineering structure.Numerical method is a kind of effective analysis means, for low frequency
Gu sound-coupled problem usually indicates structural response using discretization methods such as FInite Element and boundary element methods.But when analysis frequency
When raising, to guarantee that FEM there are enough precision, unit must be refined, this will lead to calculation scale and exponentially increases.
Gu for high frequency sound-coupled problem, existing high frequency dynamic response analysis method includes statistic energy analysis method, statistics
Energy Analysis for High can indicate subsystem average energy response in space and analysis frequency band.But SEA method is each
Item is assumed to be frequently not to fully meet, and it lays particular emphasis on the space average energy of subsystem in engineer application, it is difficult to obtain
The local energy of subsystem.
Summary of the invention
Goal of the invention: Gu in view of the above-mentioned deficiencies in the prior art, it is an object of the present invention to provide a kind of height of sound-coupled structure
Frequency local acknowledgement predicting method, solve the discretization methods computational efficiency such as conventional finite element method and boundary element method it is low, statistics energy
The every of analysis method assumes to be frequently not to fully meet and be difficult to obtain the local energy of subsystem to ask in engineer application
Topic.
Technical solution: Gu the present invention provides a kind of high frequency partials of sound-coupled structure to respond predicting method, including following
Step:
(1) Gu decoupling sound-coupled structure for structure subsystem harmony cavity subsystem, the finite element of subsystem is established respectively
Model, and model analysis is carried out to non-coupled subsystem, the modal data of structure harmony cavity subsystem is extracted respectively, utilizes structure
Modal coupling fissipation factor between the modal data computing subsystem of harmony cavity subsystem；
(2) the mode power flow equilibrium equation in all mode is established, and then obtains the mode of structure harmony cavity subsystem
Energy；
(3) non-coupled subsystem modal characteristics value and subsystem mode energy, modal stiffness are established, between modal mass
Relationship；
(4) the theoretical local energy response for solving structure harmony cavity subsystem is indicated based on local energy, is answered by structure
Local stress/strain-responsive can be solved with the relationship of stress/strain by becoming.
Further, the modal data of step (1) the structure harmony cavity subsystem includes structure subsystem in coupling edge
The displacement modes vibration shape, operatic tunes subsystem the stress Mode Shape and the intrinsic frequency of subsystem of coupling edge, modal mass,
Modal stiffness, and determine resonance mode number of the subsystem in research frequency band.
Further, the modal coupling fissipation factor between (1) two rank mode of step by the mode after subsystem decoupled come
It obtains, expression formula are as follows:
In formula,With The respectively intrinsic frequency of 1 subsystem p rank mode, damping damage
Consume the factor, mode modal stiffness；The respectively intrinsic frequency of 2 subsystem q rank mode, damping loss factor, mould
State quality；For subsystem 1 the p rank displacement modes vibration shape and subsystem 2 q rank stress Mode Shape interaction function,
Its calculation expression are as follows:
In formula,For the q rank displacement modes vibration shape of subsystem 2；For the p rank stress Mode Shape of subsystem 1；For son
Unit normal vector of the system 1 in coupling surface；Coupling surface region of the S between subsystem.
Further, step (2) each subsystem is described in excitation frequency band by a series of resonance modes, due to subsystem 1
Mode and subsystem 2 modal coupling, therefore, power flow between subsystem can by each mode of subsystem 1 with
Power stream calculation between the mode of each mode of subsystem 2；Write the power flow equilibrium equation in all mode as matrix form,
That is:
In formula, E1、E2Mode vibrational energy vector respectively in two subsystems, For 1 subsystem p rank mode energy；For 2 subsystem q rank mode energies；N1And N2Respectively
Refer to mode number of the subsystem 1 and 2 in frequency band；P1, inj、P2, injBe respectively in subsystem 1 and 2 in mode load input power to
Amount, It is p rank and q rank respectively
The input power of mode；When being motivated in frequency band Δ ω by single-point power, the input power calculating formula of structure are as follows:
In formula,It indicates after applying excitation at point Q, the Mode Shape of p rank mode at excitation point；Δ ω indicates to swash
Encourage the frequency band (research frequency band) of power；For the modal mass of 1 subsystem p rank mode；
A11And A22For diagonal matrix, diagonal element is respectively as follows:
In formula,It is the damping factor of 1 subsystem p rank and 2 subsystem q rank mode respectively；Indicate subsystem 1
Modal coupling fissipation factor between p rank mode and the q rank mode of subsystem 2,
A12For N1×N2Rank matrix, A21For N2×N1The element of rank matrix, two matrixes is respectively as follows:
Further, step (3) is if any point of known subsystem i is displaced U, the mean kinetic energy and potential energy table of subsystem
Up to formula are as follows:
In formula, ω indicates the intrinsic frequency of subsystem, and M indicates that the mass matrix of non-coupled subsystem, K indicate non-coupled son
The stiffness matrix of system, H indicate that, to matrix U progress conjugate transposition, displacement U can be indicated are as follows:
In formula, an(ω) indicates the modal characteristics value of non-coupled subsystem, ΦnIndicate the Mode Shape of non-coupled subsystem,
N is the rank number of mode in research frequency band；The kinetic energy and potential energy of subsystem i n-th order mode can be obtained in conjunction with above formula, it may be assumed that
In formula, MnIndicate the modal mass of the entire subsystem of n-th order mode, KnIndicate the mould of the entire subsystem of n-th order mode
State rigidity；
Assuming that the mean kinetic energy of integral subsystem and potential energy are equal, then subsystem i n-th order mode in frequency band Δ ω
Gross energy are as follows:
In formula,It indicates the gross energy in frequency band Δ ω intra subsystem i n-th order mode, passes through solution procedure (2)
Middle power flow equilibrium equation obtains the gross energy of subsystem i n-th order mode,Characterize mode energy in frequency band Δ ω
Relationship between modal mass,Characterize the relationship in frequency band Δ ω between mode energy and modal stiffness, an(ω)
Indicate the modal characteristics value of non-coupled subsystem.
Further, step (4) considers to calculate Energy distribution, the kinetic energy T of subsystem i midpoint Qi(Q, ω) and potential energy Vi(Q,
ω) are as follows:
In formula,Respectively indicate kinetic energy between i subsystem n-th order mode and pth rank mode and
Potential energy, calculation expression are as follows:
In formula, an(ω)、ap(ω) indicates the modal characteristics value of non-coupled subsystem, and * indicates adjoint matrix；Φn(Q) and
Φp(Q) Mode Shape of n rank and p rank at subsystem Q point, M are respectively indicatedQAnd KQRespectively indicate at Q point architecture quality matrix and
Stiffness matrix；Using third-octave Partition Analysis frequency band, if analysis frequency belongs to high band, in analysis frequency band Δ ω, suddenly
Energy between slightly same subsystem different modalities, that is, ignoreWithInfluence, therefore, research frequency band Δ
The Energy distribution of ω intra subsystem can be with approximate representation are as follows:
In formula,Modal kinetic energy and model potential energy respectively at subsystem Q point, by non-coupling
Zygote system mode vibration shape ΦnWith modal characteristics value an(ω) is indicated are as follows:
Step (3) are calculatedIt must substitute into above formula, kinetic energy and potential energy distribution of the subsystem i in frequency band Δ ω,
That is:
Thin-slab structure when for pure bending, the distribution of strain stress (z) and stress σ (z) through-thickness in thin plate are as follows:
Wherein, z is the coordinate value of some through-thickness on plate, and h is gauge of sheet, εmFor maximum strain；
For the unit strain energy V of thin plate, acquired by straining with stress:
Wherein, S0For cellar area, E is the elasticity modulus of light sheet material；
Therefore, on thin plate each unit strain stressmWith stress σmIt can respectively indicate are as follows:
The utility model has the advantages that present invention incorporates FInite Element, mode power flow equilibrium equation and local energy indication theory are pre-
Gu having shown that sound-coupled structure high frequency partial responds, structure subsystem is obtained in the displacement modes of coupling edge using FInite Element
The vibration shape, operatic tunes subsystem pass through calculating subsystem in the stress Mode Shape, the intrinsic frequency of subsystem and modal mass of coupling edge
Modal coupling fissipation factor between system resettles the mode power flow equilibrium equation between subsystem and solves, and obtains structon
The mode energy of system.Finally indicate that the theoretical structure subsystem local energy that solves responds using local energy, by each to same
Property material strain can with the relationship of ess-strain solve local stress/strain-responsive.Gu this method being capable of accurately indication sound-coupling
Close structure high frequency partial response, solve the discretization methods computational efficiency such as conventional finite element method and boundary element method it is low, statistics
The every of Energy Analysis for High assumes to be frequently not to fully meet and be difficult to obtain the local energy of subsystem in engineer application
Problem.
Detailed description of the invention
Fig. 1 is the method for the present invention flow diagram；
Fig. 2 (a) (b) is embodiment bay section/operatic tunes coupled system schematic diagram；
Fig. 3 is the local energy response distribution of bay section and the operatic tunes；
Fig. 4 is local stress/strain-responsive distribution of bay section.
Specific embodiment
Technical solution of the present invention is described in detail below, but protection scope of the present invention is not limited to the implementation
Example.
As shown in Fig. 2, carrying out part using the bay section/operatic tunes coupled system for being widely used in aerospace vehicle as research object
The local energy of flowering structure is motivated to respond indication.The finite element model of bay section and the operatic tunes is as shown, bay section basal diameter, height
Degree, wall thickness are respectively 400mm, 1000mm, 4mm, material parameter are as follows: elasticity modulus is 2 × 1011Pa, density 7800kg/
m3, Poisson's ratio 0.3, structural damping 0.01；Operatic tunes basal diameter, height are respectively 400mm, 1000mm；Operatic tunes parameter are as follows:
Density is 1.2kg/m3, velocity of sound 340m/s, structural damping 0.01.
Gu a kind of high frequency partial of sound-coupled structure responds predicting method, as shown in Figure 1, concrete operations are as follows:
(1) Gu decoupling sound-coupled structure for structure subsystem harmony cavity subsystem, the finite element of subsystem is established respectively
Model, and model analysis is carried out to the finite element model of non-coupled subsystem, it is calculated using commercial finite element software and obtains structure
Harmony cavity subsystem is in the modal data for analyzing (1414Hz-1782Hz) in frequency band.Analyze bay section harmony chamber point in frequency band Δ ω
There are not 31 ranks and 51 rank Mode Shapes, modal data includes the displacement modes vibration shape of the structure subsystem in coupling edge, operatic tunes subsystem
It unites in the stress Mode Shape and the intrinsic frequency of two subsystems, modal mass, modal stiffness of coupling edge, and determines two
Resonance mode number of a subsystem in research frequency band.Between modal data computing subsystem using structure harmony cavity subsystem
Modal coupling fissipation factor:
In formula,With The respectively intrinsic frequency of operatic tunes subsystem p rank mode, resistance
Buddhist nun's fissipation factor, mode modal stiffness；The respectively intrinsic frequency of bay section subsystem q rank mode, damping loss
The factor, modal mass；For the p rank displacement modes vibration shape of operatic tunes subsystem and the q rank stress Mode Shape of bay section subsystem
The function of interaction, calculation expression are as follows:
In formula,For the q rank displacement modes vibration shape of bay section subsystem；It shakes for the p rank stress mode of operatic tunes subsystem
Type；For operatic tunes subsystem coupling surface unit normal vector；Coupling surface region of the S between subsystem.
By combining FInite Element, the coupling surface of bay section and the operatic tunes is separated into several rectangular elements, it is assumed that coupling surface
Displacement and stress linear change in unit, then the p rank displacement modes vibration shape of subsystem 1 and the vibration of the q rank stress mode of subsystem 2
The function of type interactionAre as follows:
In formula, a, b, c, d are respectively the acoustic pressure vibration shape size of the operatic tunes i-th of unit, four points on coupling surface；e,f,g,h
The displacement vibration shape size of corresponding four points of i-th of unit respectively on bay section coupling surface；Δ x, Δ y are respectively unit two
The length on side.
(2) the mode power flow equilibrium equation in all mode is established, and then obtains the mode of structure harmony cavity subsystem
Energy.Each subsystem is described in excitation frequency band by a series of resonance modes, due to mode and the subsystem 2 of subsystem 1
Modal coupling.Therefore, the power flow between subsystem can pass through each mode and each mode of subsystem 2 of subsystem 1
Power stream calculation between mode.Write the power flow equilibrium equation in all mode as matrix form, it may be assumed that
In formula, E1、E2Mode vibrational energy vector respectively in two subsystems, For operatic tunes subsystem p rank mode energy；For bay section subsystem q rank mode energy；N1With
N2Respectively refer to the mode number of the operatic tunes and bay section subsystem in frequency band；P1, inj、P2, injIt is mould in the operatic tunes and bay section subsystem respectively
Load input power vector in state, It is the input power of p rank and q rank mode respectively.Apply the excitation of single-point power, knot to one point Q of bay section in frequency band Δ ω
The input power calculating formula of structure are as follows:
In formula,It indicates after applying excitation at point Q, the Mode Shape of p rank mode at excitation point；Δ ω indicates to swash
Encourage the frequency band (research frequency band) of power；For the modal mass of 1 subsystem p rank mode.
A11And A22For diagonal matrix, diagonal element is respectively as follows:
In formula,It is the damping factor of 1 subsystem p rank and 2 subsystem q rank mode respectively；Indicate subsystem 1
Modal coupling fissipation factor between p rank mode and the q rank mode of subsystem 2,(difference between the two is smaller, is
Raising computational efficiency, it is considered that be identical)；
A12For N1×N2Rank matrix, A21For N2×N1The element of rank matrix, two matrixes is respectively as follows:
(3) non-coupled subsystem modal characteristics value and subsystem mode energy, modal stiffness are established, between modal mass
Relationship.
If any point of known subsystem i is displaced U, the mean kinetic energy and potential energy expression formula of subsystem are as follows:
In formula, ω indicates the intrinsic frequency of subsystem；M indicates the mass matrix of non-coupled subsystem；K indicates non-coupled son
The stiffness matrix of system；H indicates to carry out conjugate transposition to matrix U；Displacement U can be indicated are as follows:
In formula, an(ω) indicates the modal characteristics value of non-coupled subsystem；ΦnIndicate the Mode Shape of non-coupled subsystem；
N is the rank number of mode in research frequency band.The kinetic energy and potential energy of subsystem i n-th order mode can be obtained in conjunction with above formula, it may be assumed that
In formula, MnIndicate the modal mass of the entire subsystem of n-th order mode；KnIndicate the mould of the entire subsystem of n-th order mode
State rigidity.
Assuming that the mean kinetic energy of integral subsystem and potential energy are equal, then subsystem i n-th order mode in frequency band Δ ω
Gross energy are as follows:
In formula,It indicates the gross energy in frequency band Δ ω intra subsystem i n-th order mode, passes through solution procedure (2)
Middle power flow equilibrium equation obtains the gross energy of subsystem i n-th order mode,Characterize mode energy in frequency band Δ ω
Relationship between modal mass, an(ω) indicates the modal characteristics value of non-coupled subsystem.
(4) the theoretical local energy response for solving structure harmony cavity subsystem is indicated based on local energy, is answered by structure
Local stress/strain-responsive can be solved with the relationship of stress/strain by becoming.
Consider to calculate Energy distribution, the kinetic energy T of subsystem i midpoint Qi(Q, ω) and potential energy Vi(Q, ω) are as follows:
In formula,Respectively indicate kinetic energy between i subsystem n-th order mode and pth rank mode and
Potential energy, calculation expression are as follows:
In formula, an(ω)、ap(ω) indicates the modal characteristics value of non-coupled subsystem, and * indicates adjoint matrix；Φn(Q) and
Φp(Q) Mode Shape of n rank and p rank at subsystem Q point is respectively indicated.MQAnd KQRespectively indicate at Q point architecture quality matrix and
Stiffness matrix.It,, can in analysis frequency band Δ ω if analysis frequency belongs to high band using third-octave Partition Analysis frequency band
To ignore the energy between same subsystem different modalities, that is, ignoreWithInfluence.Therefore, in research frequency
Energy distribution with Δ ω intra subsystem can be with approximate representation are as follows:
In formula,Respectively by the modal kinetic energy and model potential energy of subsystem Q point, by non-coupling
Zygote system mode vibration shape ΦnWith modal characteristics value an(ω) is indicated are as follows:
Formula (13) are calculatedAbove formula, kinetic energy and potential energy of the subsystem i in frequency band Δ ω point must be substituted into
Cloth, it may be assumed that
Thin-slab structure when for pure bending, the distribution of strain stress (z) and stress σ (z) in thin plate along the direction thickness z are as follows:
Wherein, z is the coordinate value of some through-thickness on plate, and h is gauge of sheet, εmFor maximum strain.
For the unit strain energy V of thin plate, can be acquired by straining with stress:
Wherein, S0For cellar area, E is the elasticity modulus of light sheet material.
Therefore, on thin plate each unit strain stressmWith stress σmIt can respectively indicate are as follows:
In conjunction with finite element as a result, being responded by formula (22) and (23) Gu sound-coupled structure local energy can be obtained, as shown in Figure 3
The kinetic energy and potential energy distribution of (centre frequency 1600Hz) bay section and the operatic tunes in 1414Hz-1782Hz frequency range.Formula (23) are tied again
Fruit substitutes into formula (26) and (27) and is illustrated in figure 4 1414Hz- Gu sound-coupled structure local stress/strain-responsive can be obtained
Bay section stress/strain is distributed in 1782Hz frequency range.By the Comparative result with other methods, result coincide and meets indication essence
Degree requires.For above-described embodiment, the kinetic energy and potential energy of bay section harmony chamber in this method indication 1414Hz-1782Hz frequency range are utilized
Distribution needs time about 45min, and needs about 3h30min using traditional FInite Element；Indicate 1414Hz- using this method
The distribution of bay section stress/strain needs time about 50min in 1782Hz frequency range, and needs about 3h using FInite Element, shows we
Gu method can efficiently indication sound-coupled structure high frequency partial respond.
Claims (6)
1. Gu a kind of high frequency partial of sound-coupled structure responds predicting method, it is characterised in that: the following steps are included:
(1) Gu decoupling sound-coupled structure for structure subsystem harmony cavity subsystem, the finite element mould of subsystem is established respectively
Type, and carry out model analysis to non-coupled subsystem, extracts the modal data of structure harmony cavity subsystem respectively, using structure and
Modal coupling fissipation factor between the modal data computing subsystem of operatic tunes subsystem；
(2) the mode power flow equilibrium equation in all mode is established, and then obtains the mode energy of structure harmony cavity subsystem；
(3) non-coupled subsystem modal characteristics value and subsystem mode energy, modal stiffness, the pass between modal mass are established
System；
(4) the theoretical local energy response for solving structure harmony cavity subsystem is indicated based on local energy, passes through structural strain energy
Local stress/strain-responsive is solved with the relationship of stress/strain.
2. Gu the high frequency partial of sound-coupled structure according to claim 1 responds predicting method, it is characterised in that: step
(1) modal data of the structure harmony cavity subsystem includes that structure subsystem is sub in the displacement modes vibration shape of coupling edge, the operatic tunes
System coupling edge stress Mode Shape and the intrinsic frequency of subsystem, modal mass, modal stiffness, and determine subsystem
Resonance mode number in research frequency band.
3. Gu the high frequency partial of sound-coupled structure according to claim 1 responds predicting method, it is characterised in that: step
(1) the modal coupling fissipation factor between the p rank mode of subsystem 1 and the q rank mode of subsystem 2 passes through after subsystem decoupled
Mode obtains, expression formula are as follows:
In formula,With Respectively the intrinsic frequency of subsystem 1p rank mode, damping loss because
Son, modal stiffness；The respectively intrinsic frequency of subsystem 2q rank mode, damping loss factor, modal mass；For the function of the q rank stress Mode Shape interaction of the p rank displacement modes vibration shape and subsystem 2 of subsystem 1, computational chart
Up to formula are as follows:
In formula,For the q rank displacement modes vibration shape of subsystem 2；For the p rank stress Mode Shape of subsystem 1；For subsystem
1 coupling surface unit normal vector；Coupling surface region of the S between subsystem.
4. Gu the high frequency partial of sound-coupled structure according to claim 3 responds predicting method, it is characterised in that: step
(2) each subsystem is described in excitation frequency band by a series of resonance modes, due to the mode of subsystem 1 and the mould of subsystem 2
State coupling, therefore, the power flow between subsystem can pass through each mode of subsystem 1 and the mould of each mode of subsystem 2
Power stream calculation between state；Write the power flow equilibrium equation in all mode as matrix form, it may be assumed that
In formula, E1、E2Mode vibrational energy vector respectively in two subsystems, For subsystem 1p rank mode energy；For subsystem 2q rank mode energy；N1And N2Respectively
Refer to mode number of the subsystem 1 and 2 in frequency band；P1,inj、P2,injBe respectively in subsystem 1 and 2 in mode load input power to
Amount,Wherein,It is p respectively
The input power of rank and q rank mode；When studying in frequency band Δ ω by the excitation of single-point power, the input power calculating formula of structure
Are as follows:
In formula,It indicates after applying excitation at point Q, the Mode Shape of p rank mode at excitation point；Δ ω indicates exciting force
Frequency band, i.e., research frequency band；For the modal mass of subsystem 1p rank mode；
A11And A22For diagonal matrix, diagonal element is respectively as follows:
In formula,It is the damping loss factor of subsystem 1p rank and subsystem 2q rank mode respectively；Indicate the p of subsystem 1
Modal coupling fissipation factor between rank mode and the q rank mode of subsystem 2,
A12For N1×N2Rank matrix, A21For N2×N1The element of rank matrix, two matrixes is respectively as follows:
5. Gu the high frequency partial of sound-coupled structure according to claim 1 responds predicting method, it is characterised in that: step
(3) if any point of known subsystem i is displaced U, the mean kinetic energy of subsystemAverage potential energyExpression formula are as follows:
In formula, ω indicates the intrinsic frequency of subsystem, and M indicates that the mass matrix of non-coupled subsystem, K indicate non-coupled subsystem
Stiffness matrix, H indicate to matrix U carry out conjugate transposition, displacement U can indicate are as follows:
In formula, an(ω) indicates the modal characteristics value of non-coupled subsystem, ΦnIndicate the Mode Shape of non-coupled subsystem, n is
Rank number of mode in research frequency band；The kinetic energy of subsystem i n-th order mode can be obtained in conjunction with above formulaAnd potential energyThat is:
In formula, MnIndicate the modal mass of the entire subsystem of n-th order mode, KnIndicate that the mode of the entire subsystem of n-th order mode is rigid
Degree；
Assuming that the mean kinetic energy of integral subsystem and potential energy are equal, then subsystem i n-th order mode in research frequency band Δ ω
Gross energy are as follows:
In formula,It indicates to pass through solution procedure (2) in the gross energy of research frequency band Δ ω intra subsystem i n-th order mode
Middle power flow equilibrium equation obtains the gross energy of subsystem i n-th order mode,Mode in characterization research frequency band Δ ω
Relationship between energy and modal mass,Pass in characterization research frequency band Δ ω between mode energy and modal stiffness
System, an(ω) indicates the modal characteristics value of non-coupled subsystem.
6. Gu the high frequency partial of sound-coupled structure according to claim 5 responds predicting method, it is characterised in that: step
(4) consider to calculate Energy distribution, the kinetic energy T of subsystem i midpoint Qi(Q, ω) and potential energy Vi(Q, ω) are as follows:
In formula,The kinetic energy and potential energy between subsystem i n-th order mode and pth rank mode are respectively indicated,
Its calculation expression are as follows:
In formula, an(ω)、ap(ω) indicates the modal characteristics value of non-coupled subsystem, and * indicates adjoint matrix；Φn(Q) and Φp(Q)
Respectively indicate the Mode Shape of n rank and p rank at subsystem Q point, MQAnd KQRespectively indicate architecture quality matrix and rigidity square at Q point
Battle array；Using third-octave Research on partition frequency band, if analysis frequency belongs to high band, in research frequency band Δ ω, ignore same
Energy between subsystem different modalities, that is, ignoreWithInfluence, therefore, research frequency band Δ ω in son
The kinetic energy and potential energy distribution < T of system ii(Q,ω)>Δω< Vi(Q,ω)>ΔωIt can be with approximate representation are as follows:
In formula,Modal kinetic energy and model potential energy respectively at subsystem Q point, by non-coupled
Subsystem Mode Shape ΦnWith modal characteristics value an(ω) is indicated are as follows:
Step (3) is calculatedAbove formula is substituted into, kinetic energy and gesture of the subsystem i in research frequency band Δ ω are obtained
It can be distributed, it may be assumed that
Thin-slab structure when for pure bending, the distribution of strain stress (z) and stress σ (z) through-thickness in thin plate are as follows:
Wherein, z is the coordinate value of some through-thickness on plate, and h is gauge of sheet, εmFor through-thickness some on plate
Maximum strain；
For the unit strain energy V of thin plate, acquired by straining with stress:
Wherein, S0For cellar area, E is the elasticity modulus of light sheet material；
Therefore, on thin plate each unit strainAnd stressIt can respectively indicate are as follows:
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| Vibro-acoustic analysis under stationary and non-stationary random excitations with KLE/FEM/BEM;Yanbin Li 等;《Aerospace Science and Technology》;20170310;第66卷;第203-215页 |
| 基于FEM-MODENA的加筋板声-固耦合分析;于士甲 等;《振动工程学报》;20170415;第30卷(第2期);第262-269页 |
| 基于混合ES-FE-SEA方法的中频声固耦合分析;吴飞 等;《机械工程学报》;20150513;第51卷(第15期);第67-74页 |
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