CN107133422B - A kind of certainty acoustic power flow response predicting method based on antithesis modal equations - Google Patents
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Abstract
The invention discloses a kind of certainty acoustic power flow based on antithesis modal equations to respond predicting method, includes the following steps：(1) structure in acoustic power flow system and the operatic tunes are divided into different subsystems；(2) mode of structure subsystem harmony cavity subsystem is calculated；(3) coupling parameter in adjacent subsystems between mode is calculated；(4) the antithesis modal equations of coupled system are established；(5) by preposition processing, obtain under the effect of certainty load, the generalized force load being subject in subsystem mode；(6) antithesis modal equations are calculated, obtain the participation factor of all mode；(7) modal superposition, the response of computing system certainty acoustic power flow are passed through.Certainty acoustic power flow provided by the invention responds predicting method, system is divided into continuous coupled subsystem, and the determination vibration of system is described with the subsystem mode in limited frequency band, and the analysis efficiency of this method is higher than conventional finite element method.
Description
Technical field
The present invention relates to acoustic power flow to respond indication technical field, and in particular to a kind of to be determined based on antithesis modal equations
Property acoustic power flow response predicting method.
Background technology
Spacecraft faces the mechanical oscillation of sternness, the environment such as noise in duty cycle, this may cause structural failure or
Precision instrument, instrument malfunction.Therefore, in the design process of spacecraft, mechanical oscillation and the influence of noise need to be considered.It can use
The acoustic power flow response of test method, theoretical method and numerical method forecasting system under the excitation of certainty load.Wherein, test
Method can obtain it is reliable as a result, but carry out analysis of experiments cost it is higher, design cycle length；Theoretical method is only applicable to simply
System, it is difficult to solve the problems, such as that complication system acoustic power flow responds indication；Numerical method has complication system good applicability, is
Effective supplementary means of analysis of experiments.System is divided into the subsystem of coupling with imaginary interface by antithesis mode Equation Theory,
And based on the mode of FEM calculation subsystem, rather than the mode of whole coupled system, therefore, antithesis mode equation method ratio
Traditional FInite Element has the analysis efficiency of higher.
There are problems that mode truncation in existing antithesis mode Equation Theory, i.e., need to intercept the subsystem in limited frequency range
Mode participates in response indication, and selected mode is very few to cause error, and selected mode can excessively cause computing resource waste.Therefore,
The frequency range that a criterion defines mode truncation is needed, to be reasonably based on antithesis modal equations forecasting system in certainty
Acoustic power flow response under load excitation.
The content of the invention
Goal of the invention：For a kind of existing antithesis mode equation method in the application there are the problem of, the present invention disclose
A kind of certainty acoustic power flow response predicting method based on antithesis modal equations, this method can effectively improve certainty load
Encourage the acoustic power flow response indication efficiency of lower structure.
Technical solution：To achieve the above object, the technical solution adopted by the present invention is：
A kind of certainty acoustic power flow response predicting method based on antithesis modal equations, comprises the following steps：
(1) structure in acoustic power flow system and the operatic tunes are divided into different subsystems；
(2) mode of structure subsystem harmony cavity subsystem is calculated；
(3) coupling parameter in adjacent subsystems between mode is calculated；
(4) the antithesis modal equations of coupled system are established；
(5) by preposition processing, obtain under the effect of certainty load, the generalized force load being subject in subsystem mode；
(6) antithesis modal equations are calculated, obtain the participation factor of all mode；
(7) modal superposition, the response of computing system certainty acoustic power flow are passed through.
Further, the acoustic power flow system in the step (1) is structure and operatic tunes coupled system, and structural vibration can shadow
Sound chamber acoustic pressure is pulsed, and the pulsation of operatic tunes acoustic pressure can also influence structural vibration；Structure subsystem with operatic tunes subsystems couple interface
On boundary condition be approximately free state, operatic tunes subsystem is near with the boundary condition on structure subsystem coupled interface
It is seemingly fixed boundary.
Further, in the step (2) based on Finite element arithmetic the mode of structure subsystem harmony cavity subsystem
Parameter and Mode Shape.
Further, the coupling parameter in the step (3) in adjacent subsystems between mode is calculated by following formula：
Wherein WmnCoupling ginseng between structure subsystem m ranks displacement modes and operatic tunes subsystem n-th order acoustic pressure mode
Number,For the vibration shape of structure subsystem m rank displacement modes,For the vibration shape of operatic tunes subsystem n-th order acoustic pressure mode,
ScFor the coupled interface between structure subsystem and operatic tunes subsystem, s is locus.
Further, the antithesis modal equations of the coupled system of foundation are in the step (4)：
Wherein MmFor structure subsystem m rank displacement modes quality, MnFor operatic tunes subsystem n-th order acoustic pressure modal mass, ηm
And ηnThe respectively damping loss factor of mode m and mode n, ω are angular frequency, φm(ω) is the participation factor of mode m, For the participation factor of mode n, Fm(ω) and Fn(ω) is respectively to be subject on mode m and mode n
Generalized force load.
Further, in the step (5), when structure subsystem is subject to deterministic face pressure load p (s, ω) excitation, mould
The generalized force load being subject on state m is given by：
Wherein SpFor face pressure load acting surface, when structure subsystem is subject to certainty concentrated force load F0When (ω) is encouraged, mould
The generalized force load being subject on state m is given by：
Wherein s0For concentrated force load F0The active position of (ω).
Further, system antithesis modal equations have been write as to the form of matrix in block form in the step (6)：
The wherein transposition of subscript " T " representing matrix,
W=[Wmn] (21)
Wherein diag () represents diagonal matrix, is diagonal matrix element in bracket, WmnMember is arranged for the m rows n-th of matrix W
Element, its value are calculated by formula (1), and the modal participation factors in each subsystem are tried to achieve based on formula (5)：
Wherein HijFor transfer function matrix (i=1,2；J=1,2), matrix element HijThe implication of (k, l) is：When j-th
In subsystem in l ranks mode during function unit generalized force, kth rank modal participation factors in i-th of subsystem, transmission function square
Battle array can invert the coefficient matrix on formula (5) left side acquisition：
The inverse matrix of subscript " -1 " representing matrix.
Further, the dynamic respond of structure subsystem is calculated in the step (7) by following formula：
WhereinThe pressure response of operatic tunes subsystem is calculated by following formula：
Wherein
Further, in the step (2)~step (7), only comprising less than 1.25 times analysis frequency band upper limits of intrinsic frequency
Subsystem mode.
Beneficial effect：
The invention discloses a kind of certainty acoustic power flow based on antithesis modal equations to respond predicting method, is a kind of excellent
Predicting method is responded in the certainty acoustic power flow of conventional finite element method, this method can effectively improve the lower knot of certainty load excitation
The acoustic power flow response indication efficiency of structure, shortens the design cycle, saves design cost.
Brief description of the drawings
Fig. 1 is the logical procedure diagram of the present invention；
Fig. 2 is the schematic diagram of a stiffened panel/operatic tunes coupling model；
Fig. 3 is the finite element model of stiffened panel；
Acceleration responsive on the lower stiffened panel of Fig. 4 (a) being to determine property concentrated forces load excitation at response point；
Pressure response in the lower operatic tunes of Fig. 4 (b) being to determine property concentrated forces load excitation at response point；
Acceleration responsive on the lower stiffened panel of being to determine property of Fig. 5 (a) acoustic loads excitation at response point；
Pressure response in the lower operatic tunes of being to determine property of Fig. 5 (b) acoustic loads excitation at response point.
Embodiment
The present invention is further described below in conjunction with the accompanying drawings.
As shown in Figure 1 predicting method logic flow frame is responded for a kind of certainty acoustic power flow based on antithesis modal equations
Figure, mainly includes the following steps that：
Structure in acoustic power flow system and the operatic tunes are divided into different subsystems by step (1)；Acoustic power flow system is
Structure and operatic tunes coupled system, structural vibration can influence the pulsation of operatic tunes acoustic pressure, and the pulsation of operatic tunes acoustic pressure can also influence structural vibration；Knot
Structure subsystem is being approximately free state with the boundary condition on operatic tunes subsystems couple interface, operatic tunes subsystem with structure
Boundary condition on subsystems couple interface is approximately fixed boundary.
Step (2) calculates the mould of less than the 1.25 times analysis frequency band upper limits of intrinsic frequency in structure subsystem harmony cavity subsystem
State；It is specifically based on the modal parameter and Mode Shape of Finite element arithmetic structure subsystem harmony cavity subsystem.
Step (3) calculates the coupling ginseng between the mode of less than the 1.25 times analysis frequency band upper limits of intrinsic frequency in adjacent subsystems
Number；Specifically it is calculated by following formula：
Wherein WmnCoupling ginseng between structure subsystem m ranks displacement modes and operatic tunes subsystem n-th order acoustic pressure mode
Number,For the vibration shape of structure subsystem m rank displacement modes,For the vibration shape of operatic tunes subsystem n-th order acoustic pressure mode,
ScFor the coupled interface between structure subsystem and operatic tunes subsystem, s is locus.
Step (4) establishes the antithesis modal equations of coupled system：
Wherein MmFor structure subsystem m rank displacement modes quality, MnFor operatic tunes subsystem n-th order acoustic pressure modal mass, ηm
And ηnThe respectively damping loss factor of mode m and mode n, ω are angular frequency, φm(ω) is the participation factor of mode m, For the participation factor of mode n, Fm(ω) and Fn(ω) is respectively to be subject on mode m and mode n
Generalized force load.
Step (5) is obtained under the effect of certainty load, the generalized force being subject in subsystem mode carries by preposition processing
Lotus；When structure subsystem is subject to deterministic face pressure load p (s, ω) excitation, the generalized force load being subject on mode m is by following formula
Provide：
Wherein SpFor face pressure load acting surface.When structure subsystem is subject to certainty concentrated force load F0When (ω) is encouraged, mould
The generalized force load being subject on state m is given by：
Wherein s0For concentrated force load F0The active position of (ω).
Step (6) calculates antithesis modal equations, obtains the participation factor of all mode；
(6.1) system antithesis modal equations have been write as to the form of matrix in block form：
The wherein transposition of subscript " T " representing matrix,
W=[Wmn] (8)
Wherein diag () represents diagonal matrix, is diagonal matrix element in bracket, WmnMember is arranged for the m rows n-th of matrix W
Element, its value are calculated by formula (1)；
(6.2) modal participation factors in each subsystem are tried to achieve based on formula (5)：
Wherein HijFor transfer function matrix (i=1,2；J=1,2), matrix element HijThe implication of (k, l) is：When j-th
In subsystem in l ranks mode during function unit generalized force, kth rank modal participation factors in i-th of subsystem.Transmission function square
Battle array can invert the coefficient matrix on formula (5) left side acquisition：
The inverse matrix of subscript " -1 " representing matrix.
Step (7) passes through modal superposition, the response of computing system certainty acoustic power flow；Structon is calculated especially by following formula
The dynamic respond of system：
WhereinThe pressure response of operatic tunes subsystem is calculated by following formula：
Wherein
By taking a stiffened panel/operatic tunes coupling model as an example, as shown in Figure 2.The boundary condition of stiffened panel is：It is simple on four edges
Branch, the finite element model of stiffened panel are as shown in Figure 3；The parameter of the panel of stiffened panel is provided by table 1, the material parameter of rib and face
The material parameter of plate is identical, parallel to x-axis to the size of rib be 1m × 0.03m × 0.005m, spacing 1/6m, parallel to y-axis
It is 1m × 0.02m × 0.005m, spacing 1/6m to the size of rib.The boundary condition of the operatic tunes is：Except the face coupled with stiffened panel,
Remaining each face is fixed boundary；The parameter of the operatic tunes is provided by table 2.
Coordinate is concentrated for the unit certainty applied at the point of (0.2m, 0.15m) perpendicular to plate face on stiffened panel panel
Power load, by above steps, it is the acceleration responsive at the response point of (0.3m, 0.1m) to obtain coordinate on stiffened panel panel
Coordinate is the pressure response frequency spectrum at the response point of (0.3m, 0.1m, 0m) in frequency spectrum, and the operatic tunes, respectively such as Fig. 4 (a) and Fig. 4
(b) shown in.
The parameter value of the panel of 1 stiffened panel of table
The parameter value of 2 operatic tunes of table
Apply unit certainty acoustic loads in the outer surface of stiffened panel panel, by above steps, obtain stiffened panel
On panel coordinate for (0.3m, 0.1m) response point at acceleration responsive frequency spectrum, and in the operatic tunes coordinate for (0.3m, 0.1m,
Pressure response frequency spectrum at response point 0m), respectively as shown in Fig. 5 (a) and Fig. 5 (b).
Reference value in Fig. 4 and Fig. 5 is calculated by finite element direct method.In antithesis mode equation method analytic process
In, it have chosen the stiffened panel mode within 2.5kHz and spectrogram parameter participate in response indication.The results show that being based in Fig. 4 and Fig. 5
Antithesis modal equations can accurately indicate that certainty concentrated force load and the acoustic power flow of the lower system of certainty acoustic loads excitation are rung
Should.
The effect explanation that the present embodiment finally obtains, method proposed by the invention can efficiently solve certainty load and swash
The acoustic power flow response indication problem of lower complication system is encouraged, improves the efficiency of analysis.
The above is only the preferred embodiment of the present invention, it should be pointed out that：For the ordinary skill people of the art
For member, various improvements and modifications may be made without departing from the principle of the present invention, these improvements and modifications also should
It is considered as protection scope of the present invention.
Claims (9)
- A kind of 1. certainty acoustic power flow response predicting method based on antithesis modal equations, it is characterised in that：Including following step Suddenly：(1) structure in acoustic power flow system and the operatic tunes are divided into different subsystems；(2) mode of structure subsystem harmony cavity subsystem is calculated；(3) coupling parameter in adjacent subsystems between mode is calculated；(4) the antithesis modal equations of coupled system are established；(5) by preposition processing, obtain under the effect of certainty load, the generalized force load being subject in subsystem mode；(6) antithesis modal equations are calculated, obtain the participation factor of all mode；(7) modal superposition, the response of computing system certainty acoustic power flow are passed through.
- 2. the certainty acoustic power flow response predicting method according to claim 1 based on antithesis modal equations, its feature It is：Acoustic power flow system in the step (1) is structure and operatic tunes coupled system；Structure subsystem with operatic tunes subsystem Boundary condition on coupled interface is approximately free state, operatic tunes subsystem with the border on structure subsystem coupled interface Condition is approximately fixed boundary.
- 3. the certainty acoustic power flow response predicting method according to claim 1 based on antithesis modal equations, its feature It is：Modal parameter and Mode Shape based on Finite element arithmetic structure subsystem harmony cavity subsystem in the step (2).
- 4. the certainty acoustic power flow response predicting method according to claim 1 based on antithesis modal equations, its feature It is：Coupling parameter in the step (3) in adjacent subsystems between mode is calculated by following formula：Wherein WmnFor the coupling parameter between structure subsystem m ranks displacement modes and operatic tunes subsystem n-th order acoustic pressure mode,For the vibration shape of structure subsystem m rank displacement modes,For the vibration shape of operatic tunes subsystem n-th order acoustic pressure mode, ScFor Coupled interface between structure subsystem and operatic tunes subsystem, s are locus.
- 5. the certainty acoustic power flow response predicting method according to claim 1 based on antithesis modal equations, its feature It is：The antithesis modal equations of the coupled system of foundation are in the step (4)：Wherein MmFor structure subsystem m rank displacement modes quality, MnFor operatic tunes subsystem n-th order acoustic pressure modal mass, ηmAnd ηn The respectively damping loss factor of mode m and mode n, ω are angular frequency, φm(ω) is the participation factor of mode m,For the participation factor of mode n, Fm(ω) and Fn(ω) be respectively on mode m and mode n by The generalized force load arrived；WmpFor the coupling between structure subsystem m ranks displacement modes and operatic tunes subsystem pth rank acoustic pressure mode Parameter, WqnFor the coupling parameter between structure subsystem q ranks displacement modes and operatic tunes subsystem n-th order acoustic pressure mode.
- 6. the certainty acoustic power flow response predicting method according to claim 1 based on antithesis modal equations, its feature It is：In the step (5), when structure subsystem is subject to deterministic face pressure load p (s, ω) excitation, it is subject on mode m Generalized force load is given by：Wherein SpFor face pressure load acting surface, when structure subsystem is subject to certainty concentrated force load F0When (ω) is encouraged, mode m On the generalized force load that is subject to be given by：Wherein s0For concentrated force load F0The active position of (ω)；For the vibration shape of structure subsystem m rank displacement modes,For structure subsystem m rank displacement modes the vibration shape in s0Value at point.
- 7. the certainty acoustic power flow response predicting method according to claim 5 based on antithesis modal equations, its feature It is：System antithesis modal equations have been write as to the form of matrix in block form in the step (6)：The wherein transposition of subscript " T " representing matrix,W=[Wmn] (8)Wherein diag () represents diagonal matrix, is diagonal matrix element in bracket, WmnFor the n-th column element of m rows of matrix W, its Value is calculated by formula (1), and the modal participation factors in each subsystem are tried to achieve based on formula (5)：Wherein HijFor transfer function matrix (i=1,2；J=1,2), matrix element HijThe implication of (k, l) is：When j-th of subsystem In in l rank mode during function unit generalized force, kth rank modal participation factors in i-th of subsystem, transfer function matrix can be right The coefficient matrix on formula (5) left side is inverted acquisition：The inverse matrix of subscript " -1 " representing matrix.
- 8. the certainty acoustic power flow response predicting method according to claim 7 based on antithesis modal equations, its feature It is：The dynamic respond of structure subsystem is calculated in the step (7) by following formula：WhereinThe pressure response of operatic tunes subsystem is calculated by following formula：WhereinFor the vibration shape of structure subsystem m rank displacement modes,For operatic tunes The vibration shape of system n-th order acoustic pressure mode.
- 9. the certainty acoustic power flow response predicting method according to claim 1 based on antithesis modal equations, its feature It is：In the step (2)~step (7), the mould of the subsystem only comprising less than the 1.25 times analysis frequency band upper limits of intrinsic frequency State.
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| PCT/CN2018/083242 WO2018219052A1 (en) | 2017-06-01 | 2018-04-16 | Dual mode equation based deterministic acoustic-structure coupling response prediction method |
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| CN107133422B (en) * | 2017-06-01 | 2018-04-24 | 东南大学 | A kind of certainty acoustic power flow response predicting method based on antithesis modal equations |
| CN107748815B (en) * | 2017-10-16 | 2018-08-21 | 东南大学 | Dynamic response analysis method based on antithesis modal equations under a kind of random noise environment |
| CN108491595B (en) * | 2018-03-07 | 2019-03-29 | 东南大学 | Gu a kind of high frequency partial of sound-coupled structure responds predicting method |
| CN109145369B (en) * | 2018-07-11 | 2019-05-31 | 东南大学 | A kind of medium-high frequency part dynamic response predicting method counted and off-resonance is transmitted |
| CN109635507A (en) * | 2019-01-11 | 2019-04-16 | 汽-大众汽车有限公司 | Method for arranging based on the car damping piece that emulation is combined with experiment |
| CN111159950B (en) * | 2019-12-30 | 2021-06-01 | 北京理工大学 | Acoustic-solid coupling-based composite propeller prestress wet mode prediction method |
| CN113688551A (en) * | 2021-09-01 | 2021-11-23 | 九江学院 | Acoustic-solid coupling system noise optimization method, system and storage medium |
| CN113836773A (en) * | 2021-09-29 | 2021-12-24 | 九江学院 | Structural vibration response prediction method and system for sound-solid coupling system and storable medium |
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| US5163015A (en) * | 1989-06-30 | 1992-11-10 | Mitsubishi Denki Kabushiki Kaisha | Apparatus for and method of analyzing coupling characteristics |
| 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 |
| CN104112070A (en) * | 2014-07-11 | 2014-10-22 | 长沙理工大学 | Solving method used for dynamic response when elastic boundary shallow arch generates internal resonance |
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| GB201104413D0 (en) * | 2011-03-16 | 2011-04-27 | Airbus Operations Ltd | Stresses induced by random loading |
| CN104850713B (en) * | 2015-05-28 | 2017-11-28 | 西北工业大学 | Mechanical structure random vibration dynamic stress high-resolution method |
| CN107133422B (en) * | 2017-06-01 | 2018-04-24 | 东南大学 | A kind of certainty acoustic power flow response predicting method based on antithesis modal equations |
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| US5163015A (en) * | 1989-06-30 | 1992-11-10 | Mitsubishi Denki Kabushiki Kaisha | Apparatus for and method of analyzing coupling characteristics |
| 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 |
| CN104112070A (en) * | 2014-07-11 | 2014-10-22 | 长沙理工大学 | Solving method used for dynamic response when elastic boundary shallow arch generates internal resonance |
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