CN108614921B - Low-frequency sound and vibration response prediction method in spacecraft - Google Patents

Low-frequency sound and vibration response prediction method in spacecraft Download PDF

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CN108614921B
CN108614921B CN201810297212.9A CN201810297212A CN108614921B CN 108614921 B CN108614921 B CN 108614921B CN 201810297212 A CN201810297212 A CN 201810297212A CN 108614921 B CN108614921 B CN 108614921B
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朱卫红
邹元杰
刘绍奎
刘峰
王泽宇
邓润然
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Beijing Institute of Spacecraft System Engineering
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Abstract

A low-frequency acoustic vibration response prediction method in a spacecraft comprises the steps of firstly establishing an acoustic indirect boundary element model containing plane wave loads, a spacecraft structure finite element model, establishing a reverberation sound field load model based on plane wave superposition, then comprehensively obtaining a low-frequency acoustic vibration response mixed model in the spacecraft, and further performing low-frequency acoustic vibration response prediction according to the low-frequency acoustic vibration response mixed model in the spacecraft. The invention provides a medium-low frequency acoustic vibration response prediction method of a structural finite element-acoustic indirect boundary element, which is convenient for establishing an acoustic model for a spacecraft structure with a complex boundary; in addition, a reverberation sound field load modeling method based on plane wave superposition is provided for an acoustic indirect boundary element, and a method for determining the number of plane waves is provided, so that engineering application is facilitated.

Description

Low-frequency sound and vibration response prediction method in spacecraft
Technical Field
The invention relates to the research fields of spacecraft mechanical environment prediction, mechanical environment condition design, sound vibration response prediction and the like, in particular to a low-frequency sound vibration response prediction method in a spacecraft.
Background
Whether the spacecraft can withstand the harsh mechanical environment of the launching section is one of the key factors for determining the success or failure of the mission in the process of the space mission, and the key factors typically comprise interstage separation load, pneumatic load, initiating explosive impact load and the like. The loads are transmitted to the spacecraft structure or critical components mainly by two ways: firstly, the mechanical environment is transmitted through a satellite-rocket interface or an installation interface and is generally examined through sine, random vibration and impact tests; secondly, the noise environment in the fairing directly acts on the structure and equipment of the spacecraft, and the spacecraft is generally examined through a noise test. The noise environment experienced by the spacecraft is very harsh, on one hand, the noise environment of medium and high frequency bands can cause the failure and the precision reduction of electromechanical equipment, optical instruments, electronic circuits and the like, and on the other hand, in the actual engineering, the medium and low frequency noise environment can occasionally have the damage cases of light and thin-wall structures such as solar wings, antennas, feed sources and the like.
In the current aerospace engineering, different analysis methods are mainly adopted for predicting the sound vibration mechanical environment aiming at different frequency bands: the method is characterized in that a structure finite element-acoustic boundary element method is adopted in a low-frequency band, the structure is modeled by adopting a finite element method in the method, the inner and outer sound fields of the spacecraft are modeled by adopting a direct boundary element method, however, a closed boundary needs to be established when the inner and outer sound field models are established by the direct boundary, but for the structure of the spacecraft, the configuration is complex, and the difficulty of establishing a closed sound cavity by using structures such as solar wings, antennas and the like is great, so that the application of the direct boundary element method is more limited; in addition, a noise load model is also important, a diffuse sound field load modeling method (DAF) is adopted at present, the model considers that a noise space is a complete reverberation space, then sound pressure is converted into a force spectrum on a structural grid node based on the reciprocal relation between a direct field and a diffuse sound field, and then the force spectrum is directly applied to a structure to solve, and the model is mainly characterized in that the modeling method is simple, the spatial correlation of the sound field load can be described, but the spatial correlation exists only in an applied area, the sound loads among different areas have no correlation, and the sound field nonuniformity caused by the existence of the structure in the reverberant sound space can not be described; in addition, the model is mainly applied to the structure, the sound radiation and scattering characteristics of the structure cannot be considered, and the characteristics of the structure such as sound radiation and the like need to be simulated by combining a semi-infinite sound field system.
Disclosure of Invention
The technical problem solved by the invention is as follows: the method is characterized in that the defects of the prior art are overcome, a low-frequency acoustic vibration response prediction method in the spacecraft is provided, a finite element-indirect boundary element mixed modeling method is provided for the problem of low-frequency acoustic vibration response prediction in the spacecraft, a reverberation sound field load model capable of being directly applied to an acoustic indirect boundary element model is provided based on a plane wave superposition theory, a method for determining the plane wave number is provided, and reference can be provided for subsequent engineering application.
The technical solution of the invention is as follows: a low-frequency sound vibration response prediction method in a spacecraft comprises the following steps:
(1) establishing an acoustic indirect boundary element model containing plane wave load;
(2) establishing a spacecraft structure finite element model;
(3) establishing a reverberation sound field load model based on plane wave superposition;
(4) establishing a low-frequency sound vibration response mixed model in the spacecraft;
(5) and performing medium-low frequency sound vibration response prediction according to the mixed model of medium-low frequency sound vibration response of the spacecraft.
The establishment of the acoustic indirect boundary element model containing the plane wave load comprises the following steps:
Figure BDA0001617065080000021
where ρ isaIs sound field air density, omega is angular frequency, u is displacement vector, mu and delta mu are double-layer potential function vector and double-layer potential function variation vector on sound field boundary, respectively, CμuAs a coupling matrix between the two-layer potential function and the displacement, DμμAutocorrelation matrix being a function of the potential of the two layers, FincFor the load to be generated by the plane wave load,<>is a row vector and { } is a column vector.
The method for establishing the spacecraft structure finite element model comprises the following steps:
<δu>([K]{u}-ω2[M]{u}+[Cuμ]{μ}-{F})＝0
wherein u and delta u respectively represent the displacement value and the displacement variation value of the corresponding spacecraft structure on the discrete point, K is the rigidity matrix of the spacecraft structure, M is the quality matrix of the spacecraft structure, CuμThe method is characterized in that the method is a coupling matrix of spacecraft structure displacement and a surface double-layer potential function, and F is an external load matrix of the spacecraft structure.
The method for establishing the reverberation sound field load model based on the plane wave superposition comprises the following steps:
(1) establishing the whole sound space in a spherical coordinate system, segmenting the spherical surface according to longitude and latitude, and dividing the spherical surface into m layers on the latitude, wherein the interval angle between each layer is
Figure BDA0001617065080000031
The latitude of the i-th layer is thetaiThe longitude is divided into n layers, and the interval angle of each layer is delta psi 2 pi/n and psijΔ ψ/2+ (j-1) Δ ψ (j 1.. multidot., n), assuming the center of the spherical coordinates as the physical coordinate origin, let the latitude be θiLongitude is psijSound pressure amplitude of plane wave of position is Pij，
Figure BDA0001617065080000032
Wherein, P is given reverberation load sound pressure;
(2) assuming that the number n of longitude divisions and the number m of latitude divisions are equal to each other, the number n of longitude divisions and the number m of latitude divisions are equal to each other
Figure BDA0001617065080000033
p00＝8.259；
p10＝-0.01022；
p01＝-1.456；
p20＝1.695e-05；
p11＝0.009679；
p02＝0.3041；
p30＝-1.024e-08；
p21＝3.783e-07；
p12＝-4.932e-05；
p03＝-0.01996
Where f is the circular frequency, c is the sound velocity of the sound field, r0Is the largest included dimension of the spacecraft structure.
The mixed model for establishing the low-frequency sound vibration response in the spacecraft is
Figure BDA0001617065080000034
The method for predicting the medium-low frequency sound vibration response according to the mixed model of the medium-low frequency sound vibration response of the spacecraft comprises the following steps:
Figure BDA0001617065080000041
Figure BDA0001617065080000042
Figure BDA0001617065080000043
where p (x) is the sound pressure at a spatial location x on a non-boundary within the sound field,
Figure BDA0001617065080000044
for the sound field boundary, μ (y) is the double-layer potential function at position y on the sound field boundary, G (x, y) is the Green function between positions x and y, nyIs a normal vector at position y on the boundary, pij(x) As a latitude of thetaiLongitude is psijThe sound pressure amplitude of the plane wave at position x. p is a radical of+(x) Is the sound pressure value, p, at the positive normal x on the boundary of the sound field-(x) Is the sound pressure value, dS, at the negative normal x on the boundary of the sound fieldyIs the area element at position y on the boundary.
A computer-readable storage medium, having stored thereon a computer program, which, when being executed by a processor, carries out the steps of the method according to any of claims 1-6.
Compared with the prior art, the invention has the advantages that:
aiming at the defects of the prior art, the invention provides a medium-low frequency acoustic vibration response prediction method of a structural finite element-acoustic indirect boundary element, which is convenient for establishing an acoustic model for a spacecraft structure with a complex boundary; in addition, a reverberation sound field load modeling method based on plane wave superposition is provided for an acoustic indirect boundary element, and a method for determining the number of plane waves is provided, so that engineering application is facilitated.
Drawings
FIG. 1 is a block flow diagram;
FIG. 2 is a schematic diagram of the acoustic-solid coupling of domains;
FIG. 3 is a schematic view of a planar position target and its effective radiation area;
FIG. 4 shows the number of plane waves and the fitting result thereof
Detailed Description
The invention provides a hybrid modeling method of a spacecraft structure finite element-acoustic indirect boundary element aiming at the problem of low-frequency acoustic response prediction of a spacecraft, provides a method for simulating reverberation sound field load by combining a plane wave superposition-based method on the hybrid modeling method, provides a method for determining plane wave number, can provide reference for subsequent space engineering application, and further completes low-frequency acoustic response prediction of the spacecraft.
The specific implementation steps of the invention are shown in fig. 1, and mainly comprise the following steps:
(1) establishing acoustic indirect boundary element model containing plane wave load
Because most spacecraft structures do not have closed areas, it is very difficult to establish a model by using direct boundary elements, and an indirect integral format is used for establishing a sound field model. For the acoustic-solid coupling problem of the spacecraft structure, the boundary of the sound field is the Newman boundary, so the sound pressure p at the position x in the sound field can be reconstructed by using a dipole source by adopting double-layer potential:
Figure BDA0001617065080000051
where p (x) is the sound pressure at point x,
Figure BDA0001617065080000052
is the boundary of the sound field, y is the boundaryAt any point above, dSyIs the area infinitesimal at the boundary position y,
Figure BDA0001617065080000053
is a position sound field Green function, r is a position vector between positions x and y, | | is a modulus symbol, k is a sound field wave number, mu (y) is a double-layer potential function at y, nyIs the normal vector at position y.
If the incident plane wave excitation is considered, on the non-boundaries there are:
Figure BDA0001617065080000054
wherein p isinc(x) Is the sound pressure of the plane at position x.
At the boundary
Figure BDA0001617065080000055
The method comprises the following steps:
Figure BDA0001617065080000056
wherein the superscript "+" represents a positive boundary normal to the boundary, the superscript "-" represents a negative boundary normal to the boundary, nxNormal to the boundary x. When the structure is coupled with the sound field, the coupling part meets the normal displacement coordination condition:
Figure BDA0001617065080000061
where ρ isaIs the density of the sound field, ω is the circular frequency, un(x) Is the normal displacement at x.
To formula (3) at nxThe direction is differentiated and the equation (4) is given by:
Figure BDA0001617065080000062
the right integral term of equation (5) is super-singular integral and cannot be directly integrated, so multiplying both sides of equation (5) by the variable δ μ (x) and integrating the variable x over the whole boundary has:
Figure BDA0001617065080000063
wherein dSxIs the area infinitesimal at position x.
The integral on the right side of the above formula is a regular integral, and the expression in the form of a matrix can be obtained by integrating after finite element dispersion:
Figure BDA0001617065080000064
wherein<>Represents a row vector, { } represents a column vector, DμμThe autocorrelation matrix, which is a function of the double-layer potential, can be obtained by directly calculating the integral of equation (7) over a series of discrete units, and μ and δ μ represent the values of the corresponding double-layer potential function at discrete points and their variation values, respectively.
The remaining integrals can be written as:
Figure BDA0001617065080000065
wherein C isμuIs a coupling matrix of a two-layer potential function mu and a displacement u, FincIs the equivalent load vector caused by the plane wave. The comprehensive formulas (7), (8) and (9) are as follows:
Figure BDA0001617065080000066
(2) establishing a finite element model of a spacecraft structure
Considering the system shown in fig. 2, a schematic diagram of the planar position object and its effective radiating area is shown in fig. 3, where u is the displacement field of the structure,
Figure BDA0001617065080000071
stress strain of the structureThe amount of the compound (A) is,
Figure BDA0001617065080000072
for the stress tensor of the structure, ρ s is the density of the structure, p is the sound pressure of the sound field coupled to the structure, k is the sound wave number of the sound field, ΩsIn the form of a domain or domains,
Figure BDA0001617065080000073
is the force boundary of the structure and,
Figure BDA0001617065080000074
in order to be a displacement boundary of the structure,
Figure BDA0001617065080000075
is the coupling boundary of the structure with the sound field.
The dynamic variational format of the structure can be established by adopting the Galerkin weak integral format:
Figure BDA0001617065080000076
wherein, the 'is tensor double dot product, and the' is dot product. After the finite element is dispersed and integrated:
Figure BDA0001617065080000077
wherein, δ u and u respectively represent the corresponding displacement variation value and displacement value on the discrete point, K is the rigidity matrix of the structure, M is the quality matrix, CupF is the external load matrix of the structure, which is the coupling matrix of displacement and sound pressure.
The dynamic response of a structure can therefore be written as:
<δu>([K]{u}-ω2[M]{u}+[Cup]{p}-{F})＝0 (12)
in the above formula, the coupling relation between the structure displacement and the sound pressure is considered, and the coupling between the structure and the direct boundary element can be realized, but in the indirect boundary element model, the independent variable is the double-layer potential function mu, so the sound pressure p around the structure and the double-layer potential function must be establishedThe relationship of μ. To obtain this relationship, the two-layer potential function μ can be described as the sound pressure crossing over in this case, assuming that the structure is a thin-walled structure and both sides are in contact with the sound field
Figure BDA00016170650800000713
The jump caused.
Hypothetical boundaries
Figure BDA0001617065080000078
The contact surfaces on both sides of
Figure BDA0001617065080000079
And
Figure BDA00016170650800000710
and p + and p-are the pressures on both faces, respectively, and thus there are:
Figure BDA00016170650800000711
the integration after the unit dispersion is adopted is as follows:
Figure BDA00016170650800000712
wherein C isuμIs the coupling matrix of the displacement u and the two-layer potential function mu.
The kinetic equation for the structure can be written as:
<δu>([K]{u}-ω2[M]{u}+[Cuμ]{μ}-{F})＝0 (15)
(2) method for establishing reverberation sound field load model based on plane wave superposition
The ideal reverberation sound field has the same acoustic energy propagation probability at each party and the acoustic energy density in the space is equal everywhere. Theoretical analysis shows that under the condition that the phases of all plane waves are random, the acoustic energy density superposition formula of the plane waves meets the linear superposition principle.
Assuming that the whole sound space is established in a spherical coordinate system, the spherical surface is advanced according to longitude and latitudeLine segmentation, dividing into m layers in latitude, and then the interval angle between each layer is
Figure BDA0001617065080000081
The latitude of the i-th layer is thetaiThe longitude is divided into n layers, and the interval angle of each layer is delta psi 2 pi/n and psijΔ ψ/2+ (j-1) Δ ψ (j 1.. multidot., n), assuming the center of the spherical coordinates as the physical coordinate origin, let the latitude be θiLongitude is psijSound pressure amplitude of position is PijThe space vector direction is:
rij＝[sin(θi)cos(ψj),sin(θi)sin(ψj),cos(θi)] (16)
the plane wave divides the sphere into m × n parts, plane wave PijThe area acting on the spherical surface is assumed to be SijIn the latitudinal direction, the spherical width of the area element is Δ θ. Thus plane wave PijThe effective area on a spherical surface is approximately:
ΔSij≈sin(θi)ΔψΔθ (17)
in order to ensure that the energy of the reverberant field is uniformly distributed over the sphere, there are:
Figure BDA0001617065080000082
wherein C is a constant.
For plane waves with uniformly distributed random phases, a linear superposition relationship is satisfied, namely:
Figure BDA0001617065080000083
where P is the reverberant load sound pressure of the soundfield.
The amplitude of each plane wave can thus be determined based on equation (19):
Figure BDA0001617065080000084
(3) determination of the number of plane waves from the structural dimensions and the analysis frequency
When the number of plane waves tends to be + ∞, the spatial correlation of the reverberation sound field load obtained by plane wave superposition completely accords with the theoretical spatial correlation:
Figure BDA0001617065080000091
where k is the wave number of the sound field, r is the distance between any two points in space, γrefIs the spatial correlation coefficient of the sound field loading between the two point locations. At medium and low frequencies, the influence of the spatial correlation of sound field load on the response analysis result is very obvious, and for practical engineering, the method has important engineering application value for determining the number of plane waves.
The number of plane waves is closely related to the upper limit of the analysis frequency and the characteristic size (maximum envelope size) of the spacecraft structure to analyze the upper limit of the frequency and the maximum envelope size (r) of the structure0) As a parameter, the number of plane waves required to satisfy a given error in the objective function is determined using the spatial theoretical correlation as an objective function and the number of plane waves in longitude and latitude (which are equal) as arguments, and since the tolerance function is a damped oscillation function having a plurality of zero points, a relative error cannot be defined at the zero points. Taking the absolute error, considering that the maximum value of the spatial correlation is 1 and approaches 0 as the analysis frequency increases with the spatial distance, only a result of 0.01 is given here:
|γ(k,r,m,n)-γref(k,r)|≤0.01 (22)
where γ (k, r, m, n) is the spatial correlation between two points in the space with distance r at wave number k when the longitude and latitude division numbers of plane waves in the sound field are m and n, respectively. Fig. 4 is a relationship between the number of plane waves and the maximum envelope size and the upper limit of the analysis frequency when the tolerance is 0.01, and for convenience of engineering application, it is assumed here that the subdivision of the longitude is the same as the subdivision of the latitude, and a quadratic surface is used for fitting, and the number of plane waves, the frequency and the maximum envelope size satisfy the following relationship:
Figure BDA0001617065080000092
Figure BDA0001617065080000101
where f is the circular frequency, c is the sound velocity of the sound field, r0Is the largest included dimension of the spacecraft structure.
(4) Establishing a mixed model according to the steps (1), (2) and (4)
And (4) after establishing an indirect boundary model, a structural model and a reverberation load model in the steps (1), (2) and (4), assembling to form a mixed sound-vibration response analysis model. For indirect boundary elements, if equation (9) holds for any δ μ, then:
ρ0ω2[Cμu(ω)]{u}-[Dμμ(ω)]{μ}＝{F'inc} (25)
since the response of the structure satisfies equation (15) for an arbitrary δ u, there are:
[K]{u}-ω2[M]{u}+[Cuμ]{μ}＝{F} (26)
the coupling of the two can be written as:
Figure BDA0001617065080000102
(5) solving to obtain a structural response and a sound field response
Based on the formula (27), the displacement response { u } of the structure and the double-layer potential { mu } of the indirect boundary element can be obtained through solving, and then the sound pressure value p of any point in the sound field can be obtained through solving according to the formula (2) and the formula (3)
Figure BDA0001617065080000103
Figure BDA0001617065080000104
Figure BDA0001617065080000105
Those skilled in the art will appreciate that those matters not described in detail in the present specification are well known in the art.

Claims (1)

1. A low-frequency sound vibration response prediction method in a spacecraft is characterized by comprising the following steps:
(1) establishing an acoustic indirect boundary element model containing plane wave load;
(2) establishing a spacecraft structure finite element model;
(3) establishing a reverberation sound field load model based on plane wave superposition;
(4) establishing a low-frequency sound vibration response mixed model in the spacecraft;
(5) performing medium-low frequency sound vibration response prediction according to a mixed model of medium-low frequency sound vibration response of the spacecraft;
the establishment of the acoustic indirect boundary element model containing the plane wave load comprises the following steps:
Figure FDA0003485462140000011
where ρ isaIs sound field air density, omega is angular frequency, u is displacement vector, mu and delta mu are double-layer potential function vector and double-layer potential function variation vector on sound field boundary, respectively, CμuAs a coupling matrix between the two-layer potential function and the displacement, DμμAutocorrelation matrix being a function of the potential of the two layers, FincFor the load to be generated by the plane wave load,< >is a row vector, and { } is a column vector;
the method for establishing the spacecraft structure finite element model comprises the following steps:
<δu>([K]{u}-ω2[M]{u}+[Cuμ]{μ}-{F})＝0
wherein u and delta u respectively represent the displacement value and the displacement variation value of the corresponding spacecraft structure on the discrete point, and K is the rigidity of the spacecraft structureDegree matrix, M being the mass matrix of the spacecraft structure, CuμThe method comprises the following steps of (1) obtaining a coupling matrix of spacecraft structure displacement and a surface double-layer potential function, wherein F is an external load matrix of a spacecraft structure;
the method for establishing the reverberation sound field load model based on the plane wave superposition comprises the following steps:
(1) establishing the whole sound space in a spherical coordinate system, segmenting the spherical surface according to longitude and latitude, and dividing the spherical surface into m layers on the latitude, wherein the interval angle between each layer is
Figure FDA0003485462140000021
The latitude of the i-th layer is thetaiThe longitude is divided into n layers, and the interval angle of each layer is delta psi 2 pi/n and psijΔ ψ/2+ (j-1) Δ ψ (j 1.. multidot., n), assuming the center of the spherical coordinates as the physical coordinate origin, let the latitude be θiLongitude is psijSound pressure amplitude of plane wave of position is Pij，
Figure FDA0003485462140000022
Wherein, P is given reverberation load sound pressure;
(2) assuming that the number n of longitude divisions and the number m of latitude divisions are equal to each other, the number n of longitude divisions and the number m of latitude divisions are equal to each other
Figure FDA0003485462140000023
p00＝8.259；
p10＝-0.01022；
p01＝-1.456；
p20＝1.695e-05；
p11＝0.009679；
p02＝0.3041；
p30＝-1.024e-08；
p21＝3.783e-07；
p12＝-4.932e-05；
p03＝-0.01996
Where f is the circular frequency, c is the sound velocity of the sound field, r0Is the largest included dimension of the spacecraft structure;
the mixed model for establishing the low-frequency sound vibration response in the spacecraft is
Figure FDA0003485462140000024
The method for predicting the medium-low frequency sound vibration response according to the mixed model of the medium-low frequency sound vibration response of the spacecraft comprises the following steps:
Figure FDA0003485462140000031
Figure FDA0003485462140000032
Figure FDA0003485462140000033
where p (x) is the sound pressure at a spatial location x on a non-boundary within the sound field,
Figure FDA0003485462140000034
for the sound field boundary, μ (y) is the double-layer potential function at position y on the sound field boundary, G (x, y) is the Green function between positions x and y, nyIs a normal vector at position y on the boundary, pij(x) As a latitude of thetaiLongitude is psijThe sound pressure amplitude of the plane wave at position x; p is a radical of+(x) Is the sound pressure value, p, at the positive normal x on the boundary of the sound field-(x) Is the sound pressure value, dS, at the negative normal x on the boundary of the sound fieldyIs the area element at position y on the boundary.
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