CN106484984A - Spaceborne flexible accessory thermic micro-vibration responds Simulation Platform - Google Patents

Abstract

The present invention relates to spaceborne flexible accessory thermic micro-vibration responds Simulation Platform, belong to high accuracy Spacecraft guidance and control and dynamics simulation and control technology field, lead calculation module, high accuracy model analyses module, high accuracy Response Analysis module, post-processing module including data input MBM, in-orbit thermal analysis module, equivalent heat load, modules are sequentially connected, the input exporting as next module of previous module；This analysis platform carries out the analysis and simulation research of spaceborne large-scale flexible adnexa thermal vibration of practical application and the research and development of corresponding software for calculation, has reached quick, effective acquisition large-scale flexible component thermic micro-vibration and its purpose with the response of celestial body coupled vibrations；Meanwhile, analysis emulation platform can promote spaceborne large-scale flexible component thermal deformation and the engineer applied of thermic micro-vibration simulation analysis technology and examination to verify, and drives Related Supporting Technologies progress, is follow-up New Satellite Project R＆D accumulation technology basis.

Description

Spaceborne flexible accessory thermic micro-vibration responds Simulation Platform

Technical field

The present invention relates to spaceborne flexible accessory thermic micro-vibration responds Simulation Platform, belong to high accuracy Spacecraft guidance and control And dynamics simulation and control technology field.

Background technology

Developing rapidly with space technology, large-size pliable structure and flexible accessory are widely used in all kinds of spacecrafts, As large-scale Deployable antenna, solar array, antenna mounting arm etc..It is big, long that these flexible structures and flexible accessory often have area And thin or long and thin, that quality is little feature, its supporting form many similar to cantilever design, lateral stiffness is relatively small, and frequency is relatively Low.This kind of flexible structure is equivalent to when temperature quickly changes by thermal shock, leads to disabler or even recurring structure to destroy. When spacecraft turnover earth's shadow area, the acute variation of temperature not only makes flexible accessory that larger thermal deformation, induction heat occur Vibration, and perturbed force effect also can be delivered in spacecraft main body, has a strong impact on stable, attitude, the pointing accuracy of spacecraft Deng.

The earth observation that China is developing and survey of deep space remote-sensing spacecraft, vast capacity telecommunication satellite etc. belong to height Precision spacecraft.For ensureing the safety of communication and the reliability of observation, this kind of high accuracy spacecraft is to pointing accuracy and degree of stability There is high requirement.With reference to external data, high accuracy spacecraft vibration index to be reached is：Angular variation amplitude is less than 0.007arcsec (Hubble HST), acceleration is less than 10^-3G (international space station ISS).Therefore, carry out spacecraft Flexible accessory thermic micro-vibration response analyses simulation Technique Study and corresponding Development of Software Platform significant and be worth.

The task of Flexible appendages of spacecraft thermic micro-vibration response analyses simulation study is mainly analysis by spatial heat environment Change the flexible accessory thermic micro-vibration response causing.Its main research includes：Flexible accessory in-orbit heat analysis modeling with Temperature calculating, the calculating of transient state temperature field equivalent heat load, spaceborne flexible accessory thermic micro-vibration model and analyze and special With simulation analysis system exploitation etc..

In terms of the in-orbit heat analysis of space structure, have some achievements in research and special-purpose software.Equivalent in transient state temperature field Hot load calculating aspect is although correlation theory comparative maturity, but is also short of very much on software is realized, and lacks special height Efficiency software module.By secondary development, existing business software has possessed the function that Steady-State Thermal Field is equivalent to hot load, but For engineering structure that is fairly large and having more time step, because data volume is very big, existing software is to its transient state temperature Degree field Equivalent Calculation be then substantially all cannot effective process it is impossible to meet calculating demand.After forming equivalent heat load, permissible Structure analysis software is called to carry out spaceborne flexible accessory thermic micro-vibration response analyses.A lot of business softwares can complete this point Analysis.However, the restriction of the scale of calculating still exists.For example the load for medium scale structure, thousands of step walks, and only reads The time fetching data and exporting result of calculation cannot stand.Therefore, in the urgent need to exploitation high efficiency, in high precision, engineering Practical dynamic response analysis software module, is analyzed with the thermic micro-vibration completing spaceborne flexible accessory, and expeditiously obtains Take results needed information.

Flexible appendages of spacecraft thermic the Dynamic Response emulates, due to being related to in-orbit Orbital heat flux/ascent, transient temperature Many calculating such as field, mode, dynamic deformation, belongs to typical multi-crossed disciplines problem, complete using single simulation analysis system Become to calculate com-parison and analysis difficult, generally require exploitation integrated analysis system.Its advantage is using each chief, so that each stage is calculated The precision of result and efficiency are able to maximum consideration, and shortcoming is to need to develop the routine interface between software, and data exchange amount compares Greatly, computational efficiency is than relatively low.In addition it is also necessary to specially develop data transfer and management, post-processing module and platform interface etc..

Content of the invention

For above-mentioned technical problem, the purpose of the present invention is for solving spaceborne large-scale flexible adnexa due to spatial heat environment The simulation and analysis of the thermic micro-vibration response changing and causing, propose a kind of spaceborne large-scale flexible adnexa thermic micro-vibration response The integrated platform system of analysis emulation.

The design principle of the platform of the present invention is：To be analyzed using the non-coupled dynamic analysis method of heat-structure and model The thermic micro-vibration response of spaceborne flexible accessory：Suppose that temperature field, hot load, the impact between displacement field are unidirectional, first Calculate the temperature field that additional hot-fluid causes change, then the time dependent hot load of equivalent one-tenth is added on flexible accessory, then counts Calculate the time-histories data of flexible accessory.The targeted object of study of the present invention is the spacecraft with flexible accessory.Attached compared to flexibility Part, the rigidity of spacecraft center nacelle is much bigger, therefore center nacelle can be approximately band lumped mass and rotary inertia Rigid body, thus using whole spacecraft as Rigid Base-flexible accessory coupled system.This coupled system is in space only constrains 3 translation displacements of the lines of heart rigid body.

Specifically technical scheme is：

Spaceborne flexible accessory thermic micro-vibration responds Simulation Platform, including data input MBM, in-orbit heat point Analysis module, equivalent heat load lead calculation module, high accuracy model analyses module, high accuracy Response Analysis module, post processing mould Block, modules are sequentially connected, the input exporting as next module of previous module；

(1) data input MBM, sets up spacecraft Rigid Base-soft using interactive mode with reference to automatic conversion mode The FEM (finite element) model of property adnexa coupled system and in-orbit thermal model.

(2) in-orbit thermal analysis module, using the spacecraft Rigid Base-in-orbit heat analysis of flexible accessory coupled system set up Model, carries out the in-orbit heat analysis of Flexible appendages of spacecraft, obtains the transient state temperature field on flexible accessory；

It is concerned with emphatically spacecraft to pass in and out during earth's shadow because the flexibility of temperature acute variation initiation in the short time is attached Part vibration problem, therefore, the Orbital heat flux suffered by flexible accessory mainly considers solar radiation hot-fluid.

The heat transfer type that the in-orbit heat analysis of flexible accessory are related to is mainly conduction of heat and heat radiation.In-orbit thermoanalytical heat passes Leading the equation of heat conduction under fundamental equation and common radiation heat transfer is identical, but increased orbit computation, ascent calculates, outer The calculating of hot-fluid.

(3) equivalent heat load leads calculation module, limited using the spacecraft Rigid Base-flexible accessory coupled system set up Meta-model, the hot load of transient state temperature field on flexible accessory is equivalent to the joint load on flexible accessory；

Using the FEM (finite element) model of the spacecraft Rigid Base-flexible accessory coupled system set up, by wink on flexible accessory The hot load in state temperature field is equivalent to the joint load on flexible accessory.Boom, beam, plate shell is generally comprised in flexible accessory structure Deng component, need for suffered temperature change on these member units to be equivalent to time dependent nodal force load, so that Carry out the coupled system micro-vibration time-histories data analysis of next step.

To calculate the equivalent nodal force of temperature load using the initial strain method in Finite Element Method；Deformation according to unit Pattern, the temperature load of boom unit is equivalent to axial force, and the temperature load of beam element is equivalent to axial force and moment, plate shell list The temperature load of unit is equivalent to face internal force dough-making powder moment of face, completes Equivalent Calculation by the integration in unit；

The thermal coefficient of expansion of hypothesis boom unit material is α, and Young's moduluss are E, and the cross-sectional area of bar is A, the temperature of boom Degree change turns to T, then the axial equivalent load of boom is：

P_t=∫_AEαT dA

The thermal coefficient of expansion of hypothesis beam element material is α, and Young's moduluss are E, and the cross-sectional area of beam is A, and the temperature of beam becomes Turn to T, then beam element in addition to having axial equivalent load, also following equivalent moment load：

M_t=∫_AEαTy dA

Wherein y is the coordinate that the point on beam cross section is with respect to neutral axis；

Hypothesis thickness of shell elements is t, and area is A, and the thermal coefficient of expansion of material is α, and the temperature change in face is T, up and down The temperature difference of surface temperature is Δ T, is linear change along the element thickness direction temperature difference；Then shell unit is except there being the equivalent force in face [P_t] beyond, the also equivalent moment [M outside face_t]：

Wherein, [B_m] and [D_m] it is respectively the strain-displacement relation matrix of plane stress problem and constitutive matrix, [B_b] and [D_b] to be respectively be the Curvature Displacement Relationship matrix of plate bending problem and constitutive matrix；

The design cycle that the equivalent heat load of time varying temperature field leads calculation module is as follows：

A () reads the Data of Finite Element Model of flexible accessory, obtain nodal information, unit information, material section information；

B () reads the transient temperature data on each node of flexible accessory；

C () is circulated to each moment temperature data：

Each unit is circulated：

Calculate the equivalent nodal force of each unit；

Nodal force is overlapped by node；

Unit loop ends；

Moment loop ends.

(4) high accuracy model analyses module, carries out spacecraft center using the direct Superposition Method of iteration WYD-Ritz vector firm The model analyses of body-flexible accessory coupled system, obtain cycle and the vibration shape of coupled system, i.e. Method for Solving Generalized Eigenproblem K Φ=λ M Φ, wherein, K and M is respectively stiffness matrix and mass matrix, and λ is characterized value, and Φ is characterized vector；

Using packet shift frequency, mode error convergence criterion, the multinomial technology such as sparse Fast Direct Method of cell improve efficiency, Solving precision and reliability.The scale of solving a problem of current eigenvalue problem on common computer ten thousand degree of freedom up to 30 to 50, can Accurately solve up to hundreds of low side mode.Mode error convergence criterion makes the process of model analyses become steady.Test knot Fruit shows, mode error bit value indicative error more can reflect the precision that eigenvalue problem calculates.When calculating more multi-modal, mode Error should be used as first-selected convergence criterion.

The flow process of high accuracy model analyses module is as follows：

I. initialize：Determine block Ritz vector method block width q and generate step number r；Choose initial vector matrix Q₀；Set every time Move maximum iteration time I of axle_max

II. move axle：Calculate and move axle μ, should try to ensure that it is not eigenvalue；Decompose and move K- μM of axle stiffness matrix=LDL^T； Sturm sequence is checked

III. iteration I_maxSecondary, complete rear steering II

A () solves to k=0,1 .., r-1Then using willCharacteristic vector to convergence and Q₁,Q₂,…,Q_kMake M- orthonomalization, and form Q_k+1；

B () calculates K in Q=(Q₁,Q₂,…,Q_r) on projection, K^*=Q^TKQ；

C () solves qxr rank Eigenvalue Problem K^*Φ^*=Φ^*Λ^*；

D () forms new approximate characteristic vector X=Q Φ^*；

E () presses the convergence of mode error judgment eigenvalue and characteristic vector, the characteristic vector of removal convergence；

If f () has reached expected eigenvalue number, exit；Otherwise using not converged front q vector approximation as first Beginning vector carries out next iteration.

Model analyses need stiffness matrix and the mass matrix of input system, and output result is front some order mode state knots Really, as frequency, cycle, the vibration shape, mode error etc..

(5) high accuracy vibration analysis respond module, the analytic solutions based on Duhamel integration and mode superposition method carry out center The high accuracy Response Analysis of rigid body-flexible accessory coupled system, obtain the time-histories data result of flexible accessory；

High accuracy micro-vibration response analysis module is used for the kinetics equation of solving system, the solution based on Duhamel integration Analysis solution and mode superposition method are developed it is not necessary to access time integration step, can efficiently and accurately carry out Rigid Base- The thermic micro-vibration response analyses of flexible accessory coupled system.

Initially with mode superposition method, governing equations of motion is decoupled, obtain one group of uncoupled second order ordinary differential side Journey；Its solution is obtained by Duhamel integration；

Involved temperature equivalent time-histories load in the present invention is that the payload values engraving during by series of discrete are constituted, In the case of this piecewise linearity or broken line load, Duhamel integration can be amassed without using numerical value in the hope of analytic solutions Point, thus avoiding the select permeability of integration step.

After Modes Decoupling, the groundwork that structural response calculates is exactly solving equation：

The solution of above formula can be obtained by Duhamel integration：

Wherein a (t), b (t), h (t) are respectively the solution of following 3 problems：

The concrete form of solution depends on the size of damping ratio ξ；It is divided into three kinds of situations by the big I of damping ratio：Sub- damping (ξ <1), critical damping (ξ=1) and overdamp (ξ>1)；

Load function for piecewise linearity or broken line form；

In order to integrate conveniently, also introduce a variable relevant with speed：

Under sub- damping situation, orderThen non trivial solution is given by following two formulas：

Wherein：

For the situation of critical damping ξ=1, non trivial solution is：

Wherein

w₁=-a₄+a₁

w₂=-a₇-a₅+a₂

w₃=-a₉-2a₈-2a₆+2a₃；

For overdamp ξ>1 situation, non trivial solution is：

Wherein

After obtaining the above-mentioned modal coordinate solution of time-histories data, can get system motive power equation using modes superposition Solution.

(6) post-processing module, is to require to extract and show, export the result of calculation of correlation according to user, for example flexible attached The temperature variation curve of each node, equivalent load change curve, micro-vibration time-histories data curve on part.

The spaceborne flexible accessory thermic micro-vibration response Simulation Platform that the present invention provides, with high pointing accuracy spacecraft For engineering background, carry out the analysis and simulation research of spaceborne large-scale flexible adnexa thermal vibration of practical application and corresponding software for calculation Research and development, reached quick, effective acquisition large-scale flexible component thermic micro-vibration and its purpose with the response of celestial body coupled vibrations； Meanwhile, analysis emulation platform can promote spaceborne large-scale flexible component thermal deformation and the engineering of thermic micro-vibration simulation analysis technology to answer With verifying with examination, and drive Related Supporting Technologies progress, be follow-up New Satellite Project R＆D accumulation technology basis.

Brief description

Fig. 1 is the structural representation of the present invention；

Fig. 2 is the bar of flexible accessory structure, beam, film, the equivalent thermal force of Slab element；

Fig. 3 is the celestial body schematic diagram with dual sided battery battle array of embodiment；

Fig. 4 is cell array node side to light temperature cycle variation diagram (4 cycles) of embodiment；

Fig. 5 is cell array node side to light and the shady face temperature variation (1 cycle) of embodiment；

Fig. 6 is cell array node side to light and the shady face difference variation figure (1 cycle) of embodiment；

Fig. 7 is side to light and shady face temperature variation curve during the cell array entrance shade of embodiment；

Fig. 8 is that the cell array of embodiment enters side to light and shady face difference variation curve during shade；

Fig. 9 is that the cell array of embodiment goes out side to light and shady face temperature variation curve during shade；

Figure 10 is that the cell array of embodiment goes out side to light and shady face difference variation curve during shade；

Figure 11 is that the sun synchronization of embodiment enters ecliptic time section equivalent nodal force change curve；

Figure 12 is that the sun synchronization of embodiment enters ecliptic time section equivalent node moment change curve；

Figure 13 is that the sun synchronization of embodiment goes out ecliptic time section equivalent nodal force change curve；

Figure 14 is that the sun synchronization of embodiment goes out ecliptic time section equivalent node moment change curve；

Figure 15 is x, y of the cell panel outermost side edge mid-points of embodiment to displacement (sun synchronization, enter ground shadow)；

Figure 16 is the z of the cell panel outermost side edge mid-points of embodiment to displacement (sun synchronization, enter ground shadow)；

Figure 17 is x, y of the cell panel outermost side edge mid-points of embodiment to displacement (sun synchronization, go out ground shadow)；

Figure 18 is the z of the cell panel outermost side edge mid-points of embodiment to displacement (sun synchronization, go out ground shadow).

Specific embodiment

In order to further illustrate objects and advantages of the present invention, with concrete case, the present invention is made into one below in conjunction with the accompanying drawings The explanation of step.

As shown in figure 1, spaceborne flexible accessory thermic micro-vibration responds Simulation Platform, model mould including data input Block, in-orbit thermal analysis module, equivalent heat load lead calculation module, high accuracy model analyses module, high accuracy Response Analysis mould Block, post-processing module, modules are sequentially connected, the input exporting as next module of previous module.

As shown in Fig. 2 generally comprising the components such as boom, beam, plate shell in flexible accessory structure, need these member units Upper suffered temperature change is equivalent to time dependent nodal force load, to carry out the coupled system micro-vibration of next step Time-histories data is analyzed.

Taking the sun synchronous satellite with dual sided battery battle array as a example, as shown in figure 3, to spacecraft during turnover earth's shadow The micro-vibration response being led to due to temperature change has carried out Numerical Simulation.Cell array in this case is by six pieces of cell panels Composition, between be hinged, cell array is connected with nacelle beam.Classification of track adopts sun-synchronous orbit.

Using platform proposed by the present invention, implement numerical simulation according to the following steps：

(1) FEM (finite element) model of coupled system and in-orbit thermal model are set up using data input MBM.

(2) the in-orbit heat analysis of solar battery array are carried out using in-orbit thermal analysis module, by heat analysis such as heat conduction, radiation Calculating acquisition Satellite vapour image flexible structure in-orbit period is especially into and out time varying temperature field data during earth's shadow area.

From local time be 18:00 (entering ground shadow) starts, and makees the satellite sun geo-stationary orbit in-orbit heat analysis meter in 4 cycles Calculate, take certain representative node of cell panel side to light and shady face, its temperature variations is as shown in Figure 4.Cycle is 5496.057s, range of temperature is side to light -79.5 to 73.1 DEG C, shady face -80.2 to 63.6 DEG C, side to light and backlight Nearly 10 DEG C of the face temperature difference.

Take the data analysiss of a cycle, as shown in figure 5, with certain representative node (certain point near cell panel central authorities) As a example side to light and shady face temperature：From the local time 18:00 (t=0s) starts, and cell panel initially enters shadow region, temperature by Gradually reduce, but be clearly visible cooling area mid-early stage cooling extent greatly, the later stage gradually tends to relaxing；2200s about reach side to light About -79.5 DEG C of lowest temperature (shady face is -80.2 DEG C), temperature raises suddenly afterwards, initially enters area of illumination, and in 4180s Left and right reaches 73.1 DEG C of side to light maximum temperature (shady face is 63.6 DEG C).From in figure it can also be seen that, when in area of illumination, battery Plate side to light is substantially higher relative to shady face temperature.

Fig. 6 is the difference variation figure of this node side to light and shady face.From the results, it was seen that in area of illumination, temperature approach It is held essentially constant, close to 11.5 DEG C about；In shadow region, there is no the temperature difference, close to 1 DEG C；But in this two regions In very short tens seconds of junction, there is acute variation in the temperature difference.

For in the present embodiment, major concern cell array temperature change in local time's section in turnover earth's shadow area is drawn The heat-driven oscillation rising, therefore take the time varying temperature field data of following two time periods to lead calculation to be applied to the equivalent of follow-up temperature loading And Response Analysis：(1) cell array enters local time's section of shade：5800s to 7000s (6000s about satellite second The individual cycle initially enters shade), the temperature on typical node and difference variation are shown in Fig. 7 and Fig. 8；(2) cell array goes out the office of shade Portion's time period：7600s to 8000s (7680s about start shade), the temperature on typical node and difference variation such as Fig. 9 and Shown in Figure 10.

(3) lead calculation module using equivalent heat load to be equivalent to be applied to too by the time varying temperature field data that previous step obtains Hot load on positive cell array flexible structure node；The heat of right side ragged edge cell panel angle point in model is given in Figure 11～14 Load nodal force and the equivalent result of moment, the situation in left side can be obtained by symmetry.

(4) using high accuracy model analyses module, model analyses are carried out to Coupling System of Flexible Structures And Rigid Body model；Whole spacecraft is made Centered on rigid body-flexible accessory coupled system, only constrain three translational degree of freedom of central point.The thermal deformation of cell array is except face Outside the bending of outer Z-direction, also in-plane deformation X, to the deformation with Y-direction, therefore, calculates the vibration shape intercepting during vibration time-histories data The vibration shape in these three fully many directions should be included.Because X is very high to the corresponding frequency of the vibration shape in face, in order to ensure response point The precision of analysis, has calculated 200 order mode states altogether.Front 3 mode are rigid body mode, and the cycle of the 4th～6 order mode state is respectively：13.1 Second, 3.87 seconds and 2.30 seconds.

(5) utilize high accuracy Response Analysis module, Coupling System of Flexible Structures And Rigid Body model is carried out with the time-histories of thermic micro-vibration Response analyses.The dynamic respond that Figure 15～18 sets forth cell panel outermost side edge mid-points during turnover earth's shadow is bent Line.

Interpretation of result：

For sun synchronous satellite during turnover earth's shadow, the displacement of the lines of X-direction is maximum, next to that the line of Z-direction Displacement, the displacement of the lines value of Y-direction is minimum.The displacement of the lines response of wherein X and Y-direction is quasi-static, and oscillation phenomenon does not occur； The displacement of the lines of Z-direction then has less fluctuation, and its reason is sun synchronous satellite when passing in and out earth's shadow area, thermal response time (20 seconds about) are closer to structural cycle (13 seconds about), thus inducing thermal vibration.

Claims (5)

1. spaceborne flexible accessory thermic micro-vibration response Simulation Platform it is characterised in that：Including data input MBM, In-orbit thermal analysis module, equivalent heat load lead calculation module, high accuracy model analyses module, high accuracy Response Analysis module, Post-processing module, modules are sequentially connected, the input exporting as next module of previous module；

(1) data input MBM, sets up spacecraft Rigid Base-flexibility using interactive mode with reference to automatic conversion mode attached The FEM (finite element) model of part coupled system and in-orbit thermal model；

(2) in-orbit thermal analysis module, using the spacecraft Rigid Base-flexible accessory coupled system in-orbit heat analysis mould set up Type, carries out the in-orbit heat analysis of Flexible appendages of spacecraft, obtains the transient state temperature field on flexible accessory；

(3) equivalent heat load leads calculation module, using the finite element mould of the spacecraft Rigid Base-flexible accessory coupled system set up Type, the hot load of transient state temperature field on flexible accessory is equivalent to the joint load on flexible accessory；

(4) high accuracy model analyses module, using iteration WYD-Ritz vector, directly Superposition Method carries out spacecraft Rigid Base-soft Property adnexa coupled system model analyses, obtain cycle of coupled system and the vibration shape, i.e. Method for Solving Generalized Eigenproblem K Φ=λ M Φ, wherein, K and M is respectively stiffness matrix and mass matrix, and λ is characterized value, and Φ is characterized vector；

(5) it is firm that high accuracy vibration analysis respond module, the analytic solutions based on Duhamel integration and mode superposition method carry out center The high accuracy Response Analysis of body-flexible accessory coupled system, obtain the time-histories data result of flexible accessory；

(6) post-processing module：The temperature variation curve extract and show, exporting each node of flexible accessory, equivalent load change are bent Line, time-histories data curve result of calculation.

2. spaceborne flexible accessory thermic micro-vibration response Simulation Platform according to claim 1 it is characterised in that：Institute The equivalent heat load stated leads calculation module, to calculate the equivalent node of temperature load using the initial strain method in Finite Element Method Power；According to the deformation pattern of unit, the temperature load of boom unit is equivalent to axial force, and the temperature load of beam element is equivalent to axle To power and moment, the temperature load of Shell Finite Element is equivalent to face internal force dough-making powder moment of face, is completed by the integration in unit equivalent Calculate；

The thermal coefficient of expansion of hypothesis boom unit material is α, and Young's moduluss are E, and the cross-sectional area of bar is A, and the temperature of boom becomes Turn to T, then the axial equivalent load of boom is：

P_t=∫_AEαTdA

The thermal coefficient of expansion of hypothesis beam element material is α, and Young's moduluss are E, and the cross-sectional area of beam is A, and the temperature change of beam is T, then beam element in addition to having axial equivalent load, also following equivalent moment load：

M_t=∫_AEαTydA

Wherein y is the coordinate that the point on beam cross section is with respect to neutral axis；

Hypothesis thickness of shell elements is t, and area is A, and the thermal coefficient of expansion of material is α, and the temperature change in face is T, upper and lower surface The temperature difference of temperature is Δ T, is linear change along the element thickness direction temperature difference；Then shell unit is except there being the equivalent force [P in face_t] with Outward, the also equivalent moment [M outside face_t]：

$\&lsqb;P_t\&rsqb;={\&Integral;}_A{\&lsqb;B_m\&rsqb;}^T\&lsqb;D_m\&rsqb;\left(\begin{array}{c}\mathrm{\&alpha;}T\\ \mathrm{\&alpha;}T\\ 0\end{array}\right)tdA$

$\&lsqb;M_t\&rsqb;={\&Integral;}_A{\&lsqb;B_b\&rsqb;}^T\&lsqb;D_b\&rsqb;\left(\begin{array}{c}0.5\mathrm{\&alpha;}\mathrm{\&Delta;}T\\ 0.5\mathrm{\&alpha;}\mathrm{\&Delta;}T\\ 0\end{array}\right)dA$

Wherein, [B_m] and [D_m] it is respectively the strain-displacement relation matrix of plane stress problem and constitutive matrix, [B_b] and [D_b] to be respectively be the Curvature Displacement Relationship matrix of plate bending problem and constitutive matrix；

3. spaceborne flexible accessory thermic micro-vibration according to claim 1 and 2 responds Simulation Platform, and its feature exists In：The flow process that described equivalent heat load leads calculation module is as follows：

A () reads the Data of Finite Element Model of flexible accessory, obtain nodal information, unit information, material section information；

B () reads the transient temperature data on each node of flexible accessory；

C () is circulated to each moment temperature data：

Each unit is circulated：

Calculate the equivalent nodal force of each unit；

Nodal force is overlapped by node；

Unit loop ends；

Moment loop ends.

4. spaceborne flexible accessory thermic micro-vibration response Simulation Platform according to claim 1 it is characterised in that：Institute The flow process of the high accuracy model analyses module stated is as follows：

I. initialize：Determine block Ritz vector method block width q and generate step number r；Choose initial vector matrix Q₀；Set and move axle every time Maximum iteration time I_max

II. move axle：Calculate and move axle μ, should try to ensure that it is not eigenvalue；Decompose and move K- μM of axle stiffness matrix=LDL^T；Sturm Sequence is checked

III. iteration I_maxSecondary, complete rear steering II

A () solves to k=0,1 .., r-1Then using willCharacteristic vector to convergence and Q₁, Q₂,…,Q_kMake M- orthonomalization, and form Q_k+1；

B () calculates K in Q=(Q₁,Q₂,…,Q_r) on projection, K^*=Q^TKQ；

C () solves qxr rank Eigenvalue Problem K^*Φ^*=Φ^*Λ^*；

D () forms new approximate characteristic vector X=Q Φ^*；

E () presses the convergence of mode error judgment eigenvalue and characteristic vector, the characteristic vector of removal convergence；

If f () has reached expected eigenvalue number, exit；Otherwise using not converged front q vector approximation as initial to Amount carries out next iteration.

5. spaceborne flexible accessory thermic micro-vibration response Simulation Platform according to claim 1 it is characterised in that：Institute The high accuracy vibration analysis respond module stated, decouples to governing equations of motion initially with mode superposition method, obtains one group Uncoupled second order ordinary differential equation；

After Modes Decoupling, carry out solving equation：

$\stackrel{\&CenterDot;\&CenterDot;}{u}+2\mathrm{\&omega;}\mathrm{\&xi;}\stackrel{\&CenterDot;}{u}+{\mathrm{\&omega;}}^{2}u=p\left(t\right)$

The solution of above formula can be obtained by Duhamel integration：

$u\left(t\right)=u\left(0\right)a\left(t\right)+\stackrel{\&CenterDot;}{u}\left(0\right)b\left(t\right)+\underset{0}{\overset{t}{\&Integral;}}p\left(\mathrm{\&tau;}\right)h(t-\mathrm{\&tau;})d\mathrm{\&tau;}$

Wherein a (t), b (t), h (t) are respectively the solution of following 3 problems：

$\left\{\begin{array}{c}\stackrel{\&CenterDot;\&CenterDot;}{u}+2\mathrm{\&omega;}\mathrm{\&xi;}\stackrel{\&CenterDot;}{u}+{\mathrm{\&omega;}}^{2}u=0\\ u\left(0\right)=1,\stackrel{\&CenterDot;}{u}\left(0\right)=0\end{array}\right.$

$\left\{\begin{array}{c}\stackrel{\&CenterDot;\&CenterDot;}{u}+2\mathrm{\&omega;}\mathrm{\&xi;}\stackrel{\&CenterDot;}{u}+{\mathrm{\&omega;}}^{2}u=0\\ u\left(0\right)=0,\stackrel{\&CenterDot;}{u}\left(0\right)=1\end{array}\right.$

$\left\{\begin{array}{c}\stackrel{\&CenterDot;\&CenterDot;}{u}+2\mathrm{\&omega;}\mathrm{\&xi;}\stackrel{\&CenterDot;}{u}+{\mathrm{\&omega;}}^{2}u=\mathrm{\&delta;}\left(t\right)\\ u\left(0\right)=0,\stackrel{\&CenterDot;}{u}\left(0\right)=0\end{array}\right.;$

The concrete form of solution depends on the size of damping ratio ξ；It is divided into three kinds of situations by the big I of damping ratio：ξ<1 is sub- damping, ξ=1 is critical damping, ξ>1 is overdamp；

Load function for piecewise linearity or broken line form；

In order to integrate conveniently, also introduce a variable relevant with speed：

$v\left(t\right)=\frac{\stackrel{\&CenterDot;}{u}\left(t\right)+\mathrm{\&xi;}\mathrm{\&omega;}u\left(t\right)}{{\mathrm{\&omega;}}_D}$

Under sub- damping situation, orderThen non trivial solution is given by following two formulas：

$u(t_i+\mathrm{\&tau;})=\frac{1}{{\mathrm{\&omega;}}_D}\&lsqb;-a_{t_i}{p}_1+(a_{t_i}t+b_{t_i})k_1\&rsqb;+u_{t_i}{a}_{10}+v_{t_i}{a}_9$

$v(t_i+\mathrm{\&tau;})=\frac{1}{{\mathrm{\&omega;}}_D}\&lsqb;-a_{t_i}{p}_2+(a_{t_i}t+b_{t_i})k_2\&rsqb;-u_{t_i}{a}_9+v_{t_i}{a}_{10}$

Wherein：

${\mathrm{\&omega;}}_R=1+{\left(\frac{\mathrm{\&omega;}\mathrm{\&xi;}}{{\mathrm{\&omega;}}_D}\right)}^2$

$\left\{\begin{array}{c}{a}_1=\frac{1}{{\mathrm{\&omega;}}_D}{e}^{-\mathrm{\&omega;}\mathrm{\&xi;}\mathrm{\&tau;}}{\mathrm{sin\&omega;}}_D\mathrm{\&tau;},a_2=\frac{1}{{\mathrm{\&omega;}}_D}(e^{-\mathrm{\&omega;}\mathrm{\&xi;}\mathrm{\&tau;}}{\mathrm{cos\&omega;}}_D\mathrm{\&tau;}-1),a_3=\frac{\mathrm{\&omega;}\mathrm{\&xi;}}{{{\mathrm{\&omega;}}_D}^2}{e}^{-\mathrm{\&omega;}\mathrm{\&xi;}\mathrm{\&tau;}}{\mathrm{sin\&omega;}}_D\mathrm{\&tau;}\\ a_4=\frac{\mathrm{\&omega;}\mathrm{\&xi;}}{{{\mathrm{\&omega;}}_D}^2}(e^{-\mathrm{\&omega;}\mathrm{\&xi;}\mathrm{\&tau;}}{\mathrm{cos\&omega;}}_D\mathrm{\&tau;}-1),a_5=\frac{1}{{\mathrm{\&omega;}}_D}{\mathrm{\&tau;e}}^{-\mathrm{\&omega;}\mathrm{\&xi;}\mathrm{\&tau;}}{\mathrm{sin\&omega;}}_D\mathrm{\&tau;}\\ a_6=\frac{1}{{\mathrm{\&omega;}}_D}{\mathrm{\&tau;e}}^{-\mathrm{\&omega;}\mathrm{\&xi;}\mathrm{\&tau;}}{\mathrm{cos\&omega;}}_D\mathrm{\&tau;},a_7=\frac{\mathrm{\&omega;}\mathrm{\&xi;}}{{{\mathrm{\&omega;}}_D}^2}{\mathrm{\&tau;e}}^{-\mathrm{\&omega;}\mathrm{\&xi;}\mathrm{\&tau;}}{\mathrm{sin\&omega;}}_D\mathrm{\&tau;}\\ a_8=\frac{\mathrm{\&omega;}\mathrm{\&xi;}}{{{\mathrm{\&omega;}}_D}^2}{\mathrm{\&tau;e}}^{-\mathrm{\&omega;}\mathrm{\&xi;}\mathrm{\&tau;}}{\mathrm{cos\&omega;}}_D\mathrm{\&tau;},a_9=e^{-\mathrm{\&omega;}\mathrm{\&xi;}\mathrm{\&tau;}}{\mathrm{sin\&omega;}}_D\mathrm{\&tau;},a_{10}=e^{-\mathrm{\&omega;}\mathrm{\&xi;}\mathrm{\&tau;}}{\mathrm{cos\&omega;}}_D\mathrm{\&tau;}\\ a_{11}=2\mathrm{\&omega;}\mathrm{\&xi;},a_{12}={\mathrm{\&omega;}}^2,a_{13}={\mathrm{\&omega;}}_D,a_{14}=\mathrm{\&omega;}\mathrm{\&xi;}\end{array}\right.$

$k_1=\frac{-a_2-a_3}{{\mathrm{\&omega;}}_R},k_2=\frac{-a_4+a_1}{{\mathrm{\&omega;}}_R}$

$p_1=\frac{-a_6+\frac{1}{{\mathrm{\&omega;}}_D}{k}_2-a_7+\frac{\mathrm{\&omega;}\mathrm{\&xi;}}{{{\mathrm{\&omega;}}_D}^2}{k}_1}{{\mathrm{\&omega;}}_R},p_2=\frac{a_5-\frac{1}{{\mathrm{\&omega;}}_D}{k}_1-a_8+\frac{\mathrm{\&omega;}\mathrm{\&xi;}}{{{\mathrm{\&omega;}}_D}^2}{k}_2}{{\mathrm{\&omega;}}_R};$

For the situation of critical damping ξ=1, non trivial solution is：

$u(t_i+\mathrm{\&tau;})=-w_3{a}_{t_i}+w_2(a_{t_i}\mathrm{\&tau;}+b_{t_i})+a_{10}{u}_{t_i}+a_7{a}_{12}{v}_{t_i}$

$v(t_i+\mathrm{\&tau;})=a_1\&lsqb;-a_{t_i}{w}_2+(a_{t_i}\mathrm{\&tau;}+b_{t_i})w_1\&rsqb;+v_{t_i}{a}_{10}$

Wherein

$\left\{\begin{array}{c}{a}_1=\frac{1}{\mathrm{\&omega;}},a_2=\frac{1}{{\mathrm{\&omega;}}^2},a_3=\frac{1}{{\mathrm{\&omega;}}^3}\\ a_4=\frac{1}{\mathrm{\&omega;}}{e}^{-\mathrm{\&xi;}\mathrm{\&omega;}\mathrm{\&tau;}},a_5=\frac{1}{{\mathrm{\&omega;}}^2}{e}^{-\mathrm{\&xi;}\mathrm{\&omega;}\mathrm{\&tau;}},a_6=\frac{1}{{\mathrm{\&omega;}}^3}{e}^{-\mathrm{\&xi;}\mathrm{\&omega;}\mathrm{\&tau;}}\\ a_7=\frac{1}{\mathrm{\&omega;}}{\mathrm{\&tau;e}}^{-\mathrm{\&xi;}\mathrm{\&omega;}\mathrm{\&tau;}},a_8=\frac{1}{{\mathrm{\&omega;}}^2}{\mathrm{\&tau;e}}^{-\mathrm{\&xi;}\mathrm{\&omega;}\mathrm{\&tau;}},a_9=\frac{1}{\mathrm{\&omega;}}{\mathrm{\&tau;}}^2{e}^{-\mathrm{\&xi;}\mathrm{\&omega;}\mathrm{\&tau;}}\\ a_{10}=e^{-\mathrm{\&xi;}\mathrm{\&omega;}\mathrm{\&tau;}},a_{11}=2\mathrm{\&xi;}\mathrm{\&omega;},a_{12}={\mathrm{\&omega;}}^2,a_{13}=1.0,a_{14}=\mathrm{\&xi;}\mathrm{\&omega;}\end{array}\right.$

w₁=-a₄+a₁

w₂=-a₇-a₅+a₂

w₃=-a₉-2a₈-2a₆+2a₃；

For overdamp ξ>1 situation, non trivial solution is：

$u(t_i+\mathrm{\&tau;})=u_{t_i}{a}_{10}+v_{t_i}{a}_9+\frac{1}{\widehat{\mathrm{\&omega;}}}\&lsqb;-p_1{a}_{t_i}+(a_{t_i}\mathrm{\&tau;}+b_{t_i})k_1\&rsqb;$

$v(t_i+\mathrm{\&tau;})=-u_{t_i}{a}_9+v_{t_i}{a}_{10}+\frac{1}{\widehat{\mathrm{\&omega;}}}\&lsqb;-p_2{a}_{t_i}+(a_{t_i}\mathrm{\&tau;}+b_{t_i})k_2\&rsqb;$

Wherein

$\widehat{\mathrm{\&omega;}}=\mathrm{\&omega;}\sqrt{{\mathrm{\&xi;}}^2-1}$

$\left\{\begin{array}{c}{\mathrm{\&omega;}}_R=1-{\left(\frac{\mathrm{\&omega;}\mathrm{\&xi;}}{\widehat{\mathrm{\&omega;}}}\right)}^2,a_1=\frac{1}{\widehat{\mathrm{\&omega;}}}{e}^{-\mathrm{\&omega;}\mathrm{\&xi;}\mathrm{\&tau;}}sh\widehat{\mathrm{\&omega;}}\mathrm{\&tau;},a_2=\frac{1}{\widehat{\mathrm{\&omega;}}}(e^{-\mathrm{\&omega;}\mathrm{\&xi;}\mathrm{\&tau;}}ch\widehat{\mathrm{\&omega;}}\mathrm{\&tau;}-1)\\ a_3=\frac{\mathrm{\&omega;}\mathrm{\&xi;}}{{\widehat{\mathrm{\&omega;}}}^2}{e}^{-\mathrm{\&omega;}\mathrm{\&xi;}\mathrm{\&tau;}}sh\widehat{\mathrm{\&omega;}}\mathrm{\&tau;},a_4=\frac{\mathrm{\&omega;}\mathrm{\&xi;}}{{\widehat{\mathrm{\&omega;}}}^2}(e^{-\mathrm{\&omega;}\mathrm{\&xi;}\mathrm{\&tau;}}ch\widehat{\mathrm{\&omega;}}\mathrm{\&tau;}-1),a_5=\frac{1}{\widehat{\mathrm{\&omega;}}}{\mathrm{\&tau;e}}^{-\mathrm{\&omega;}\mathrm{\&xi;}\mathrm{\&tau;}}sh\widehat{\mathrm{\&omega;}}\mathrm{\&tau;}\\ a_6=\frac{1}{\widehat{\mathrm{\&omega;}}}{\mathrm{\&tau;e}}^{-\mathrm{\&omega;}\mathrm{\&xi;}\mathrm{\&tau;}}ch\widehat{\mathrm{\&omega;}}\mathrm{\&tau;},a_7=\frac{\mathrm{\&omega;}\mathrm{\&xi;}}{{\widehat{\mathrm{\&omega;}}}^2}{\mathrm{\&tau;e}}^{-\mathrm{\&omega;}\mathrm{\&xi;}\mathrm{\&tau;}}sh\widehat{\mathrm{\&omega;}}\mathrm{\&tau;},a_8=\frac{\mathrm{\&omega;}\mathrm{\&xi;}}{{\widehat{\mathrm{\&omega;}}}^2}{\mathrm{\&tau;e}}^{-\mathrm{\&omega;}\mathrm{\&xi;}\mathrm{\&tau;}}ch\widehat{\mathrm{\&omega;}}\mathrm{\&tau;}\\ a_9=e^{-\mathrm{\&omega;}\mathrm{\&xi;}\mathrm{\&tau;}}sh\widehat{\mathrm{\&omega;}}\mathrm{\&tau;},a_{10}=e^{-\mathrm{\&omega;}\mathrm{\&xi;}\mathrm{\&tau;}}ch\widehat{\mathrm{\&omega;}}\mathrm{\&tau;},a_{11}=2\mathrm{\&omega;}\mathrm{\&xi;}\\ a_{12}={\mathrm{\&omega;}}^2,a_{13}=\widehat{\mathrm{\&omega;}},a_{14}=\mathrm{\&omega;}\mathrm{\&xi;}\end{array}\right.$

$k_1=\underset{0}{\overset{\mathrm{\&tau;}}{\&Integral;}}{e}^{-\mathrm{\&omega;}\mathrm{\&xi;}y}sh\widehat{\mathrm{\&omega;}}ydy=\frac{a_2+a_3}{{\mathrm{\&omega;}}_R}$

$k_2=\underset{0}{\overset{\mathrm{\&tau;}}{\&Integral;}}{e}^{-\mathrm{\&omega;}\mathrm{\&xi;}y}ch\widehat{\mathrm{\&omega;}}ydy=\frac{a_4+a_1}{{\mathrm{\&omega;}}_R}$

$p_1=\underset{0}{\overset{\mathrm{\&tau;}}{\&Integral;}}{\mathrm{ye}}^{-\mathrm{\&omega;}\mathrm{\&xi;}y}sh\widehat{\mathrm{\&omega;}}ydy=\frac{a_6-\frac{1}{\widehat{\mathrm{\&omega;}}}{k}_2+a_7-\frac{\mathrm{\&omega;}\mathrm{\&xi;}}{{\widehat{\mathrm{\&omega;}}}^2}{k}_1}{{\mathrm{\&omega;}}_R}$

$p_2=\underset{0}{\overset{\mathrm{\&tau;}}{\&Integral;}}{\mathrm{ye}}^{-\mathrm{\&omega;}\mathrm{\&xi;}y}ch\widehat{\mathrm{\&omega;}}ydy=\frac{a_5-\frac{1}{\widehat{\mathrm{\&omega;}}}{k}_1+a_8-\frac{\mathrm{\&omega;}\mathrm{\&xi;}}{{\widehat{\mathrm{\&omega;}}}^2}{k}_2}{{\mathrm{\&omega;}}_R};$

After obtaining the above-mentioned modal coordinate solution of time-histories data, can get system motive power equation using modes superposition Solution.