CN106294975B - A kind of girder structure free vibration analysis method based on reduced-order model - Google Patents
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Abstract
The invention belongs to aerospace complexity beam type structural elements calculating fields, provide a kind of girder structure free vibration analysis method based on reduced-order model, comprising the following steps: 1) Mass matrix and Stiffness Matrix of fine structure are obtained using finite element software；2) using polynomial interpolating function construction decrement base vector, former complicated girder structure depression of order is realized；3) kinetics equation for solving reduced-order model, obtains the overall frequency and part low order frequency of structure.This method constructs decrement base vector by polynomial interpolating function, and the node in labyrinth finite element model is condensed to cross-section centroid in the form of positional displacement interpolation, realizes original structure depression of order, and the computational accuracy of reduced-order model can be controlled by polynomial order.The invention has the benefit that the experience independent of user, reduces the different adverse effects to computational accuracy selected due to master and slave freedom degree；It is not required to a large amount of matrix manipulation, improves the computational efficiency of model reduction；Obtained reduced-order model is applied widely.
Description
Technical field
The invention belongs to aerospace girder structure component calculating fields, are related to a kind of girder structure based on reduced-order model
Free vibration analysis method.
Background technique
With the development of computational science and technology, computer disposal speed and storage capacity are continuously improved, but need simultaneously
The engineering of calculating and the scale of problem in science and complexity are also being continuously improved.It, can be with for the static problems of complex engineering
Foundation is on a grand scale, grid is very close, at large describe the finite element model of CONSTRUCTED SPECIFICATION and carries out structural analysis to it, still
Due to the calculation amount of dynamic structural analysis several amount ranks bigger than static analysis, as a consequence it is hardly possible to be tied using such model
Structure kinematic analysis.In addition, designing initial stage, deformation characteristic of the designer more concerned with entire component, excessive consideration structure in structure
Details interferes the understanding to overall performance sometimes.Therefore, it in the initial design stage, finds one and suitably contains less freedom
The reduced-order model substitution refined model of degree, which completes the design of structure and optimization, to be very important.
In recent years, dynamic model depression of order is theoretical and application has been achieved for huge progress, according to different thinkings, can incite somebody to action
Common Structural Dynamic Model order reducing method is divided into three classes: agent model method, physics order reducing method, structure equivalent method.Generation
Reason model, which refers to the mathematic(al) representation of a small calculation amount, replaces original labyrinth, but its calculated result and high-precision mould
The calculated result of type is close.Commonly used agent model approximation method has response surface model, Kriging model, radial basis function
Model, artificial nerve network model etc..But the physical significance for being lost original model using agent model is not easy to original knot
The parameter of structure adjusts, in addition, the sample point needed is more when design variable quantity is more, the construction of agent model need to be by multiple
Modification, computational efficiency are lower.Physics reduced-order model utilizes the mathematics or mechanical characteristics of original structure finite element model, selects a combination
Suitable decrement base vector, by large-scale Structural Dynamics depression of order.Common physics order reducing method has: Guyan static concentration
Method improves polycondensation systems approach (IRS), modal synthesis method etc..Most of physics order reducing method be it is relevant with structure, work as original structure
When some parameters (boundary condition, material property) of model change, new reduced-order model, and these depression of order moulds need to be re-established
The Successful utilization of type relies on the experience of user mostly.Structure equivalent method is the master using the equivalent labyrinth of simple structure
Feature is wanted, the mechanical model being simplified.Common equivalent structure method has: asymptotic homogenization, RVE method etc., should
Method is directed to specific structure, it is desirable that simple structure can reflect the mechanical response of labyrinth by correcting certain parameter approximations.
Lateral large-scale girder structure is noticeably greater than for this kind of longitudinal size of rocket, domestic and foreign scholars propose some new
Physics order reducing method: local rigid body dynamic model order reducing method, this method is based on fine finite element, by structure
It is divided into several synchronism regions and uses the real displacement in the approximate each region of rigid body mode, obtains one group of decrement basal orientation
Amount, establishes the higher reduced-order model of precision on this basis；Based on the model order reducing method of beam plane cross-section assumption, this method will be tied
Finite element node on each section of structure agglomerates to the centroid in the section by being displaced transition matrix, is used for quickly establish
The decrement base vector of model reduction, and it is directed to the structure of big opening, obtain indicating the warpage of section loss rates deformation with numerical method
Base vector compensates for the deficiency of plane cross-section assumption；But the reduced-order model that above two method obtains is only capable of obtaining the entirety of structure
Frequency.The displacement of structure finite element node is expressed as the more of beam element modal displacement by high-order beam model order reducing method, this method
Formula function, and derive using the principle of virtual work Stiffness Matrix and Mass matrix of reduced-order model, but the application of this method need it is a large amount of
Matrix calculate, and cannot utilize existing finite element software, limit the application range of this method.
Therefore, the finite element model based on existing girder structure, it is low to establish a calculation amount, being capable of quick obtaining beam type knot
The entirety of structure and the reduced-order model of part low order frequency, are still focus on research direction.
Summary of the invention
It is low that structure is lost after present invention mainly solves existing model order reducing methods complicated for operation, computationally intensive, model reduction
The problem of order frequency, proposes a kind of girder structure free vibration analysis method based on reduced-order model, and this method is easy to operate, fills
Divide the finite element model information using former girder structure, constructs decrement base vector, realization beam type knot in conjunction with polynomial interpolating function
The depression of order of structure.Reduced-order model can obtain the overall frequency and part low order frequency of girder structure, and computational accuracy can be by multinomial
Formula order is controlled.
In order to achieve the above object, the technical solution of the present invention is as follows:
A kind of girder structure free vibration analysis method based on reduced-order model, specifically includes the following steps:
The first step is handled girder structure using finite element software, obtains the Mass matrix M and Stiffness Matrix of girder structure
K。
Second step constructs decrement base vector using polynomial interpolating function, carries out model reduction to girder structure.
2.1) polynomial interpolating function is utilized, by any finite element on the section of girder structure in the form of positional displacement interpolation
The displacement of node is condensed at the Ω centroid of section；
Girder structure uses axially as the rectangular coordinate system of x-axis forward direction, and any finite element node j passes through this section on the Ω of section
The column u that generalized displacement indicates at the centroid i of facejAre as follows:
uj=Rjqi (1)
Wherein, ujIndicate the motion vector of upper j-th of finite element node of section Ω, qiIndicate the broad sense at section Ω centroid i
Motion vector, RjIndicate the displacement transition matrix of j point；
ujExpanded form are as follows:
Wherein, { ujx ujy ujz}TThree displacement components for being finite element node j at rectangular coordinate system Oxyz, { qixτ
qiyτ qizτ}TThe generalized displacement component for being cross-section centroid i at rectangular coordinate system Oxyz, FτjFor polynomial interpolating function expression
Formula, repeating subscript τ indicates summation, and W is multinomial item number.
2.2) finite element node all on the Ω of section agglomerates at the centroid i of section Ω, obtains such as formula (3) institute
The displacement dress shown changes relational expression:
Ui=(u1..., us)T=Tiqi=(R1..., Rs)Tqi (3)
Wherein, UiIndicate the motion vector of s finite element node in the Ω of section, TiIndicate that square is converted in the displacement of section Ω
Battle array.
2.3) by entire girder structure, in axial direction subdivision is p section, then by the displacement transformational relation on p section
Formula is assembled into decrement base vector T, realizes the depression of order of former girder structure.
Specifically, the decrement base vector T that the displacement conversion relational expression on p section is assembled into are as follows:
Wherein, U indicate total finite element modal displacement vector, be 3n × 1 column vector (n be girder structure from
By degree), it is the column vector of 3pW × 1, U that Q, which is the finite element modal displacement vector of model after depression of order,pIt indicates in p-th of section
The motion vector of node, TpIndicate the displacement transition matrix of p-th of section interior nodes, size is extended to 3n × 3W, qpIndicate pth
Generalized displacement at a cross-section centroid, size are 3W × 1.
2.4) do not consider that damping effect, the finite element governing equation of former girder structure analysis indicate are as follows:
Wherein, M, K are the square matrix of 3n × 3n, are the Mass matrix and Stiffness Matrix of original structure respectively, U,It is 3n dimensional vector,
It is displacement structure and acceleration responsive vector respectively, 3n dimensional vector F is the load acted in structure.
2.5) displacement transfer equation (4) is introduced in the finite element governing equation shown in formula (5), and same on equation both sides
Shi Zuocheng TT, kinetics equation after obtaining depression of order:
Wherein, MR=TTMT、KR=TTKT is the Mass matrix and Stiffness Matrix of reduced-order model, M respectivelyR、KRFor 3pW × 3pW's
Square matrix, Q,It is 3pW dimensional vector, is displacement and the acceleration responsive vector of reduced-order model respectively, due to W < < s, so depression of order
The freedom degree sharp fall of model, FR=TTF is the load vectors that 3pW ties up reduced-order model.
Third step utilizes the Mass matrix M of girder structure reduced-order modelRWith Stiffness Matrix KR, after calculating depression of order by formula (7)
The frequency and the vibration shape of girder structure.
Specifically, Structural Dynamics generalized eigenvalue equation corresponding with formula (6) is solved:
Wherein, λ,The respectively feature value vector of reduced-order model and the corresponding vibration shape,For former beam type knot
The vibration shape of structure.
A kind of girder structure dynamic model order reducing method provided by the invention, for existing model order reducing method calculation amount
Greatly, complicated for operation, lose original structure low order frequency information the disadvantages of, first with finite element software obtain girder structure quality
Battle array and Stiffness Matrix.Then, decrement base vector is constructed by polynomial interpolating function, has girder structure in the form of positional displacement interpolation
Node in limit meta-model is condensed to cross-section centroid, realizes original structure depression of order.Finally, the kinetics equation of reduced-order model is solved,
Obtain the overall frequency and part low order frequency of girder structure.
Experience of the present invention independent of user reduces the difference due to the selection of master and slave freedom degree to computational accuracy
Adverse effect；A large amount of matrix manipulation is not needed, the computational efficiency of model reduction is improved；Obtained reduced-order model is applicable in model
It encloses extensively, need to only apply different edge-restraint conditions on the reduced-order model under freedom-free state, so that it may quickly calculate a variety of
The frequency values of the original structure of different boundary constraint condition.The computational efficiency of girder structure can be improved in the present invention, reduction is initially set
The calculating cost of meter is extremely expected to become complicated girder structure in the aerospace fields such as China's carrier rocket, Missile Design
One of dynamic model order reducing method.
Detailed description of the invention
Fig. 1 (a) is elongated smooth barrel structure schematic diagram.
Fig. 1 (b) is the elongated barrel structure schematic diagram of the reinforcement containing grid.
Fig. 2 is girder structure dynamic model depression of order schematic diagram.
Fig. 3 is the implementation flow chart of girder structure dynamic model order reducing method.
Fig. 4 is cylindrical shell structure and schematic cross-section.
Specific embodiment
To keep the technical problems solved, the adopted technical scheme and the technical effect achieved by the invention clearer, below
The present invention is described in further detail in conjunction with the embodiments.
Fig. 3 is the implementation flow chart of girder structure dynamic model order reducing method provided in an embodiment of the present invention.Fig. 4 is cylinder
The schematic diagram of shell structure, radius R=1000mm, length L=15000mm, skin thickness t=2.0mm, elasticity modulus of materials E=
73GPa, Poisson's ratio υ=0.3, density p=2.7E-6kg/mm3.Two fixed ends, girder structure finite element model use entity mould
Type, axial to divide p=40 unit, circumferential direction divides 82 units, number of nodes n=6560.
The first step is handled girder structure using finite element software, obtains the Mass matrix M and Stiffness Matrix of girder structure
K.The present invention carries out model reduction for girder structure.Specifically, girder structure can have different structure type.Fig. 1 a-b
For part girder structure schematic diagram, Fig. 1 a is elongated smooth barrel structure schematic diagram, and Fig. 1 b is that the elongated barrel structure of the reinforcement containing grid shows
It is intended to, referring to Fig.1 a-b, girder structure dynamic model order reducing method provided by the invention can be carried out for various girder structures
Model reduction.Fig. 2 is girder structure dynamic model depression of order schematic diagram.
Second step, constructs decrement base vector using polynomial interpolating function, carries out depression of order to the dynamic model of girder structure.
2.1) polynomial interpolating function is utilized, by any finite element on the section of girder structure in the form of positional displacement interpolation
The displacement of node is condensed at cross-section centroid；
For girder structure using rectangular coordinate system shown in Fig. 2, the axial direction of girder structure is that x-axis is positive, any limited on section
The column u that first node j is indicated by generalized displacement at cross-section centroid ijAre as follows:
uj=Rjqi (1)
Wherein, ujIndicate the motion vector of upper j-th of finite element node of section Ω, qiIndicate the broad sense at section Ω centroid i
Motion vector, RjIndicate the displacement transition matrix of j point.
This example uses N=4 rank multinomial (W=15), and any finite element node j passes through cross-section centroid i in the Ω of section
Locate the column u that generalized displacement indicatesjAre as follows:
ujx=qix1+yqix2+zqix3+y2qix4+…+z4qix15=Fτjqixτ
ujy=qiy1+yqiy2+zqiy3+y2qiy4+…+z4qiy15=Fτjqiyτ
ujz=qiz1+yqiz2+zqiz3+y2qiz4+…+z4qiz15=Fτjqizτ
The displacement transforming relationship formula of any finite element node j in the Ω of section:
Table 1 provides FτjExpanded form, y, z are the position coordinates of finite element node j in table.
Table 1FτjExpanded form
2.2) a finite element node of s (s=164) agglomerates at the centroid i of section Ω on the Ω of section, obtains such as formula
(3) displacement dress shown in changes relational expression:
Ti=(R1..., R164)T 492×45
2.3) by entire girder structure, in axial direction subdivision is p=40 section, then by the displacement on p=40 section
Conversion relational expression is assembled into decrement base vector T:
2.4) do not consider that damping effect, the finite element governing equation of former girder structure analysis indicate are as follows:
Wherein, the square matrix that M, K are 19680 × 19680, is the Mass matrix and Stiffness Matrix of former girder structure respectively, U,It is
19680 dimensional vectors are displacement and the acceleration responsive vector of girder structure respectively, and 19680 dimensional vector F are to act on structure
On load.
2.5) displacement transition matrix T is introduced in above-mentioned finite element governing equation, and in equation both sides while premultiplication TT, obtain
Kinetics equation after to depression of order:
Wherein, MR=TTMT、KR=TTKT is the Mass matrix and Stiffness Matrix of reduced-order model, M respectivelyR、KRIt is 1800 × 1800
Square matrix, Q,It is 1800 dimensional vectors, is displacement and the acceleration responsive vector of reduced-order model, F respectivelyR=TTF is 1800 dimensions
The load vectors of reduced-order model, freedom degree reduce about 91%, and computational efficiency increases substantially.
Third step utilizes the Mass matrix M of girder structure reduced-order modelRWith Stiffness Matrix KR, calculate the frequency and vibration of girder structure
Type.
It solves generalized eigenvalue equation (7) and obtains the frequency and formation of girder structure.Calculated result is as shown in table 2, table 2
In provide first three rank corner frequency, first three rank torsional frequency and the part low order frequency of girder structure entirety, wherein L indicates the vibration shape
Along half wave number of girder structure axis direction, M indicates the wave number in circumferentially direction.With the calculating of Lanczos method in ANSYS software
It as a result is standard, while model reduction is carried out using Guyan static condensation algorithm in ANSYS software, to make comparisons.Compare three meters
Result is calculated it can be found that the computational accuracy of two reduced-order models is all acceptable, error is able to satisfy engineering within 10%
The requirement of calculating, but the computational accuracy of model order reduction proposed by the present invention is higher than Guyan condensing method, especially for knot
The high order of frequency of structure.
The elongated smooth barrel structure calculated result comparison provided in an embodiment of the present invention of table 2
Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention., rather than its limitations；To the greatest extent
Present invention has been described in detail with reference to the aforementioned embodiments for pipe, those skilled in the art should understand that: its is right
Technical solution documented by foregoing embodiments is modified, or is equally replaced to some or all of the technical features
It changes, the range for technical solution of various embodiments of the present invention that it does not separate the essence of the corresponding technical solution.
Claims (1)
1. a kind of girder structure free vibration analysis method based on reduced-order model, it is characterised in that following steps:
The first step is handled girder structure using finite element software, obtains the Mass matrix M and Stiffness Matrix K of girder structure；
Second step constructs decrement base vector using polynomial interpolating function, carries out model reduction to girder structure；
2.1) polynomial interpolating function is utilized, by any finite element node on the section of girder structure in the form of positional displacement interpolation
Displacement be condensed at the Ω centroid of section；
Girder structure uses axially as the rectangular coordinate system of x-axis forward direction, and any finite element node j passes through the section shape on the Ω of section
The column u that generalized displacement indicates at heart ijAre as follows:
uj=Rjqi (1)
Wherein, ujIndicate the motion vector of upper j-th of finite element node of section Ω, qiIndicate the generalized displacement at section Ω centroid i
Vector, RjIndicate the displacement transition matrix of j point；
ujExpanded form are as follows:
Wherein, { ujx ujy ujz}TThree displacement components for being finite element node j at rectangular coordinate system Oxyz, { qixτ qiyτ
qizτ}TThe generalized displacement component for being cross-section centroid i at rectangular coordinate system Oxyz, FτjFor polynomial interpolating function expression formula, weight
Multiple subscript τ is indicated to { ujx ujy ujz}TSummation, W are multinomial FτjItem number；
2.2) finite element node all on the Ω of section agglomerates at the centroid i of section Ω, obtains as shown in formula (3)
Displacement dress changes relational expression:
Ui=(u1,…,us)T=Tiqi=(R1,…,Rs)Tqi (3)
Wherein, UiIndicate the motion vector of s finite element node in the Ω of section, TiIndicate the displacement transition matrix of section Ω；
2.3) by entire girder structure, in axial direction subdivision is p section, then by the displacement conversion relational expression group on p section
Decrement base vector T is dressed up, realizes the depression of order of former girder structure；
The decrement base vector T that displacement conversion relational expression on the p section is assembled into are as follows:
Wherein, U indicates total finite element modal displacement vector, is the column vector of 3n × 1, and n is the freedom degree of girder structure
Number；Q is the finite element modal displacement vector of model after depression of order, is the column vector of 3pW × 1；UpIndicate p-th of section interior nodes
Motion vector；TpIndicate the displacement transition matrix of p-th of section interior nodes, size is extended to 3n × 3W；qpIndicate p-th of section
Generalized displacement at centroid, size are 3W × 1；
2.4) do not consider that damping effect, the finite element governing equation of former girder structure analysis indicate are as follows:
Wherein, M, K are the square matrix of 3n × 3n, are the Mass matrix and Stiffness Matrix of original structure respectively；U,It is 3n dimensional vector, respectively
It is displacement structure and acceleration responsive vector；3n dimensional vector F is the load acted in structure；
2.5) displacement transfer equation (4) is introduced in the finite element governing equation shown in formula (5), and left simultaneously on equation both sides
Multiply TT, kinetics equation after obtaining depression of order:
Wherein, MR=TTMT、KR=TTKT is the Mass matrix and Stiffness Matrix of reduced-order model respectively；MR、KRFor the square matrix of 3pW × 3pW；
Q、It is 3pW dimensional vector, is displacement and the acceleration responsive vector of reduced-order model respectively, due to W < < s, so reduced-order model
Freedom degree sharp fall；FR=TTF is the load vectors that 3pW ties up reduced-order model；
Third step utilizes second step 2.5) the obtained Mass matrix M of girder structure reduced-order modelRWith Stiffness Matrix KR, by formula (7)
The frequency and the vibration shape of girder structure after calculating depression of order；
Solve Structural Dynamics generalized eigenvalue equation corresponding with formula (6):
Wherein, λ,The respectively feature value vector of reduced-order model and the corresponding vibration shape；For the vibration of former girder structure
Type.
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101887474A (en) * | 2010-06-25 | 2010-11-17 | 哈尔滨工程大学 | Structural vibration analysis method based on finite element method and generalized Fourier series method |
| CN102866637A (en) * | 2012-10-07 | 2013-01-09 | 西北工业大学 | Quadratic order-reduction based method for simulating unsteady aerodynamic force of aerofoil with operation surface |
| CN102982202A (en) * | 2012-11-15 | 2013-03-20 | 中国电子科技集团公司第二十八研究所 | Model correcting method based on defective modal structure |
| CN103412988A (en) * | 2013-08-01 | 2013-11-27 | 电子科技大学 | Three-dimensional electromagnetic field simulation method of periodic structure based on phase-shift reduced model |
| CN104091033A (en) * | 2014-07-25 | 2014-10-08 | 哈尔滨工业大学 | Bridge static force finite element model correcting method based on super-element combination virtual deformation method |
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| JP6128414B2 (en) * | 2012-05-21 | 2017-05-17 | 株式会社リコー | Image forming apparatus |
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Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101887474A (en) * | 2010-06-25 | 2010-11-17 | 哈尔滨工程大学 | Structural vibration analysis method based on finite element method and generalized Fourier series method |
| CN102866637A (en) * | 2012-10-07 | 2013-01-09 | 西北工业大学 | Quadratic order-reduction based method for simulating unsteady aerodynamic force of aerofoil with operation surface |
| CN102982202A (en) * | 2012-11-15 | 2013-03-20 | 中国电子科技集团公司第二十八研究所 | Model correcting method based on defective modal structure |
| CN103412988A (en) * | 2013-08-01 | 2013-11-27 | 电子科技大学 | Three-dimensional electromagnetic field simulation method of periodic structure based on phase-shift reduced model |
| CN104091033A (en) * | 2014-07-25 | 2014-10-08 | 哈尔滨工业大学 | Bridge static force finite element model correcting method based on super-element combination virtual deformation method |
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