CN106528952A - Pseudorandom vector-based assumed mode set construction method - Google Patents
Pseudorandom vector-based assumed mode set construction method Download PDFInfo
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- CN106528952A CN106528952A CN201610906677.0A CN201610906677A CN106528952A CN 106528952 A CN106528952 A CN 106528952A CN 201610906677 A CN201610906677 A CN 201610906677A CN 106528952 A CN106528952 A CN 106528952A
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- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
Abstract
The invention discloses a pseudorandom vector-based assumed mode set construction method. The method comprises the following steps of constructing a dynamics equation of an N-freedom system by adopting a finite unit method; performing eigenvalue analysis on the system to obtain a plurality of order modes of the system; generating a group of pseudorandom vectors, wherein the number of the pseudorandom vectors is determined according to the number of the obtained modes; constructing an assumed mode set by adopting the obtained system modes and the pseudorandom vector group; and forming a new mode set by the obtained assumed mode set and the system modes to construct a residual flexibility matrix of the system. According to the method, the assumed mode set can be constructed according to any known mode vector group, and the process for calculating the residual flexibility matrix by a sub-structure mode synthesis technology is greatly simplified.
Description
Technical field
The invention belongs to structural dynamical model technical field, particularly a kind of hypothesis mode collection based on pseudo-random vector
Building method.
Background technology
With the development of science and technology, need during Structural Design in the face of increasing large complicated knot
Structure.When dynamic analyses are carried out to such large and complex structure, often face FEM (finite element) model it is excessively huge and cause meter
The problem of high cost is calculated, so can virtually extend the total design cycle.
At present, component mode synthesis method is a kind of technological means for effectively reducing scale of model.Wherein due to freedom
Component mode synthesis method in interface can be docked with experimental data with more convenient, then obtained wide in Structural Design
General application.The method that this method employs mode truncation during reducing to model, mainly, only retains to structure
Dynamicss affect more significantly lower mode to reach the purpose of model reduction.However, directly casting out high order mode
Often computational accuracy is relatively low for free interface method, cannot adapt to Structural Design Requirement at this stage.Then, it is surplus by considering
Remaining flexibility retains impact of the high order mode to Structure Dynamic Characteristics, becomes and improves calculating for free interface component mode synthesis method
The main thought of precision.
Existing Free-Interface Method for Mode Synthesis calculate the main flow of Residual Flexibility matrix as shown in figure 1, mainly have with
The problem of lower two aspects：
1) generally to not there is no unified computation schema to being processed with there are two kinds of situations of rigid body mode respectively without rigid body mode.
2) when process has the Solve problems of minor structure Residual Flexibility matrix of rigid body mode, it usually needs first assume
Apply one group of constraint in minor structure, obtain additional static determinacy constraint matrix, original equation of motion is converted to by tool by this matrix
The equation of motion of Constrained displacement, then to solve Residual Flexibility matrix.This processing mode implements relatively complicated.
The content of the invention
It is an object of the invention to provide a kind of new hypothesis mode set construction method based on pseudo-random vector, can be with root
Mode collection is assumed according to any known modal vector set constructor, simplify the mistake that component mode synthesis technology calculates Residual Flexibility matrix
Journey.
The technical solution for realizing the object of the invention is：A kind of hypothesis mode collection construction side based on pseudo-random vector
Method, comprises the following steps：
Step 1, builds N system with one degree of freedom kinetics equations using Finite Element；
Step 2, carries out Eigenvalues analysis to the system in step 1, obtains some order mode states of system；
Step 3, generates one group of pseudo-random vector, and the pseudo-random vector number is determined according to the mode number that step 2 is obtained；
Step 4, using the pseudo-random vector group obtained in the system mode and step 3 obtained in step 2, construction assumes mould
State collection；
The system mode obtained in step 5, the hypothesis mode collection that step 4 is obtained and step 2 constitutes new mode collection, is used for
Construction system spare flexibility matrix.
Compared with prior art, its remarkable advantage is the present invention：(1) can the modal vector set constructor vacation according to known to any
If mode collection；(2) without the need for being processed with there are two kinds of situations of rigid body mode respectively without rigid body mode to structure, give unified calculating
Pattern, greatly simplify the process that component mode synthesis technology calculates Residual Flexibility matrix.
Below in conjunction with the accompanying drawings the present invention is described in further detail.
Description of the drawings
Fig. 1 is the conventional processing routes figure that Free-Interface Method for Mode Synthesis calculates Residual Flexibility matrix.
Fig. 2 is hypothesis mode set construction method flow chart of the present invention based on pseudo-random vector.
Specific embodiment
One group vector set of the present invention based on pseudo-random vector set constructor and all known modal vector weighted orthogonals, can be with
For building the aspects such as equivalent high order mode, construction Residual Flexibility matrix, the radio-frequency component disappearance that mode truncation is caused is caught, point
The problem that analysis precision is not enough.
With reference to Fig. 2, hypothesis mode set construction method of the present invention based on pseudo-random vector, comprise the following steps：
Step 1, builds N system with one degree of freedom kinetics equations using Finite Element, specific as follows：
Wherein, M is mass of system matrix, and K is system stiffness matrix, and u is generalized displacement vector, and f is generalized load vector.
Step 2, carries out Eigenvalues analysis to the system in step 1, obtains some order mode states of system；
Eigenvalues analysis are carried out to formula (1), can be in the hope of some rank modal vectors, wherein some order mode state composition of vector groups
It is designated as
Step 3, generates one group of pseudo-random vector, and the pseudo-random vector number is determined according to the mode number that step 2 is obtained,
It is specific as follows：
Given one group of pseudo-random vector x, x=[x1 x2 … xn], wherein number n of pseudo-random vector is that system is always free
Number of degrees N deducts the exponent number of the mode that step 2 is obtained.
Step 4, using the pseudo-random vector group obtained in the system mode and step 3 obtained in step 2, construction assumes mould
State collection, it is specific as follows：
Assume
Wherein,WithRefer to the Vector Groups of some order mode state compositions respectivelyJth row and r row,Construct
Vector, ajsFor coefficient to be asked, then a is tried to achieve according to formula (2) and formula (3)js：
By a for obtainingjsSubstitution formula (2), then obtain：
As above, by pseudo-random vector set constructor one group with the Vector Groups of known vector group weighted orthogonal, it is as wanted
The hypothesis mode collection of construction.
The system mode obtained in step 5, the hypothesis mode collection that step 4 is obtained and step 2 constitutes new mode collection, is used for
Construction system spare flexibility matrix, it is specific as follows：
By the Vector Groups for having constructedWith known vector groupIt is combined into one group of new Vector Groups
Φ, wherein s=1,2 ..., n, j=1,2 ..., m, Φ are designated as
For N degree of freedom sub-structure models, minor structure kinetics equation is transformed into from physical coordinates system by mode by Φ
Under coordinate system, and try to achieve corresponding Residual Flexibility matrix.
And the minor structure Residual Flexibility matrix tried to achieve by this method can meet the son knot under Arbitrary Boundary Conditions
Structure synthtic price index, solves the problems of existing Substructure Synthesis technology well.
Embodiment 1
Flow process with reference to shown in Fig. 2, as a example by building equivalent high order mode, specific implementation step is as follows：
Step 1：For certain N degree of freedom dynamic system, its equation of motion is represented by
Wherein, M is mass of system matrix, and K is system stiffness matrix, and u is generalized displacement vector, and f is generalized load vector.
Step 2：By Eigenvalues analysis, l rank lower modes before structure are tried to achieveIt is designated as
Step 3：One group of pseudo-random vector group is given, x=[x are designated as1 x2 ... xN-l]。
Step 4：Assume that the equivalent high order mode of any single order isAnd meet
Wherein,WithRefer to the lower mode Vector Groups that step 2 is tried to achieve respectivelyJth row and r row, ajsFor waiting to ask it is
Number.
Formula (8) is substituted into formula (9) to obtain
Arrangement can be obtained
According to mode with regard to mass matrix weighted orthogonal, during and if only if j=r,Then have
Can be obtained according to formula (11)
Undetermined coefficient a has been obtained thusrsR=1,2 ..., l；S=1,2 ..., n-l
By a for obtainingrsSubstitution formula (8) then has
Formula (14) can also be written as following form
Hypothesis high order mode needed for so just having obtained.From said process as can be seen that this hypothesis high order mode collection
It is orthogonal with known mode-weighting.
Step 5：Assume that high order mode and the Vector Groups tried to achieve by Eigenvalues analysis carry out group by what is tried to achieve in step 4
Close, form one group of new Vector Groups Φ
Make u=Φ p, expansion obtain
Wherein p is modal coordinate, formula (17) is substituted into formula (7), and uses ΦTEquation obtained by premultiplication, then be obtained
Formula (18) is launched, its second prescription journey is
Wherein,
Carry out Laplace conversion to obtain to formula (19)
Taylor expansion being carried out to above formula and only retaining Section 1, then carrying out inverse Laplace conversion again can obtain
Then
OrderAs Residual Flexibility matrix.
The physical coordinates of kinetics equation can be converted into by modal coordinate by above formula, while having carried out subtracting for degree of freedom
Contracting.And here when Residual Flexibility matrix is solved, need not consider that structure, whether comprising rigid body mode, greatly simplifies model and subtracts
The process of contracting, solves the problems, such as existing component mode synthesis technology when Residual Flexibility matrix is calculated.
Claims (6)
1. a kind of hypothesis mode set construction method based on pseudo-random vector, it is characterised in that comprise the following steps：
Step 1, builds N system with one degree of freedom kinetics equations using Finite Element；
Step 2, carries out Eigenvalues analysis to the system in step 1, obtains some order mode states of system；
Step 3, generates one group of pseudo-random vector, and the pseudo-random vector number is determined according to the mode number that step 2 is obtained；
Step 4, using the pseudo-random vector group obtained in the system mode and step 3 obtained in step 2, construction assumes mode
Collection；
The system mode obtained in step 5, the hypothesis mode collection that step 4 is obtained and step 2 constitutes new mode collection, for constructing
System spare flexibility matrix.
2. the hypothesis mode set construction method based on pseudo-random vector according to claim 1, it is characterised in that step 1
The employing Finite Element builds N system with one degree of freedom kinetics equations, specific as follows：
Wherein, M is mass of system matrix, and K is system stiffness matrix, and u is generalized displacement vector, and f is generalized load vector.
3. the hypothesis mode set construction method based on pseudo-random vector according to claim 1, it is characterised in that step 2
The system in step 1 carries out Eigenvalues analysis, obtains some order mode states of system, wherein some order mode state composition of vector groups
4. the hypothesis mode set construction method based on pseudo-random vector according to claim 1, it is characterised in that step 3
One group of pseudo-random vector of the generation, the pseudo-random vector number are determined according to the mode number that step 2 is obtained, specific as follows：
Given one group of pseudo-random vector x, x=[x1 x2 … xn], wherein number n of pseudo-random vector is the total number of degrees of freedom, of system
N deducts the exponent number of the mode that step 2 is obtained.
5. the hypothesis mode set construction method based on pseudo-random vector according to claim 1, it is characterised in that step 4
The system mode obtained in the employing step 2 and the pseudo-random vector group obtained in step 3, construction assume mode collection, specifically
It is as follows：
Assume
Wherein,WithRefer to the Vector Groups of some order mode state compositions respectivelyJth row and r row,For vector to be constructed,
ajsFor coefficient to be asked, then a is tried to achieve according to formula (2) and formula (3)js
By a for obtainingjsSubstitution formula (2), then obtain：
As above, by pseudo-random vector set constructor one group with the Vector Groups of known vector group weighted orthogonal, to as construct
Hypothesis mode collection.
6. the hypothesis mode set construction method based on pseudo-random vector according to claim 1, it is characterised in that step 5
The system mode obtained in the hypothesis mode collection that step 4 is obtained and step 2 constitutes new mode collection, remains for constructing system
Remaining flexibility matrix, it is specific as follows：
By the Vector Groups for having constructedWith known vector groupOne group of new Vector Groups Φ is combined into,
Wherein s=1,2 ..., n, j=1,2 ..., m, Φ are designated as
For N degree of freedom sub-structure models, minor structure kinetics equation is transformed into from physical coordinates system by modal coordinate by Φ
Under system, and try to achieve corresponding Residual Flexibility matrix.
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| CN112818580A (en) * | 2021-02-07 | 2021-05-18 | 上海机电工程研究所 | Gap structure dynamic model order reduction method and system based on extended modal matrix |
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| CN112818580A (en) * | 2021-02-07 | 2021-05-18 | 上海机电工程研究所 | Gap structure dynamic model order reduction method and system based on extended modal matrix |
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