CN109933898A - A kind of siding aeroelastic stability analysis method considering Hybrid parameter matrix - Google Patents

A kind of siding aeroelastic stability analysis method considering Hybrid parameter matrix Download PDF

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CN109933898A
CN109933898A CN201910187129.0A CN201910187129A CN109933898A CN 109933898 A CN109933898 A CN 109933898A CN 201910187129 A CN201910187129 A CN 201910187129A CN 109933898 A CN109933898 A CN 109933898A
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siding
sto
formula
hybrid
equation
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邱志平
郑宇宁
王晓军
王磊
李云龙
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Beihang University
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Beihang University
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Abstract

The invention discloses a kind of siding aeroelastic stability analysis methods for considering Hybrid parameter matrix, belong to siding aeroelastic design field, existing uncertain environment is mixed for stochastic variable and interval variable are common, quantization signifying is carried out to hybrid uncertain parameters using stochastic model and interval model, establishes the siding aeroelastic stability analysis model containing hybrid uncertain parameters.On this basis, it is combined by the way that Probability Density Evolution Method is propagated analysis method with bounded-but-unknown uncertainty, propose random-section mixing Probability Density Evolution Method, the probability statistics feature of siding aeroelasticity response interval border can be estimated when parameter fluctuation is larger, limitation of the conventional method in computational efficiency and applicability is overcome, the research blank of Hybrid parameter matrix environment lower wall panels aeroelastic stability analysis has been filled up.

Description

A kind of siding aeroelastic stability analysis method considering Hybrid parameter matrix
Technical field
The invention belongs to siding aeroelastic design field, in particular to a kind of siding for considering Hybrid parameter matrix is pneumatic Analyse dlasto method.
Background technique
There are three distinguishing features for aeroelasticity tool, first is that it is substantially a fluid structurecoupling problem, structure is in gas Flexible deformation occurs under the action of power, while malformation changes the boundary in flow field again in turn;Second is that is be related to is non-linear Factor is more, the non-linear factor including structure and pneumatic aspect, as at control plane hinge backlash nonlinearity and big angles-of-attack Caused pneumatic nonlinearity;Further, since aeroelastic system is a complicated multidisciplinary coupled system, it is related to pneumatic, knot Multiple subjects such as structure, heat are inevitably present uncertain factor in practical aeroelastic system.For practical wall panel structure Speech, probabilistic source be it is diversified, in terms of being embodied in following four: (1) uncertainty of model, in modeling process Having carried out simplifying or ignore secondary cause to correlative factor causes between established aeroelastic analysis model and practical object There are model errors;(2) uncertainty of material parameter, due to factors such as manufacturing environment, technical conditions, the multiphase features of material It influences, makes the elasticity modulus of material, Poisson's ratio, mass density that there is uncertainty;(3) uncertainty of geometric dimension, due to Manufacture and installation error make geometrical scale such as thickness, cross-sectional area etc. have uncertainty;(4) uncertainty of load, Since the factors such as measuring condition, external environment influence, making to act on the pneumatic and thermal force on wall panel structure has uncertainty.
Because of the limitation of objective condition or Subjective, designer often faces following two categories typical project problem: first, Parameter can be divided into clearly two classes according to the size of test data sample size, and one kind is that test data is sufficient, can be with high-precision Degree is fitted its probability density function, and one kind is that can not obtain the probability of corresponding parameter because test data sample size is extremely limited Density function and with interval model carry out quantification.Therefore, occur that stochastic variable and interval variable are common existing to be mixed not Determine environment, wherein the uncertain parameter of sample information abundance is defined as stochastic variable, the limited uncertain ginseng of sample data Number is defined as interval variable, and the interval border that hybrid uncertain parameters input will lead to the response of siding aeroelasticity has statistics Characteristic.
The method of existing processing Hybrid parameter matrix is mainly Monte-carlo Simulation Method, however, Monte Carlo simulation side Method needs to carry out a large amount of sample point analysis, and it is larger to expend computing resource.When needing to obtain characteristic value maximum real part interval border Probability density function when, there is presently no effective analysis methods to be able to solve, and it is pneumatic to limit siding to a certain extent The development of Analyse dlasto technology.In conclusion siding aeroelasticity side can quickly, accurately be solved by needing to develop one kind Journey corresponds to the new method of generalized eigenvalue interval border probability density function, and to overcome conventional method to calculate, of long duration, precision is low The drawbacks of, to provide technical support for stability analysis.
Summary of the invention
The technical problem to be solved in the present invention are as follows: the siding aeroelasticity for conventional process containing hybrid uncertain parameters is steady Method for qualitative analysis computational efficiency is low, characteristic value interval border probability density function is difficult to the problems such as obtaining, and proposes a kind of consideration The siding aeroelastic stability analysis method of Hybrid parameter matrix.This method exists for stochastic variable with interval variable jointly Mixing uncertain environment, quantization signifying is carried out to hybrid uncertain parameters using stochastic model and interval model, establishes and contains The siding aeroelastic stability analysis model of hybrid uncertain parameters.On this basis, by by Probability Density Evolution Method Analysis method is propagated with bounded-but-unknown uncertainty to combine, and is proposed random-section mixing Probability Density Evolution Method, can joined The probability statistics feature of siding aeroelasticity response interval border is estimated when number fluctuation is larger, conventional method is overcome and exists Limitation in computational efficiency and applicability.
The present invention solves the technical solution that above-mentioned technical problem uses are as follows: a kind of siding for considering Hybrid parameter matrix is pneumatic Analyse dlasto method, comprising the following steps:
Step (1) establishes the siding aeroelasticity finite element equation containing hybrid uncertain parameters:
In formula, αsto=(αsto,1sto,2,…,αsto,m) it is random vector, αin=(αin,1in,2,…,αin,l) it is section Vector, m, l are vector dimension, and M is siding mass matrix, and C is siding damping matrix,For air damping matrix, K is siding Stiffness matrix,For aerodynamic stiffness matrix, x (t) is generalized coordinates,For generalized velocity,For generalized acceleration, t For the time;
Step (2) enables x (t)=x0eλt, the siding aeroelasticity finite element equation containing hybrid uncertain parameters can be turned Turn to generalized eigenvalue equation:
A(αstoin) u=λ B (αstoin)u (2)
In formula, λ is generalized eigenvalue;
Step (3), characteristic value maximum real part μ can be obtained by following formula:
μ=μ (αstoin)=max { Re [λi(A(αstoin),B(αstoin))], (i=1,2 ..., 2n) (3)
In formula, Re indicates characteristic value real part;
Step (4) establishes the probability density evolution equation containing random-section hybrid parameter, is expressed as form:
In formula,μWithSection lower bound and the section upper bound for μ, p μ αWithFor (μ, α) andJoint probability it is close Function is spent,
Step (5), in uncertain parameter αstoDomain of variation ΩstoIt is interior, equably take NtotalA sample point, is denoted as αsto,q (q=1 ..., Ntotal), and by domain of variation ΩstoIt is divided into NtotalA subdomain, is denoted as Ωsto,q(q=1 ..., Ntotal);
Step (6), by equation (4)-(5) in subdomain Ωsto,qInterior integral, available:
Step (7) passes through exchange integral and sequence of solving the derivation, can be by equation (6)-(7) abbreviation are as follows:
In formula,WithFor the probability density function corresponding to q-th of sample point;
Step (8) introduces virtual parameter τ, enablesIt substitutes into equation (8)- (9) available in:
Step (9) determines primary condition are as follows:
In formula, δ is Dirac function,
Step (10) reduces the available following difference scheme of format using finite difference method and total variance:
In formula, τk=k Δ τ (k=0,1 ...), rLAXFor difference gridding ratio,For current limiter,WithIt may be expressed as:
Step (11), will be in NtotalIt is calculated at a sample pointSummation, available:
Step (12) takes τk=1, then the probability density function expression formula of characteristic value maximum real part μ can be obtained:
Step (13), basisIf it existsThen the siding has flutter failure risk.
It wherein, can be discrete by primary condition in the step (9) are as follows:
In formula,WithForWithThe size of mesh opening in direction;
Wherein, in the step (10), the difference scheme condition of convergence to be met are as follows:
The beneficial effects of the present invention are:
The invention proposes a kind of siding aeroelastic stability analysis methods for considering Hybrid parameter matrix, can be to containing The siding aeroelasticity equation of hybrid uncertain parameters corresponds to generalized eigenvalue and is analyzed, and obtains characteristic value maximum real part section The probability density function on boundary, to determine siding aeroelastic stability.The characteristic value that the method for the present invention obtains is real The characteristic value real part interval probability density function that portion's interval probability density function and monte carlo method obtain coincide preferably, and It can significantly reduce and calculate the time, provide new think of for the siding aeroelastic stability analysis containing hybrid uncertain parameters Road.
Detailed description of the invention
Fig. 1 is two-dimentional curved wall Slab schematic diagram;
Fig. 2 is VWhen=2500m/sμProbability density function;
Fig. 3 is VWhen=2500m/sProbability density function;
Fig. 4 is VWhen=3200m/sμProbability density function;
Fig. 5 is VWhen=3200m/sProbability density function;
Fig. 6 is method implementation process of the invention.
Specific embodiment
Hereinafter reference will be made to the drawings, and design example of the invention is described in detail.The invention belongs to siding aeroelasticities Design field, it should be understood that selected example limits the scope of the invention only for illustrating the present invention.
(1) using two-dimentional bent wall panel structure as object, geometrical model is as shown in Figure 1;
(2) bent wall panel structure unit material property parameters and incoming flow parameter are given, as shown in table 1;
The bent wall panel structure material properties of table 1 and incoming flow parameter
In table 1, E is elasticity modulus, ρTo come current density, ρsFor curved wall plate density, αsFor thermal expansion coefficient;
(3) for 1 stochastic variable α of tablesto, Normal Distribution, coefficient of variation cov is taken as 0.01;For interval variable αin, interval border αin c[1- β, 1- β], β is uncertain factor, and β is taken as 0.05 in this example;
(4) by E and ρConstant interval [+6 σ of θ -6 σ, θ] be divided into 20 subintervals, then the E and ρ of subinterval boundary Are as follows:
In this way, sample point (the E formedi∞j) share 441;
(5) q-th of sample point (E is takeni∞j)q, according to (Ei∞j)qMaterial and incoming flow parameter are set, the siding gas is established Dynamic elasticity finite element equation is obtained by interval analysis to applied to sample point (Ei∞j)qCharacteristic value maximum real part section side BoundaryμWith
(6) it establishes and is directed toμWithProbability density evolution equation:
(7) primary condition can be discrete are as follows:
(8) finite difference scheme is set are as follows:
(9) current limiterSetting are as follows:
(10) step (5)~(9) are repeated, the corresponding probability density function of all 441 sample points is calculated It is summed available:
(11) τ is takenk=1, then it can calculate the probability density function expression formula of characteristic value maximum real part interval border are as follows:
(12) Monte-carlo Simulation Method is utilized, the sample point of N=10000 Normal Distribution is taken, by each Sample point corresponding eigenvalue maximum real part interval borderμWithCalculating, obtainμWithProbability density function;
(13) it under conditions of speed of incoming flow is 2500m/s and 3200m/s, is obtained using both the above methodμWith's Probability density function is as shown in Figure 2-5, and result illustrates the result and monte carlo method result kiss that the method for the present invention obtains in figure It closes preferable;
(14) two methods calculating total time-consuming is respectively as follows: TThe method of the present invention=5200s, TMonte-carlo Simulation Method=14210s.Time comparison The result shows that the method for the present invention can reduce calculating time-consuming, to significantly improve the computational efficiency of probability density function;
(15) -5 stability analysis can be carried out according to fig. 2, works as VWhen=2500m/s, due toSystem is not present Flutter failure risk;Work as VWhen=3200m/s, existThe case where, i.e., system has flutter failure risk.
In conclusion the invention proposes a kind of siding aeroelastic stability analysis sides for considering Hybrid parameter matrix Method.For stochastic variable and interval variable it is common it is existing mix uncertain environment, using stochastic model and interval model to mixing It closes uncertain parameter and carries out quantization signifying, establish the siding aeroelastic stability analysis model containing hybrid uncertain parameters. On this basis, combined by the way that Probability Density Evolution Method is propagated analysis method with bounded-but-unknown uncertainty, propose it is random- Section mixes Probability Density Evolution Method, can be when parameter fluctuation is larger to the probability of siding aeroelasticity response interval border Statistical nature is estimated, and is overcome limitation of the conventional method in computational efficiency and applicability, has been filled up Hybrid parameter matrix The research blank of environment lower wall panels aeroelastic stability analysis.
The above is only specific steps of the invention, are not limited in any way to protection scope of the present invention, expansible to answer For flight vehicle aerodynamic elasticity design field, any technical scheme formed by adopting equivalent transformation or equivalent replacement, all falls within Within rights protection scope of the present invention.

Claims (3)

1. a kind of siding aeroelastic stability analysis method for considering Hybrid parameter matrix, it is characterised in that: this method is realized Steps are as follows:
Step (1) establishes the siding aeroelasticity finite element equation containing hybrid uncertain parameters:
In formula, αsto=(αsto,1sto,2,…,αsto,m) it is random vector, αin=(αin,1in,2,…,αin,l) be section to Amount, m, l are vector dimension, and M is siding mass matrix, and C is siding damping matrix,For air damping matrix, K is siding Stiffness matrix,For aerodynamic stiffness matrix, x (t) is generalized coordinates,For generalized velocity,For generalized acceleration, t For the time;
Step (2) enables x (t)=x0eλt, the siding aeroelasticity finite element equation containing hybrid uncertain parameters can be converted to Generalized eigenvalue equation:
A(αstoin) u=λ B (αstoin)u (2)
In formula, λ is generalized eigenvalue;
Step (3), characteristic value maximum real part μ can be obtained by following formula:
μ=μ (αstoin)=max { Re [λi(A(αstoin),B(αstoin))], (i=1,2 ..., 2n) (3)
In formula, Re indicates characteristic value real part;
Step (4) establishes the probability density evolution equation containing random-section hybrid parameter, is expressed as form:
In formula,μWithSection lower bound and the section upper bound for μ, p μ αWithFor (μ, α) andJoint probability density letter Number,
Step (5), in uncertain parameter αstoDomain of variation ΩstoIt is interior, equably take NtotalA sample point, is denoted as αsto,q(q= 1,...,Ntotal), and by domain of variation ΩstoIt is divided into NtotalA subdomain, is denoted as Ωsto,q(q=1 ..., Ntotal);
Step (6), by equation (4)-(5) in subdomain Ωsto,qInterior integral, available:
Step (7) passes through exchange integral and sequence of solving the derivation, can be by equation (6)-(7) abbreviation are as follows:
In formula,WithFor the probability density function corresponding to q-th of sample point;
Step (8) introduces virtual parameter τ, enablesSubstituting into can in equation (8)-(9) To obtain:
Step (9) determines primary condition are as follows:
In formula, δ is Dirac function,
Step (10) reduces the available following difference scheme of format using finite difference method and total variance:
In formula, τk=k Δ τ (k=0,1 ...), rLAXFor difference gridding ratio,For current limiter,WithIt may be expressed as:
Step (11), will be in NtotalIt is calculated at a sample pointSummation, available:
Step (12) takes τk=1, then the probability density function expression formula of characteristic value maximum real part μ can be obtained:
Step (13), basisIf it existsThen the siding has flutter failure risk.
2. a kind of siding aeroelastic stability analysis method for considering Hybrid parameter matrix according to claim 1, It is characterized in that:, can be discrete by primary condition in the step (9) are as follows:
In formula,WithForWithThe size of mesh opening in direction.
3. a kind of siding aeroelastic stability analysis method for considering Hybrid parameter matrix according to claim 1, It is characterized in that: in the step (10), the difference scheme condition of convergence to be met are as follows:
CN201910187129.0A 2019-03-13 2019-03-13 A kind of siding aeroelastic stability analysis method considering Hybrid parameter matrix Pending CN109933898A (en)

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