CN109933898A - A kind of siding aeroelastic stability analysis method considering Hybrid parameter matrix - Google Patents
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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
Technical Field
The invention belongs to the field of panel aeroelasticity design, and particularly relates to a panel aeroelasticity stability analysis method considering mixing uncertainty.
Background
Aeroelasticity has three remarkable characteristics, one is that it is essentially a fluid-solid coupling problem, the structure elastically deforms under the action of pneumatic force, and the structure deformation in turn changes the boundary of the flow field; secondly, the involved nonlinear factors are many, including the nonlinear factors in the aspects of structure and aerodynamics, such as gap nonlinearity at the control surface hinge and aerodynamic nonlinearity caused by large attack angle flight; in addition, since the aeroelastic system is a complex multidisciplinary coupling system, involving multiple disciplines of pneumatics, structure, heat, etc., there is inevitably an uncertainty factor in the actual aeroelastic system. The sources of uncertainty for the actual panel structure are diverse and are reflected in the following four areas: (1) model errors exist between the established aeroelastic analysis model and an actual object due to the fact that relevant factors are simplified or secondary factors are ignored in the modeling process; (2) uncertainty of material parameters, due to the influence of factors such as manufacturing environment, technical conditions, multiphase characteristics of the material and the like, the elastic modulus, the Poisson ratio and the mass density of the material have uncertainty; (3) uncertainty in geometry, uncertainty in structure geometry such as thickness, cross-sectional area, etc. due to manufacturing and installation errors; (4) uncertainty in load, both aerodynamic and thermal loads acting on the wall structure, are subject to uncertainty due to factors such as measurement conditions, external environment, etc.
Due to the limitations of objective conditions or subjective cognition, designers often face the following two typical engineering problems: firstly, parameters can be clearly divided into two types according to the volume of a test data sample, one type is that test data is sufficient and a probability density function of the test data can be fitted with high precision, and the other type is that the probability density function of the corresponding parameters cannot be obtained due to the fact that the volume of the test data sample is very limited and quantification is carried out by using an interval model. Therefore, a mixed uncertain environment with the coexistence of random variables and interval variables occurs, wherein uncertain parameters with sufficient sample information are defined as random variables, uncertain parameters with limited sample data are defined as interval variables, and the interval boundary of the aeroelastic response of the wall plate is provided with statistical characteristics due to the input of the mixed uncertain parameters.
The existing method for processing the mixing uncertainty is mainly a Monte Carlo simulation method, however, the Monte Carlo simulation method needs a large amount of sample point analysis and consumes a large amount of computing resources. When the probability density function of the boundary of the maximum real part interval of the characteristic value needs to be obtained, no effective analysis method can be provided at present, and the development of the analysis technology of the pneumatic elastic stability of the wall plate is limited to a certain extent. In summary, it is highly desirable to develop a new method capable of rapidly and accurately solving the boundary probability density function of the corresponding generalized eigenvalue interval of the panel aeroelastic equation, so as to overcome the disadvantages of long calculation time and low precision of the conventional method, thereby providing technical support for stability analysis.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: aiming at the problems that the traditional analysis method for the aerodynamic elastic stability of the wallboard containing mixing uncertain parameters is low in calculation efficiency, a characteristic value interval boundary probability density function is difficult to obtain and the like, the analysis method for the aerodynamic elastic stability of the wallboard considering mixing uncertainty is provided. The method aims at a mixed uncertain environment with coexisting random variables and interval variables, quantitative characterization is carried out on mixed uncertain parameters by using a random model and an interval model, and a wallboard aeroelastic stability analysis model containing the mixed uncertain parameters is established. On the basis, the probability density evolution method is combined with the interval uncertainty propagation analysis method, the random-interval mixed probability density evolution method is provided, the probability statistical characteristics of the boundary of the panel aeroelastic response interval can be estimated when the parameter fluctuation is large, and the limit of the traditional method on the calculation efficiency and the applicability is overcome.
The technical scheme adopted by the invention for solving the technical problems is as follows: a method for analyzing aeroelastic stability of a wall panel in consideration of mixing uncertainty, comprising the steps of:
step (1), establishing a panel pneumatic elastic finite element equation containing mixing uncertain parameters:
in the formula, αsto＝(αsto,1,αsto,2,…,αsto,m) As a random vector, αin＝(αin,1,αin,2,…,αin,l) Is an interval vector, M and l are vector dimensions, M is a wallboard mass matrix, C is a wallboard damping matrix,is a pneumatic damping matrix, K is a wallboard stiffness matrix,is an aerodynamic stiffness matrix, x (t) is a generalized coordinate,in the case of a speed in a broad sense,generalized acceleration, t is time;
step (2) of letting x (t) be x0eλtThe wall plate aeroelasticity finite element equation containing the mixed uncertain parameters can be converted into a generalized characteristic value equation:
A(αsto,αin)u＝λB(αsto,αin)u (2)
in the formula, λ is a generalized eigenvalue;
in the step (3), the maximum real part μ of the eigenvalue can be obtained by the following formula:
μ＝μ(αsto,αin)＝max{Re[λi(A(αsto,αin),B(αsto,αin))]},(i＝1,2,...,2n) (3)
in the formula, Re represents a real part of a characteristic value;
step (4), establishing a probability density evolution equation containing random-interval mixed parameters, wherein the probability density evolution equation is expressed as the following form:
in the formula,μandlower and upper intervals of μ, p μ αAndis prepared from (a)μα) andthe joint probability density function of (a) is,
step (5), at uncertain parameter αstoChange domain omega ofstoTaking N evenlytotalA sample point, noted αsto,q(q＝1,...,Ntotal) And will change the domain omegastoIs divided into NtotalIndividual field, denoted as Ωsto,q(q＝1,…,Ntotal)；
Step (6), equations (4) - (5) are placed in the sub-domain omegasto,qInternal integration, one can get:
by exchanging the integration and derivation order, equations (6) - (7) can be reduced to:
in the formula,andis the probability density function corresponding to the qth sample point;
step (8), introduce the fictitious parameter tau, orderSubstituting equations (8) - (9) can result in:
step (9), determining the initial conditions as follows:
where, δ is the dirac function,
the following difference format can be obtained by adopting the finite difference method and the total variation reduction format in the step (10):
in the formula, τk＝kΔτ(k＝0,1,…)，rLAXin order to be a differential grid ratio,in the form of a flow restrictor or flow restrictor,andcan be expressed as:
step (11) will be at NtotalAt one sample point to calculateSumming, one can get:
step (12) of taking τk1, the probability density function expression of the maximum real part μ of the eigenvalue can be obtained:
step (13) according toIf present, isThe panel is at risk of flutter failure.
In step (9), the initial condition may be discretized into:
in the formula,andis composed ofAndgrid size of direction;
wherein,in the step (10), the convergence condition to be satisfied by the difference format is as follows:
the invention has the beneficial effects that:
the invention provides a wallboard aeroelasticity stability analysis method considering mixing uncertainty, which can analyze a generalized characteristic value corresponding to a wallboard aeroelasticity equation containing mixing uncertainty parameters, and obtain a probability density function of a boundary of a maximum real part interval of the characteristic value, so as to judge the aeroelasticity stability of a wallboard. The characteristic value real part interval probability density function obtained by the method is well matched with the characteristic value real part interval probability density function obtained by the Monte Carlo method, the calculation time can be greatly reduced, and a new thought is provided for the aeroelastic stability analysis of the wall plate containing mixed uncertain parameters.
Drawings
FIG. 1 is a schematic view of a two-dimensional curved wall panel model;
FIG. 2 is V∞When the speed is 2500m/sμA probability density function of;
FIG. 3 is V∞When the speed is 2500m/sA probability density function of;
FIG. 4 is V∞When the speed is 3200m/sμA probability density function of;
FIG. 5 is V∞When the speed is 3200m/sA probability density function of;
fig. 6 is a flow chart of the method implementation of the present invention.
Detailed Description
Hereinafter, a design example of the present invention will be described in detail with reference to the accompanying drawings. The present invention is in the field of aeroelastic design of wall panels, and it should be understood that the examples have been chosen only to illustrate the invention, and not to limit the scope of the invention.
(1) The geometric model of the two-dimensional curved wall plate structure is shown in figure 1;
(2) giving material property parameters and inflow parameters of the curved wall plate structure unit, as shown in table 1;
table 1 curved wall panel structure material properties and incoming flow parameters
In Table 1, E is the modulus of elasticity, ρ∞As density of incoming flow, ρsDensity of curved wall board, αsIs the coefficient of thermal expansion;
(3) random variable α for Table 1stoThe coefficient of variation cov was taken to be 0.01 for the interval variable α, subject to a normal distributioninWith interval boundary of αin c[1-β,1-β]β is an uncertain factor, in this case β is 0.05;
(4) e and rho∞The variation interval [ theta-6 sigma, theta +6 sigma ]]Equally divided into 20 subintervals, E and ρ at the subinterval boundaries∞Comprises the following steps:
thus, a sample point (E) is formedi,ρ∞j) There were 441 total;
(5) taking the q sample point (E)i,ρ∞j)qAccording to (E)i,ρ∞j)qSetting material and inflow parameters, establishing a aeroelastic finite element equation of the wall plate, and obtaining a corresponding sample point (E) through interval analysisi,ρ∞j)qInterval boundary of maximum real part of eigenvalue ofμAnd
(6) set up toμAndthe probability density evolution equation of (a):
(7) the initial conditions may be discretized as:
(8) the finite difference format is set as:
(9) current limiterThe following settings are set:
(10) repeating the steps (5) to (9), and calculating probability density functions corresponding to all 441 sample points Summing them can yield:
(11) take tauk1, the probability density function expression of the interval boundary with the maximum real part of the eigenvalue can be calculated as:
(12) taking 10000 sample points which are obeyed normal distribution by using a Monte Carlo simulation method, and corresponding each sample point to the interval boundary of the maximum real part of the characteristic valueμAndis calculated to obtainμAnda probability density function of;
(13) obtained by the above two methods under the conditions of inflow velocity of 2500m/s and 3200m/sμAndthe probability density function is shown in fig. 2-5, and the results in the figure show that the results obtained by the method of the invention are better matched with the results obtained by the Monte Carlo method;
(14) the two methods respectively calculate the total time consumption as follows: t isThe method of the invention＝5200s,TMonte Carlo simulation method14210 s. The time comparison result shows that the method can reduce the calculation time consumption, thereby obviously improving the calculation efficiency of the probability density function;
(15) stability analysis can be performed according to FIGS. 2-5 when V is∞When it is 2500m/s, the reason is thatThe system has no flutter failure risk; when V is∞When 3200m/s, existI.e. the system has a risk of flutter failure.
In summary, the present invention provides a method for analyzing the aero-elastic stability of a wall panel in consideration of mixing uncertainty. And aiming at a mixed uncertain environment in which random variables and interval variables coexist, carrying out quantitative characterization on mixed uncertain parameters by using a random model and an interval model, and establishing a wallboard aeroelastic stability analysis model containing the mixed uncertain parameters. On the basis, the probability density evolution method is combined with the interval uncertainty propagation analysis method, the random-interval mixed probability density evolution method is provided, the probability statistical characteristics of the boundary of the panel aeroelastic response interval can be estimated when the parameter fluctuation is large, the limitations of the traditional method on the calculation efficiency and the applicability are overcome, and the blank of the research on the analysis of the panel aeroelastic stability under the mixed uncertainty environment is filled.
The above are only the specific steps of the present invention, and the protection scope of the present invention is not limited at all, and the present invention can be extended to be applied in the field of aeroelastic design of aircrafts, and any technical solution formed by equivalent transformation or equivalent replacement falls within the protection scope of the present invention.
Claims (3)
1. A method for analyzing the aeroelastic stability of a wall plate by considering mixing uncertainty is characterized by comprising the following steps: the method comprises the following implementation steps:
step (1), establishing a panel pneumatic elastic finite element equation containing mixing uncertain parameters:
in the formula, αsto＝(αsto,1,αsto,2,…,αsto,m) Is composed ofRandom vector, αin＝(αin,1,αin,2,…,αin,l) Is an interval vector, M and l are vector dimensions, M is a wallboard mass matrix, C is a wallboard damping matrix,is a pneumatic damping matrix, K is a wallboard stiffness matrix,is an aerodynamic stiffness matrix, x (t) is a generalized coordinate,in the case of a speed in a broad sense,generalized acceleration, t is time;
step (2) of letting x (t) be x0eλtThe wall plate aeroelasticity finite element equation containing the mixed uncertain parameters can be converted into a generalized characteristic value equation:
A(αsto,αin)u＝λB(αsto,αin)u (2)
in the formula, λ is a generalized eigenvalue;
in the step (3), the maximum real part μ of the eigenvalue can be obtained by the following formula:
μ＝μ(αsto,αin)＝max{Re[λi(A(αsto,αin),B(αsto,αin))]},(i＝1,2,...,2n) (3)
in the formula, Re represents a real part of a characteristic value;
step (4), establishing a probability density evolution equation containing random-interval mixed parameters, wherein the probability density evolution equation is expressed as the following form:
in the formula,μandlower and upper intervals of μ, p μ αAndis prepared from (a)μα) andthe joint probability density function of (a) is,
step (5), at uncertain parameter αstoChange domain omega ofstoTaking N evenlytotalA sample point, noted αsto,q(q＝1,...,Ntotal) And will change the domain omegastoIs divided into NtotalIndividual field, denoted as Ωsto,q(q＝1,…,Ntotal)；
Step (6), equations (4) - (5) are placed in the sub-domain omegasto,qInternal integration, one can get:
by exchanging the integration and derivation order, equations (6) - (7) can be reduced to:
in the formula,andis the probability density function corresponding to the qth sample point;
step (8), introduce the fictitious parameter tau, orderSubstituting equations (8) - (9) can result in:
step (9), determining the initial conditions as follows:
where, δ is the dirac function,
the following difference format can be obtained by adopting the finite difference method and the total variation reduction format in the step (10):
in the formula, τk＝kΔτ(k＝0,1,…)，rLAXin order to be a differential grid ratio,in the form of a flow restrictor or flow restrictor,andcan be expressed as:
step (11) will be at NtotalAt one sample point to calculateSumming, one can get:
step (12) of taking τk1, the probability density function expression of the maximum real part μ of the eigenvalue can be obtained:
step (13) according toIf present, isThe panel is at risk of flutter failure.
2. The method of claim 1 for analyzing aeroelastic stability of a wall panel taking into account mixing uncertainty, wherein: in the step (9), the initial conditions may be discretized into:
in the formula,andis composed ofAndthe grid size of the direction.
3. The method of claim 1 for analyzing aeroelastic stability of a wall panel taking into account mixing uncertainty, wherein: in the step (10), the convergence condition to be satisfied by the difference format is as follows:
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