Numerical Analysis Method Of Interval And Random Uncertain Structural-acoustic Coupling System

Composite structural-acoustic coupling systems are used in various transportation industries,such as trains,cars,and ships.The numerical analysis of them has very important significance in reducing radiated noise and improving passenger comfort.Due to cognitive limitations,technical means,and various objective reasons,uncertainty is widespread in the composite structural-acoustic coupling system.This paper proposes numerical analysis methods based on Chebyshev polynomials and arbitrary orthogonal polynomials for the problems of interval uncertain parameters and interval and random hybrid uncertain parameters in composite structural-acoustic systems.And validate the effectiveness of the proposed method through an example.The main research contents of this article are as follows:(1)In view of the problem that interval parameters exist in the composite structural-acoustic coupled system,Chebyshev polynomials are introduced into the finite element calculation model,and the Chebyshev polynomial interval finite element method(HCI-FEM)based on the homogenization method is proposed to study the influence of interval variables on sound pressure response.HCI-FEM constructs a proxy model through Chebyshev series,and finally uses Monte Carlo simulation to calculate the upper and lower bounds of the sound pressure response.The results of numerical analysis show that a good precision numerical solution can be obtained by the Chebyshev series approximation,and it is more accurate than the Taylor series.Due to the non-invasive nature of the Chebyshev series approximation method,there is no need for complicated derivation to construct a high-order Chebyshev polynomial expansion.Therefore,the high-order Chebyshev series can be used to analyze complex system with large uncertainty level.(2)In view of the problem that the interval and random parameters exist in the composite structural-acoustic coupling system at the same time,the arbitrary polynomial chaos expansion is introduced into the interval and random hybrid uncertain model,and the interval and random arbitrary polynomial expansion method(IRAPEM)is proposed to study the hybrid variables Impact on system response.In IRAPEM,PDF is selected as the weight function for random parameters,and Chebyshev weight function is selected as the weight function for interval parameters.The research results show that the calculation accuracy of IRAPEM is good,and as the truncation order n increases,the calculation accuracy increases accordingly.Therefore,when the system uncertainty is large or the uncertainty problem is more complicated,IRAPEM is still applicable.(3)When the random parameters in the interval and random hybrid model exist in the form of raw data,and the estimated probability density function is prone to deviation,the traditional IRAPEM is no longer applicable.At this time,arbitrary polynomial expansion based on moments is introduced into the interval and random hybrid model.An interval and random moment-based polynomial expansion method(IRMAPEM)is proposed.Since the weight function of the random variable in IRAPEM is taken as its probability density function,the deviation generated in the estimated PDF is brought into the elements in the Hankel matrix,so it affects the polynomial expansion.The new method IRMAPEM avoids such errors.