Hybrid Uncertain Analysis For Structural-acoustic Problem With Stochastic And Evidence Variables

The nosie and vibration rising from the acoustic-structural coupled system has attracted a lot of attention. Generally, the researches of the acoustic-structural coupled system by domestic and international scholars are based on the deterministic numerical analysis. However, in the engineering practice, many uncertainties associated with acoustic-structural coupled system are unavoidable, such as material property, external excitations, boundary conditions, and so on. In most cases, the uncertainty of a single nondeterministic parameters are small. But when many parameters are coupled, these small uncertainties may result in a large deviation of the response of the acoustic-structural coupled system.In order to research the influence on the response of the acoustic-structural coupled system by the uncertainties, the stochastic uncertainty, evidence theory uncertainty and the stochastic and evidence hybrid uncertainty are introduced into the acoustic-structural coupled system in this paper. And based on the three uncertain models, the numerical analysis model of the acoustic-structural coupled system should be constructed, accordingly. Futhermore, the three nondeterministic numerical analysis techniques should be developed.The main works of this thesis are as follows:(1) A stochastic perturbation finite element method(SPFEM) was researched for the prediction of the expectation and variance of the response of the stochastic acoustic-structural coupled system. In SPFEM, the formulation of the stochastic structural-acoustic finite element method was constructed firstly. And then the expectation and variance of the response of the stochastic acoustic-structural coupled system were calculated by the stochastic perturbation technique. SPFEM was applied to the numerical analysis of a shell structural-acoustic coupled system. The numerical results showed that SPFEM can be effectively employed to predict the expectation and variance of the response of the stochastic acoustic-structural coupled system.(2) A evidence theory finite element method(ETFEM) was researched to predict the variational ranges of expectation and variance of the response of the evidence acoustic-structural coupled system. In ETFEM, the lower and upper bounds of the response of the evidence subinterval acoustic-structural coupled system was constructed by interval perturbation technique. Then, the variational ranges of expectation and variance of the response of the evidence acoustic-structural coupled system were calculated by moments technique of evidence function. ETFEM was applied to the numerical analysis of a shell structural-acoustic coupled system. The numerical results showed that ETFEM can be effectively employed to predict the variational ranges of expectation and variance of the response of the evidence acoustic-structural coupled system.(3) A hybrid evidence and stochastic finite element method(HESFEM) was researched to predict the variational ranges of expectation and variance of the response of the evidence and stochastic acoustic-structural coupled system. In HESFEM, the formulation of the evidence subinterval and stochastic structural-acoustic coupled system was constructed by interval random perturbation technique. Then, the expectation and variance of the response of the evidence subinterval and stochastic acoustic-structural coupled system were calculated by the random moment technique. And the variational ranges of expectation and variance of the response of the evidence subinterval and stochastic acoustic-structural coupled system were calculated by the vertex method. Finally, the variational ranges of expectation and variance of the response of the evidence and stochastic acoustic-structural coupled system were calculated by repeating stochastic interval analysis for each combination of the random variables and the joint focal elements. HESFEM was applied to the numerical analysis of a shell structural-acoustic coupled system. The numerical results showed that HESFEM can be effectively employed to predict the expectation and variance of the response of the stochastic acoustic-structural coupled system.