A Research On The Numerical Analysis And Optimization Method For The Nondeterministic Acoustic-structural Coupled System

The acoustic-structural coupled system widely exists in the automobile, ship,airplane, submarine, spacecraft, and so on. The low-and mid-freuqucy nosie risingfrom the vibration of structure is the main source of the above transportations. Theoptimization design technique based on the acoustic performance analysis of theacoustic-structural coupled system is the most direct and the most promising approachto control the low-and mid-freuqucy nosie of structure. The traditional numericalanalysis and optimization of the acoustic-structural coupled system is emplementedby the classical CAE technique and the optimization method on the basis of thedeterministic parameters. However, due to the effects of manufacturing/assemblingerrors, aggressive environment factors and unpredictable external excitations, theuncertainties associated with the acoustic-structural coupled system are unavoidable.In most cases, the uncertainties of nondeterministic parameters are small.Unfortunately, due to the coupling effects among nondeterministic parameters, thesesmall uncertainties may result in a great deviation of the response of theacoustic-structural coupled system, and even lead to an antiphase phenomenon. Basedon the unreliable response, the acoustic-structural coupled system afther optimizationmay fail to achieve the excepted purpose.In order to realize the numerical analysis and optimization of thenondeterministic acoustic-structural coupled system effectively, the numericalanalysis model of the acoustic-structural coupled system should be constructed byusing the nondeterministic theory. Furthermore, the nondeterministic numericalanalysis techniques should be developed to investigate on the effects of thenondeterministic parameters on the response of the acoustic-structural coupled system.Subsequently, according to the obtained effects of the nondeterministic parameters onthe response of the acoustic-structural coupled system, the nondeterministicoptimization model can be constructed and the corresponding efficient optimizationapproach should be developed. For this purpose, the random model, the intervalmodel, the random and interval hybrid model and the interval random model areintroduced into the acoustic-structural coupled system. Based on thesenondeterministic models, this dissertation conducted a systematical research for thenumerical analysis and optimization of the nondeterministic acoustic-structural coupled system.The main research work and innovative achievements in this dissertation are：(1) A new stochastic perturbation finite element method, namely thechange-of-variable stochastic perturbation finite element method (CVSPFEM), wasproposed for the response analysis of the random acoustic-structural coupled system.In CVSPFEM, the response of the acoustic-structural coupled system is approximatedas a linear function of random variables by the first-order perturbation technique. Andthen the probability density function of the response was calculated by thechange-of-variable technique. Finally, the confidence interval of the response wasestimated according to the definition of the confidence interval. The numerical resultson a shell acoustic-structural coupled system showed that CVSPFEM can beefficiently and effectively employed to predict the probability density function andthe confidence interval of the response of the random acoustic-structural coupledsystem.(2) A modified interval perturbation finite element method (MIPFEM) wasproposed for the response analysis of the interval acoustic-structural coupled system.In the traditional interval perturbation finite element method (IPFEM), the variationalinterval of the response was evaluated on the basis of the first-order Taylor seriesexpansion and the the first-order Neumann series expansion. In the sub-intervalperturbation finite element method (SIPFEM), by substituting the interval into severalsub-intervals, the variational interval of the response was calculated by IPFEM andthe interval union arithmetic. In MIPFEM, the variational interval of the response wasevaluated on the basis of the first-order Taylor series expansion and the the modifiedNeumann series expansion. The numerical example on a shell acoustic-structuralcoupled system verified that IPFEM can only be applied to the response analysis ofthe interval acoustic-structural coupled system with small uncertainties. Bysubstituting the interval into several sub-intervals, the accuracy of the responseanalysis of the interval acoustic-structural coupled system can be improved. However,the computational burden of SIPFEM increases exponentially with the increase of thenumber of sub-intervals. By considering the higher order terms of Neumann series,the computational accuracy of MIPFEM can be improved greatly with a littlteincrease of the computational burden.(3) A hybrid perturbation vertex method (HPVM) was proposed to predict thevariational ranges of expectation and variance of the response of the random andinterval hybrid acoustic-structural coupled system. In HPVM, the response of the random and interval hybrid uncertain acoustic-structural coupled system wasapproximated as a linear function of random variables and interval variables by thehybrid perturbation technique. And then, according to the linear relationship betweenthe approximated response and interval variables, the vertex method was introducedto calculate the lower and upper bounds of response. Finally, the expectations andvariances of the lower and upper bounds were calculated by the random momenttechnique. The expectations of the lower and upper bounds were used as the the lowerand upper bounds of expectation. The variances of the lower and upper bounds wereused as the the lower and upper bounds of variance. The numerical results on a shellacoustic-structural coupled system verified that computational accuracy of HPVMequates to that of the hybrid perturbation Monte-Carlo method (HPMCM) with a largenumber of samples, while the computational efficiency of HPVM is much higher thanthat of HPMCM with a large number of samples.(4) An interval random perturbation vertex method (IRPVM) was proposed to theresponse analysis of the interval random acoustic-structural coupled system. InIRPVM, the response of the interval random acoustic-structural coupled system wasapproximated as a linear function of interval random variables and interval variablesby the interval random perturbation technique. And then, according to the linearrelationship between the approximated response and interval variables, the vertexmethod was introduced to calculate the lower and upper bounds of response. Finally,the expectations and variances of the lower and upper bounds were calculated by therandom moment technique. The expectations of the lower and upper bounds were usedas the the lower and upper bounds of expectation. The variances of the lower andupper bounds were used as the the lower and upper bounds of variance. The numericalresults on a shell acoustic-structural coupled system and the interior acoustic field ofan automobile showed that IRPVM can be efficiently and effectively employed topredict the variational ranges of expectation and variance of the response of theinterval random acoustic-structural coupled system.(5) A unified nest loop optimization model of two hybrid uncertain models (therandom and interval hybrid uncertain model and the interval random model) wasconstructed. To efficiently calculate the objective functions and constraint conditionsof the optimization model, a hybrid perturbation-random moment method (HPRMM)and a hybrid perturbation-change-of-variable method (HPCVM) were proposed.Based on HPRMM and HPCVM, the nest loop optimization model was transferred toa single loop one. The numerical results on two plate acoustic-structural coupled systems showed that HPRMM and HPCVM can be efficiently employed to calculatethe objective functions and constraint conditions. Furthermore, the numerical resultsshow that the hybrid uncertain optimization method based on HPRMM and HPCVMcan be successfully used to reduce the sound pressure and improve the acousticperformance of the hybrid uncertain acoustic-structural coupled system under certainconstraints.(6) An interval perturbation wave-based method (IPWBM) was proposed to thelow-and mid-frequency response analysis of the interval acoustic field. A hybridperturbation wave-based method (HPWBM) was proposed to the low-and mid-frequency response analysis of the random and interval hybrid acoustic field. Thenumerical results on a3D acoustic cavity problem show that IPWBM can be appliedto the prediction of the upper bound of the low-and mid-frequency response of theinterval acoustic field, and HPWBM can be applied to the prediction of the upperbounds of expectation and variance of the low-and mid-frequency response of therandom and interval hybrid acoustic field.This dissertation conducted a systematical research for the numerical analysisand optimization of the nondeterministic acoustic-structural coupled system. For thelow-frequency response analysis of the nondeterministic acoustic-structural coupledsystem, four nondeterministic finite element methods named as CVSPFEM, MIPFEM,HPVM and IRPVM are proposed. For the optimization of the acoustic-structuralcoupled system under the two hybrid uncertain models, a unified hybrid uncertainoptimization method named as the optimization method based on HPRMM andHPCVM is proposed. For the mid-frequency response analysis of the interval acousticfield and the byrid uncertain acoustic field, two nondeterministic wave-based methodsnamed as IPWBM and HPWBM are developed. The proposed numetical analysis andoptimization methods were applied to the response analysis and optimization of theshell/plate acoustic-structural coupled system, the interior acoustic field of anautomobile and a3D acoustic cavity. The numerical results verified the efficiency andeffectiveness of the proposed methods.