Analysis And Optimization Of Acoustic-Structural Coupled System Based On Convex Model

With the development of automotive technology,more and more attention has been attached to the comfortableness of automobile.As an important indicator that influences vehicle comfort,the interior noise is also attracting increasing attention.Because the interior noise generally involves the interaction between structure and fluid,the study of acoustic-structure coupling system has been the hotspot in noise control field.Uncertain parameters existed widely in engineering,affecting the accuracy of the research.The origin of the uncertain parameters is form material density,sound velocity,manufacturing error and surrounding environment and so on.The coupling of small uncertain parameters may lead the actual response to deviate from the design value.Hence,to make the analysis precisely,it is necessary to consider the impact of uncertain parameters.Probability model,fuzzy model and convex model are common uncertain models used to describe uncertainty parameters.In convex model,numerous samples to obtain the precise probability distribution are no longer needed.So the convex model is more suitable for describing the complex uncertain parameters in engineering.At present,in the field of non-probabilistic convex model research,interval model and ellipsoid model are the two most widely used models.Interval models can be applied to describing independent variables,while ellipsoid models can be applied to deal with relevant variables.Based on Chebyshev approximation method and convex models,this paper studies the analysis and optimization method of acoustic-structure coupling systems.The main research work is as follows:(1)Chebyshev Interval Finite Element Method of Acoustic-Structural SystemBased on the acoustic Helmholtz wave equation,a finite element model of shell structure-acoustic coupling system is established.The Chebyshev Interval Finite Element Method(CIFEM)of structural-acoustic coupled system is proposed.The interval model was introduced to describe the uncertain parameters of the system and the Chebyshev approximate function of the system response is obtained with the interpolation information.Taking the shell-structure acoustic-solid coupling system as an example,the response variation range of the structure-acoustic coupling system can be calculated by CIFEM.The numerical example illustrated the feasibility of CIFEM and the efficiency of CIFEM is much higher than that of Monte-carlo method.(2)Chebyshev Convex Finite Element Method of Structure-Acoustic SystemConsidering the correlation of uncertain parameters,the elliptic model is used to describe the parameters that are relavant.To analyze the response of sound field with elliptic models,the Chebyshev Convex Finite Element Method of structural-acoustic coupled system(CCFEM)is proposed.The numerical results show that CCFEM is an effective analysis method in dealing with acoustic uncertain problem.Moreover,since the polynomial order was increased,the accuracy of calculation distinctly is improved,and the computational efficiency declined.Therefore,the order of the Chebyshev approximation polynomial should be chosen according to the demand of solution precision.(3)Reliability Analysis of Acoustic-Structural Coupled System Based on Ellipsoid ModelsIn the reliability analysis,it is often too conservative to calculate the structural reliability with all the uncertain parameters took the extremes.Based on the analysis of the reliability theory,the ellipsoid model is transformed to a sphere model in standard space,and the reliability index is defined by the sphere norm.According the concerned performance approach and CCFEM,a reliability analysis method of the acoustic-solid coupled system is proposed.In the numerical example,the performance value of the fluid-solid coupling system response is obtained by the concerned performance approach.And the feasibility of a reliability constraint was checked according to the concerned performance value at a concerned point.(4)Robust Optimization Design of Acoustic-Structural Coupled System Based on Ellipsoid Models.To improve the robustness of systems,a acoustic-structural coupled system is taken as the numerical example.The thickness of the upper and lower shells is regarded as the design variable and the total mass of the shell structure as the reliability constraint condition.The optimization model of acoustic-structural coupled system with uncertain objective function and constraint is established.Based on Chebyshev polynomial and reliability theory,the robustness of the acoustic-structural coupled system is optimized.In addition,the optimization objective function was corrected to avoid the problem that the weight coefficient is too large or too small.The results show that the robust optimization method can improve the robustness of the system effectively.For the uncertain analysis of acoustic-structural system based on interval models and ellipsoid models,CIFEM and CCFEM are proposed respectively.The two methods can effectively predict the variation range of sound field response.Besides,combined the care performance method with Chebyshev approximation polynomial,the reliability analysis of acoustic-structural coupled system with convex models is developed.And to avoid the weight coefficient unsuitable,the objective function is modified in the robustness optimization.The result of numerical examples shows that this optimization method can improve the robustness of the system effectively.