Design sensitivity analysis and optimization of high frequency structural-acoustic problems using energy finite element method and energy boundary element method.

摘要

In order to design structures with the best noise, vibration and harshness (NVH) performance level and the least material usage, a thorough research has been conducted in this thesis to analyze the structural-acoustic behavior and perform design sensitivity analysis of the structural-acoustic response with respect to such design variables as material property, sizing, shape and configuration design variables of the structural parts, etc.; First of all, the Finite Element Method (FEM) and Boundary Element Method (BEM) are popular numerical approaches for a low frequency structural-acoustic analysis. Once the structural and acoustic problems are de-coupled, a sequential adjoint variable method is proposed using FEM-BEM specifically for the acoustic performance measure, with the adjoint load calculated only as a function of the geometry of the acoustic cavity, and independent of the structural sizing design. It provides a great advantage during the optimization process because updating the sizing design does not require an update of the adjoint load, saving a significant amount in computational costs.; The Energy Finite Element Method (EFEM) has emerged as an appropriate and popular analysis tool for solving high frequency structural-acoustic problems in terms of energy variables. A variational equation is developed for EFEM, where continuum energy terms are defined for structural and acoustic domains and power transfer coefficients are used to assemble the structural-acoustic system. Continuum design sensitivity formulations for EFEM are developed for parametric, shape and configuration design variables using the direct differentiation method and adjoint variable method. It is shown that the configuration design sensitivity formulation can be reduced to a parametric design sensitivity formulation, and that the adjoint variable method can be developed for system with un-symmetric matrix.; Given the structural energy response obtained using EFEM, the Energy Boundary Element Method (EBEM) can be used to solve high frequency radiation problems. For DSA of high frequency acoustic radiation using EFEM-EBEM, a sequential adjoint variable method similar to the one developed for FEM-BEM is developed and applied for different fluid materials such as air and water as radiation media, which extends applications of the proposed approach from mechanical to naval engineering.