Eigenvalues gap optimization with sensitivity criteria in coupled acoustic-structural systems

Abstract

The design optimization can be made following a hard repetitive time consuming process, through the analysis of the design with a few modifications in its parameters, until the required system is encountered. To solve this problem, it is better to use the sensitivity analysis, letting one evaluate the model performance without realizing new analysis. The purpose of this work is to optimize the gap between two eigenvalues in coupled acoustic-structure systems in order to avoid the resonance phenomena in a certain frequency interval, taking the thickness of the structural elements as control variables subject to one constant structural volume. The finite element method is used for discretization of the system, and one nonsymmetrical formulation up with Hermissian matrices in displacement of the structure and fluid pressure describes the system, being necessary to use the left and right eigenvectors concept. For simplicity the nonzero and nonrepeated eigenvalue case is considered. The sequential quadratic programming algorithm is used for the constrained nonlinear optimization, and in the optimization process is considered the modal sensitivity analysis to choose the more sensible parameters. The validity of the study is verified by applying it to a coupled bidimensional system. a)Currently at UNICAMP-FEM-DMC.