Parametric design sensitivity analysis of high-frequency structural-acoustic problems using energy finite element method

Abstract

SUMMARYA design sensitivity analysis of high-frequency structural-acoustic problems is formulated and presented. The energy finite element method (EFEM) is used to predict structural-acoustic responses in the high frequency range, where the coupling between structural junctions and the structural-acoustic interface are modelled using power transfer coefficients. The continuum design sensitivity formulation is derived from the governing equation of EFEM and the discrete method is applied in the variation of the structural-structural and structural-acoustic coupling matrices. The direct differentiation and adjoint variable method are both developed for the sensitivity analysis, where the difficulty of the adjoint variable method is overcome by solving a transposed system equation. Parametric design variables such as panel thickness and material damping are considered for sensitivity analysis, and numerical sensitivity results show excellent agreement as compared to analytical finite difference results.

Topology optimization of acoustic–structure interaction problems using a mixed finite element formulation

“…For the procedure, the interfacing boundaries should be exactly or at least approximately defined with parametric curves such as splines, which, for optimization, can be controlled by design variables [8,29]. Thus, shape optimization has become a natural choice with this analysis procedure [10,12,17,18,19,20,21,25,26,30]. However, in topology optimization the design variables are normally the local material densities.…”

“…In structural optimization, this segregated analysis method with the explicit boundary representation has been used for shape optimization of acoustic devices [11,20,25,26,27].…”

“…This implies that the position and parameters of the boundary conditions depend on the given topology. The level set method [12,[16][17][18][19][20][21] inherently has a welldescribed boundary, however, it is at present not clear how to deal with the two different sets of governing equations using the method. To circumvent the problem, we suggest to look at the interface 3 problem in an alternative way.…”

Random energy flow analysis of coupled beam structures and its correlation with SEA

“…Since the simple relationship between averaged intensity and energy density, which is the most significant theoretical foundation of EFA, is deduced by assuming that waves with identical frequency propagate oppositely in structures, most applications of EFA are limited to loading cases of single-frequency excitation [1][2][3][4][5][11][12][13][14][15][16], where only waves with the same frequency as the acting force are provoked in structures. For broadband excitation, current application with EFA is to predict the energy response at discrete frequencies as single-frequency excitation and obtain the results through frequency averaging or only predict the response at the central frequency of the band [8][9][10]13].…”

Sampling-Based RBDO Using the Dynamic Kriging (D-Kriging) Method and Stochastic Sensitivity Analysis

“…eliability-based design optimization (RBDO) has been widely applied to various engineering applications such as stamping 1,2 , vehicle design with durability 3,4 , and noise, vibration, harshness (NVH) analysis 5,6 , where accurate sensitivities of performance functions are available. If accurate sensitivities are available in a complex physical system, then the most probable point (MPP)-based reliability analysis, which includes the First-Order Reliability Method (FORM) [7][8][9][10] , the Second-Order Reliability Method (SORM) 11,12 , and the MPP-based Dimension Reduction Method (DRM) [13][14][15] , can be used for approximately assessing the reliability of the system, which is used as a probabilistic constraint in RBDO.…”