Developments in structural-acoustic optimization for passive noise control

Low noise constructions receive more and more attention in highly industrialized countries. Consequently, decrease of noise radiation challenges a growing community of engineers. One of the most efficient techniques for finding quiet structures consists in numerical optimization. Herein, we consider structural-acoustic optimization understood as an (iterative) minimum search of a specified objective (or cost) function by modifying certain design variables. Obviously, a coupled problem must be solved to evaluate the objective function. In this paper, we will start with a review of structural and acoustic analysis techniques using numerical methods like the finite- and/or the boundary-element method. This is followed by a survey of techniques for structural-acoustic coupling. We will then discuss objective functions. Often, the average sound pressure at one or a few points in a frequency interval accounts for the objective function for interior problems, wheareas the average sound power is mostly used for external problems. The analysis part will be completed by review of sensitivity analysis and special techniques. We will then discuss applications of structural-acoustic optimization. Starting with a review of related work in pure structural optimization and in pure acoustic optimization, we will categorize the problems of optimization in structural acoustics. A suitable distinction consists in academic and more applied examples. Academic examples iclude simple structures like beams, rectangular or circular plates and boxes; real industrial applications consider problems like that of a fuselage, bells, loudspeaker diaphragms and components of vehicle structures. Various different types of variables are used as design parameters. Quite often, locally defined plate or shell thickness or discrete point masses are chosen. Furthermore, all kinds of structural material parameters, beam cross sections, spring characteristics and shell geometry account for suitable design modifications. This is followed by a listing of constraints that have been applied. After that, we will discuss strategies of optimization. Starting with a formulation of the optimization problem we review aspects of multiobjective optimization, approximation concepts and optimization methods in general. In a final chapter, results are categorized and discussed. Very often, quite large decreases of noise radiation have been reported. However, even small gains should be highly appreciated in some cases of certain support conditions, complexity of simulation, model and large frequency ranges. Optimization outcomes are categorized with respect to objective functions, optimization methods, variables and groups of problems, the latter with particular focus on industrial applications. More specifically, a close-up look at vehicle panel shell geometry optimization is presented. Review of results is completed with a section on experimental validation of optimization gains. The conclusions bring together a number of open problems in the field.