Acoustic shape optimization using the finite element method

Abstract

Information to predict the sensitivity of acoustical response to geometric shape variations can be calculated using the acoustic finite element formulation [R. J. Bernhard, J. Sound Vib. 98, 55–65 (1985)]. Such sensitivity information can be utilized to indicate to a designer the change of each geometric design variable necessary to achieve a better solution. The sensitivity information also indicates which design variables have minimal effect on the solution and how close the current solution is to an optimal condition. When the condition of the design can be quantified with a performance equation, numerical optimization procedures can be used to systematically find the optimal solution. Sensitivity information also permits the use of efficient gradient optimization algorithms. This paper will illustrate the incorporation of the acoustic finite element shape sensitivity information into a gradient optimization procedure. The design procedures for reactive mufflers will be illustrated. When modal techniques are appropriate for the solution of a particular problem, the shape sensitivity information may also be utilized to find modal sensitivity information.