Acoustic shape optimization

Joseph Ray Milner, Purdue University

Abstract

A methodology for the parametric shape determination of acoustic finite elements is presented. Because the elements are parametrically defined, shape sensitivities are readily obtained. The method depends upon the linear transformations of specified regions. Using these transformations, the acoustic finite element mass and stiffness matrices of the transformed regions may be determined in a parametrically dependent fashion. The assembly of finite elements comprising a region yields a parametrically dependent region, or super-element. By utilizing assumed-modes modal reduction techniques on the super-element regions, a parametrically dependent eigenvalue problem of reduced size may be generated. The smaller size of the reduced eigenvalue problem facilitates optimization, since the computational effort involved in eigenvalue extraction is related to the cube of the problem size. The explicit parametrically dependent mass and stiffness matrices allow the analytical calculation of derivatives of any order, enabling first and second order optimization algorithms to be used directly. In this research, the mass and stiffness matrix sensitivities are used in the formulation of the sensitivity of forced acoustic response by both direct and modal methods. Analytical and numerical correlation studies are presented in order to verify the accuracy of the methods. Examples include the acoustic shape optimization of an automobile interior, and one and two dimensional room acoustics resonance and mode shape sensitivities. A global optimization study of the non-rectangular acoustic reverberation room is presented. A brief application example related to automobile cavity acoustic optimization is also presented.

Degree

Ph.D.

Advisors

Bernhard, Purdue University.

Subject Area

Mechanical engineering

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