Finite element applications in acoustics

Abstract

A review of finite element methods in acoustics is presented. General concepts of FEM such as weighted residual and variational formulations, element types and interpolation within elements, the assembly of elements, continuity of the solution at element boundaries, requirements placed on FEM meshes by high frequencies, the imposition of boundary conditions on rigid, flexible, and absorbing surfaces, the representation of sources, and the approximation of far-field radiation conditions are discussed. The application of FEM to several types of problems in acoustics is demonstrated by reference to published results. Specific examples include: (1) interior problems such as resonant frequencies and forced response in enclosures such as car bodies, aircraft cabins, auditoria, and combustors; (2) sound propagation in moving media in ducts and propagation and radiation in and around aircraft turbofan engines; (3) structure and acoustic interatction such as transmission of sound through aircraft fuselages; (4) acoustic radiation problems which are related to (2) and (3). Emphasis is placed on the physical content of the various problems, mesh generation, the choice of elements, solution procedures, accuracy, and computer resource requirements.