USE OF HARMONIC BASIS FUNCTIONS IN ACOUSTIC FINITE ELEMENTS
Abstract
An acoustic finite element is developed which employs harmonic of trigonometric basis functions in the element interpolation function. The harmonic element is conformable due to the use of an amplitude coordinate system for the harmonic terms. The calculation of the finite element matrices employ Filon numerical integration methods which make the use of harmonic terms competitive with polynomials. The harmonic element uses subparametric curvilinear mapping to approximate domain boundaries. The harmonic finite element is formulated for two dimensional axisymmetric duct acoustics. The element is applied to plane wave and higher mode inputs in a variable cross-sectional area duct. The finite element is used in the solution of dynamic equilibrium and eigenvalue acoustic matrices. A methodology for condensation of acoustic finite element matrices using a trial solution for the system domain consisting of harmonic basis functions is developed. Choosing linearly independent basis functions for the condensation is necessary. Three limitations on the choice of the basis functions are discussed and the Gram determinant is used as a measure of basis function independence. Coordinate mapping of complex systems into a simple domain, in which basis functions which approximate the domain boundary conditions are chosen is employed. The condensation method was applied to the eigenproblem for hard-wall acoustic cavities of various boundary complexity.
Degree
Ph.D.
Subject Area
Mechanical engineering
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