On Rapidly Convergent Solutions to Acoustics Problems with Time-Dependent Boundary Conditions

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Engineering (HMC)

Publication Date



The purpose of this letter is to present to the acoustics community a technique for solving the wave equation with time-dependent boundary conditions, in terms of a rapidly converging eigenfunction expansion. The technique, variously called the Williams Method or the modal acceleration method, makes use of the principle of superposition and eigenfunction expansions which are similar to the conventional normal mode solutions commonly used in structural dynamics [1]. The method has been applied to the three-dimensional elasticity equations [2, 3], to the forced vibrations of beams, plates and shells [1, 4, 5, 6], to transient heat conduction problems [7], and to the uncoupled transient thermo-elastic problem of an isotropic, elastic solid [8].

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© 1973 Published by Elsevier Ltd.