A BEM-Perturbation Technique for Membrane Structuresby G. Steven Gipson, Oklahoma State Univ, Stillwater, OK, USA,
D. D. Reible, Oklahoma State Univ, Stillwater, OK, USA,
Document Type: Proceeding Paper
Part of: Recent Applications in Computational Mechanics
Most of the previous work has concentrated on the free vibration problem. The present paper examines the problem of low frequency forced vibrations of a membrane due to an oscillatory, but otherwise arbitrary, force distribution over the surface of the membrane. A hybrid method is developed which interleaves classical regular perturbation theory with the direct boundary element method (BEM) to achieve an approximate solution to the problem. The new method is of interest because the spatial part of the problem is solved as a superposition of solutions of several static membrane problems; the time dependence is eliminated from the approximate formulation at the outset of the analysis. The result gives rise to a very simple boundary element algorithm to obtain quickly a forced deflection solution for a membrane of arbitrary shape at any point in time under a low frequency oscillating load.
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