Boundary Element Formulation for Random Vibration Problems

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Abstract
A new method is proposed to deal with a class of probabilistic mechanics problems. It is based on the application of the boundary element concept to problems involving random excitations. The method circumvents the issue of adequacy of the mesh size associated with the application of the finite element concept. Only the boundary of the domain of interest is discretized. The method is exemplified by analyzing a beam that is continuous over multiple supports and is excited by a force that exhibits spatially correlated random fluctuations in time. For this problem, the boundary of the domain consists of a discrete set of points and the exact solution is obtained. In addition, the Karhunen‐Loeve expansion is incorporated to improve the numerical efficiency of the method by uncoupling the double integrals involved and permitting their calculation as products of single integrals. The new method is applicable to a broad class of probabilistic mechanics problems.

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