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Shock and Vibration
Volume 2015 (2015), Article ID 812069, 13 pages
Research Article

Hybrid Stochastic Finite Element Method for Mechanical Vibration Problems

Department of Mathematics and Systems Analysis, School of Science, Aalto University, P.O. Box 11100, 00076 Aalto, Finland

Received 9 April 2015; Revised 23 June 2015; Accepted 28 June 2015

Academic Editor: Evgeny Petrov

Copyright © 2015 Harri Hakula and Mikael Laaksonen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present and analyze a new hybrid stochastic finite element method for solving eigenmodes of structures with random geometry and random elastic modulus. The fundamental assumption is that the smallest eigenpair is well defined over the whole stochastic parameter space. The geometric uncertainty is resolved using collocation and random material models using Galerkin method at each collocation point. The response statistics, expectation and variance of the smallest eigenmode, are computed in numerical experiments. The hybrid approach is superior to alternatives in practical cases where the number of random parameters used to describe geometric uncertainty is much smaller than that of the material models.