Hybrid Stochastic Finite Element Method for Mechanical Vibration Problems

Abstract EN

We present and analyze a new hybrid stochastic finite element method for solvingeigenmodes of structures with random geometry and random elastic modulus.

The fundamental assumption is that the smallest eigenpair is well definedover the whole stochastic parameter space.

The geometric uncertainty is resolved using collocation and random materialmodels using Galerkin method at each collocation point.

The response statistics,expectation and variance of the smallest eigenmode, are computed in numericalexperiments.

The hybrid approach is superior to alternatives in practicalcases where the number of random parameters used to describe geometric uncertaintyis much smaller than that of the material models.