Abstract
A set of novel hybrid projection approaches are proposed for approximating the response of stochastic partial differential equations which describe structural dynamic systems. An optimal basis for the response of a stochastic system has been computed from the eigen modes of the parametrized structural dynamic system. The hybrid projection methods are obtained by applying appropriate approximations and by reducing the modal basis. These methods have been further improved by an implementation of a sample based Galerkin error minimization approach. In total four methods are presented and compared for numerical accuracy and efficiency by analysing the bending of a Euler-Bernoulli cantilever beam.
Highlights
Propagation of uncertainties in complex engineering dynamical systems is receiving increasing attention
When uncertainties are taken in to account, the equations of motion of discretised dynamical systems can be expressed by coupled ordinary differential equations with stochastic coefficients
The computational cost for the solution of such system mainly depends on the number of degrees of freedom and number of random variables
Summary
Propagation of uncertainties in complex engineering dynamical systems is receiving increasing attention. When uncertainties are taken in to account, the equations of motion of discretised dynamical systems can be expressed by coupled ordinary differential equations with stochastic coefficients. The computational cost for the solution of such system mainly depends on the number of degrees of freedom and number of random variables. The computational cost increases significantly with the number of random variables and the results tend to become less accurate for longer length of time. The rationale behind proposing a set of methods is to analyse the effect of altering the nature of the coefficients and vectors associated with projection methods. Altering the nature of the coefficients and the vectors could result in great computational savings, it could induce additional error
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