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Sample-based and sample-aggregated based Galerkin projection schemes for structural dynamics

Pryse, S.E., Adhikari, S. and Kundu, Abhishek 2018. Sample-based and sample-aggregated based Galerkin projection schemes for structural dynamics. Probabilistic Engineering Mechanics 54 , pp. 118-130. 10.1016/j.probengmech.2017.09.002

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Abstract

A comparative study of two new Galerkin projection schemes to com- pute the response of discretised stochastic partial di�erential equations is presented for discretised structures subjected to static and dynamic loads. By applying an eigen-decomposition of a discretised system, the response of a discretised system can be expressed with a reduced basis of eigen-components. Computational reduction is subsequently achieved by approximating the random eigensolutions, and by only including dominant terms. Two novel error minimisation techniques have been proposed in order to lower the error introduced by the approximations and the trunca- tions: a) Sample-based Galerkin projection scheme, b) Sample-aggregated based Galerkin projection scheme. These have been applied through intro- ducing unknown multiplicative scalars into the expressions of the response. The proposed methods are applied to analyse the bending of a cantilever beam with stochastic parameters undergoing both a static and a dynamic load. For the static case the response is real, however the response for the case of a dynamic loading is complex and frequency-dependent. The re- sults obtained through the proposed approaches are compared with those obtained by utilising a direct Monte Carlo approach.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Engineering
Publisher: Elsevier
ISSN: 0266-8920
Date of First Compliant Deposit: 12 October 2017
Date of Acceptance: 20 September 2017
Last Modified: 04 Oct 2018 06:24
URI: http://orca.cf.ac.uk/id/eprint/105476

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