A hybrid approach for the random dynamics of uncertain systems under stochastic loading
type: Item
instance of: scholarly article
title: A hybrid approach for the random dynamics of uncertain systems under stochastic loading
zbMATH Open document ID: 1382.70024
DOI: 10.1155/2011/213094
author: Michele Betti
author: Paolo Biagini
author: Luca Facchini
published in: Mathematical Problems in Engineering
publication date: 2011-06-07T00:00:00Z
review text: Summary: This paper presents a hybrid Galerkin/perturbation approach based on Radial Basis Functions for the dynamic analysis of mechanical systems affected by randomness both in their parameters and loads. In specialized literature various procedures are nowadays available to evaluate the response statistics of such systems, but sometimes a choice has to be made between simpler methods (that could provide unreliable solutions) and more complex methods (where accurate solutions are provided by means of a heavy computational effort). The proposed method combines a Radial Basis Functions (RBF) based Galerkin method with a perturbation approach for the approximation of the system response. In order to keep the number of differential equations to be solved as low as possible, a Karhunen-Loève (KL) expansion for the excitation is used. As case study a non-linear single degree of freedom (SDOF) system with random parameters subjected to a stochastic windtype load is analyzed and discussed in detail; obtained numerical solutions are compared with the results given by Monte Carlo Simulation (MCS) to provide a validation of the proposed approach. The proposed method could be a valid alternative to the classical procedures as it is able to provide satisfactory approximations of the system response.
Mathematics Subject Classification ID: 70K55
Mathematics Subject Classification ID: 70L05
Mathematics Subject Classification ID: 37N05
zbMATH DE Number: 5904885
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/213094
OpenAlex ID: W1977388175
Wikidata QID: Q58692813
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description: scientific article; zbMATH DE number 5904885