Non-linear multi-degree-of-freedom system random vibration by equivalent statistical quadratization
type: Item
instance of: scholarly article
title: Non-linear multi-degree-of-freedom system random vibration by equivalent statistical quadratization
zbMATH Open document ID: 0765.70019
DOI: 10.1016/0020-7462(92)90030-B
published in: International Journal of Non-Linear Mechanics
publication date: 1993-03-29T00:00:00Z
review text: The method of statistical quadratization is generalized to multi-degree- of-freedom systems. The statistical quadratization solution procedure involves replacing the nonlinear system by an ``equivalent'' system with polynomial nonlinearities up to quadratic order. The nonlinear equivalent system has a form whose solutions can be approximated by using the Volterra series method. The non-Gaussian joint response probability distribution is approximated by a third-order Gram-Charlier expansion. The method is formulated for systems with general nonlinearities and with nonlinearities of a special form. To demonstrate the usefulness of the method, solutions are obtained for a specific system.
Mathematics Subject Classification ID: 70L05
zbMATH DE Number: 109416
zbMATH Keywords: Monte Carlo simulation
zbMATH Keywords: polynomial nonlinearities
zbMATH Keywords: quadratic order
zbMATH Keywords: Volterra series method
zbMATH Keywords: non-Gaussian joint response
zbMATH Keywords: third-order Gram- Charlier expansion
author: P. D. Spanos
author: Mark G. Donley
MaRDI profile type: Publication
full work available at URL: 0020-7462(92)90030-b
OpenAlex ID: W2072849988
description: scientific article; zbMATH DE number 109416