The stochastic Newmark algorithm for random analysis of multi-degree-of-freedom nonlinear systems

L. Zhang, J. W. Zu, Z. Zheng

Research output: Contribution to journalArticlepeer-review

31 Scopus citations

Abstract

Based on deterministic Newmark integration formulation, a stochastic Newmark algorithm (SNA) is proposed and developed in this paper. A one-step recursive expression is derived to calculate the covariance matrix response of nonlinear systems subjected to non-stationary random disturbances. The autoregressive moving average (ARMA) algorithm is used for simulating realizations of nonwhite random excitation. Closed form parameters of ARMA model are given for a class of random process possessing rational spectral density. This method is illustrated by calculating the mean value and mean square response of systems with symmetric and asymmetrical nonlinearity. Numerical simulations are carried out to demonstrate the accuracy and effectiveness of the method.

Original languageEnglish
Pages (from-to)557-568
Number of pages12
JournalComputers and Structures
Volume70
Issue number5
DOIs
StatePublished - Mar 1999

Keywords

  • Newmark algorithm
  • Nonlinear system
  • Random excitation
  • Stochastic process
  • White noise

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