A STOCHASTIC NEWMARK METHOD FOR ENGINEERING DYNAMICAL SYSTEMS

✍ Scribed by D. ROY; M.K. DASH

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 533 KB
• Volume: 249
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.2001.3854

✦ Synopsis

The purpose of this study is to develop a stochastic Newmark integration principle based on an implicit stochastic Taylor (Ito}Taylor or Stratonovich}Taylor) expansion of the vector "eld. As in the deterministic case, implicitness in stochastic Taylor expansions for the displacement and velocity vectors is achieved by introducing a couple of non-unique integration parameters, and . A rigorous error analysis is performed to put bounds on the local and global errors in computing displacements and velocities. The stochastic Newmark method is elegantly adaptable for obtaining strong sample-path solutions of linear and non-linear multi-degree-of freedom (m.d.o.f.) stochastic engineering systems with continuous and Lipschitz-bounded vector "elds under ("ltered) white-noise inputs. The method has presently been numerically illustrated, to a limited extent, for sample-path integration of a hardening Du$ng oscillator under additive and multiplicative white-noise excitations. The results are indicative of consistency, convergence and stochastic numerical stability of the stochastic Newmark method (SNM).