Enhanced stochastic averaging of non-integrable nonlinear systems subjected to stochastic excitations. Issue 113 (October 2018)

• Record Type: Journal Article
• Authors: El-Khoury, Omar; Shafieezadeh, Abdollah
• Is Part Of: Soil dynamics and earthquake engineering. Issue 113(2018)
• Page Start: 256
• Page End: 264
• Publication Date: 2018-10
• Subjects: Stochastic averaging of energy envelope -- Itô calculus -- Non-integrable systems -- Soil-structure interactions -- Hysteretic behavior; Soil dynamics -- Periodicals; Earthquake engineering -- Periodicals; Sols -- Dynamique -- Périodiques; Génie parasismique -- Périodiques; 624.176205
• DOI: 10.1016/j.soildyn.2018.06.005
• Languages: English
• ISSNs: 0267-7261

Abstract

Abstract: Stochastic averaging method based on energy envelope for a non-integrable system reduces the dimension of dynamic systems, while preserving the nonlinearity in system behavior and its stochasticity arising from input excitations. However, this approach for a general system neglects effects of off-diagonal damping components, considers a lumped effect of diagonal damping entries, and assumes independent stochastic excitations for involved degrees of freedom. These constraints may limit the application of stochastic averaging as nonlinear systems often do not satisfy these conditions. This paper addresses these shortcomings and proposes a new strategy to derive an equivalent nonlinear stochastic system. For this purpose, an equivalent excitation intensity and modified damping parameters are derived by equating drift and diffusion components of the modified and the original system through the method of weighted residuals using high order moments of system velocities. The proposed approach, called enhanced stochastic averaging, is demonstrated for a one-story building on a raft foundation in loose sand subjected to lateral stochastic excitations. Results, such as probability density function at different intensity levels, indicate that the enhanced stochastic averaging method significantly improves the analytical predictions of the probabilistic properties of system responses compared to the conventional stochastic averaging method. Highlights: Enhanced stochastic averaging of energy for coupled hysteretic systems is proposed. Modified damping and excitation are derived using weighted residuals method. The proposed method is applied to a nonlinear foundation-structure system. The derived PDF of energy agrees well with Monte Carlo simulation results. The proposed method has applications in reliability analysis and control design.