Stochastic Stability Analysis of Coupled Viscoelastic Systems with Nonviscously Damping Driven by White Noise. (16th September 2018)

• Record Type: Journal Article
• Authors: Liu, Di; Wu, Yanru; Xie, Xiufeng
• Other Names: Xie Xue-Jun Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2018(2018)
• Publication Date: 2018-09-16
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2018/6532305
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : Nonviscously damped structural system has been raised in many engineering fields, in which the damping forces depend on the past time history of velocities via convolution integrals over some kernel functions. This paper investigates stochastic stability of coupled viscoelastic system with nonviscously damping driven by white noise through moment Lyapunov exponents and Lyapunov exponents. Using the coordinate transformation, the coupled Itô stochastic differential equations of the norm of the response and angles process are obtained. Then the problem of the moment Lyapunov exponent is transformed to the eigenvalue problem, and then the second-perturbation method is used to derive the moment Lyapunov exponent of coupled stochastic system. Lyapunov exponent also can be obtained according to the relationship between moment Lyapunov exponent and Lyapunov exponent. Finally, the effects of various physical quantities of stochastic coupled system on the stochastic stability are discussed in detail. These results are validated by the direct Monte Carlo simulation technique.