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.
Highlights
Viscoelastic materials are widely used in aerospace, construction, textile, and other industries, because they have a series of excellent properties, including light weight, high strength, wide source, and good shock absorption
This paper investigates stochastic stability of coupled viscoelastic system with nonviscously damping driven by white noise through moment Lyapunov exponents and Lyapunov exponents
The research of dynamical behavior of viscoelastic system has received a lot of interests in recent years [1,2,3,4]
Summary
Viscoelastic materials are widely used in aerospace, construction, textile, and other industries, because they have a series of excellent properties, including light weight, high strength, wide source, and good shock absorption. [23] proposed the direct Lyapunov method to investigate the almost-sure stochastic stability of a viscoelastic double-beam system under parametric excitation They used the same method to analyze the instability of coupled nanobeam systems subject to compressive axial loading [24]. Deng [33] investigated stochastic stability of two-degrees-of-freedom coupled viscoelastic system under white noise through moment Lyapunov exponent, but its damping term is viscous. The purpose of this paper is to study stochastic stability of a viscoelastic coupled system with nonviscous damping subject to Gaussian white noise excitation through moment Lyapunov exponents and Lyapunov exponents, in which the nonviscous damping term is expressed by Boltzmanns superposition integral with a hereditary relaxation kernel.
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