Abstract
The moment stochastic stability and almost-sure stochastic stability of two-degree-of-freedom coupled viscoelastic systems, under the parametric excitation of a real noise, are investigated through the moment Lyapunov exponents and the largest Lyapunov exponent, respectively. The real noise is also called the Ornstein-Uhlenbeck stochastic process. For small damping and weak random fluctuation, the moment Lyapunov exponents are determined approximately by using the method of stochastic averaging and a formulated eigenvalue problem. The largest Lyapunov exponent is calculated through its relation with moment Lyapunov exponents. The stability index, the stability boundaries, and the critical excitation are obtained analytically. The effects of various parameters on the stochastic stability of the system are then discussed in detail. Monte Carlo simulation is carried out to verify the approximate results of moment Lyapunov exponents. As an application example, the stochastic stability of a flexural-torsional viscoelastic beam is studied.
Highlights
In the study of dynamic stability of structures, Lyapunov exponents play an important role in characterizing sample or almost-sure stability of stochastic systems [1]
The objective of this paper is to study the moment stability and almost-sure stability of 2DOF coupled viscoelastic systems under the real noise excitations
The stochastic stability of coupled viscoelastic systems described by stochastic integrodifferential equations of 2DOF was investigated
Summary
In the study of dynamic stability of structures, Lyapunov exponents play an important role in characterizing sample or almost-sure stability of stochastic systems [1]. For stability of one-degree-of-freedom (1DOF) systems under both white noise and real noise excitations, many interesting results have been obtained in the past [2, 3]. Ariaratnam [6] was among the first who studied the stochastic almost-sure stability by evaluating the largest Lyapunov exponent and the rotation number. Ling et al [7] discussed the response and almost-sure stability of a 1DOF viscoelastic system with strongly nonlinear stiffness under wideband noise excitations. Sufficient conditions for almost-sure stability were obtained for both elastic and viscoelastic columns under the excitation of a random wideband stationary process using Lyapunov’s direct method [10]. The objective of this paper is to study the moment stability and almost-sure stability of 2DOF coupled viscoelastic systems under the real noise excitations. This study carries out Monte Carlo simulation of moment Lyapunov exponents for coupled systems
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