Abstract
In this paper, the moment Lyapunov exponent and stochastic stability of a fractional viscoelastic plate driven by non-Gaussian colored noise is investigated. Firstly, the stochastic dynamic equations with two degrees of freedom are established by piston theory and Galerkin approximate method. The fractional Kelvin–Voigt constitutive relation is used to describe the material properties of the viscoelastic plate, which leads to that the fractional derivation term is introduced into the stochastic dynamic equations. And the noise is simplified into an Ornstein–Uhlenbeck process by utilizing the path-integral method. Then, via the singular perturbation method, the approximate expansions of the moment Lyapunov exponent are obtained, which agree well with the results obtained by the Monte Carlo simulations. Finally, the effects of the noise, viscoelastic parameters and system parameters on the stochastic dynamics of the viscoelastic plate are discussed.
Highlights
In the past several decades, the flutter problem of plates has attracted more and more attention with the development of supersonic aircraft
For a fractional viscoelastic plate excited by non-Gaussian colored noise, the stochastic stability and pth moment Lyapunov exponent are investigated in the present paper
Based on the moment Lyapunov exponents, the stochastic dynamics of fractional-order viscoelastic plate under non-Gaussian colored noise excitation is investigated in the present paper
Summary
In the past several decades, the flutter problem of plates has attracted more and more attention with the development of supersonic aircraft. For a wide-band noise or non-Gaussian colored noise excited viscoelastic plate, Huang[25, 26] studied the pth moment Lyapunov exponent and obtained an asymptotic expansion of the moment Lyapunov exponent using the stochastic averaging method. Wu[28] discussed the moment stability of a viscoelastic plate under non-Gaussian colored noise excitation by calculating the pth moment Lyapunov exponent. For a fractional viscoelastic plate excited by non-Gaussian colored noise, the stochastic stability and pth moment Lyapunov exponent are investigated in the present paper. Based on the pth moment Lyapunov exponent and largest Lyapunov exponent, the impacts of the noise, viscoelastic parameters and system parameters on the stochastic dynamics of the fractional viscoelastic plate are studied and discussed in detail
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