Stochastic stability of a fractional viscoelastic plate driven by non-Gaussian colored noise

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.

Proposing a Caputo-Land System for active tension. Capturing variable viscoelasticity

“…FDEs are based on fractional calculus, which is a branch of mathematics that deals with non-integer order derivatives and integrals. It has been proven to be a powerful modeling tool in many fields, such as control theory [ 34 ], medical electronics [ 35 ], cell-biology [ [36] , [37] , [38] ], topology [ 39 ], environmental science [ 40 , 41 ], and other viscoelastic applications [ [42] , [43] , [44] , [45] , [46] , [47] , [48] , [49] ]. As noted above, fractional calculus is especially helpful in describing viscoelastic behavior for its non-local definition of derivatives, which feature finite time-history integrals [ 50 ].…”