Stochastic stability analysis of a fractional viscoelastic plate excited by Gaussian white noise

• The constitutive relation of viscoelastic materials is described by the fractional Kelvin–Voigt model. And based on the p th moment Lyapunov exponent, the stochastic dynamics of a fractional viscoelastic plate excited by Gaussian white noise is investigated in detail. • Applying the singular perturbation method and Fourier series expansion, the p th moment Lyapunov exponent is calculated analytically. • With the introduction of the fractional Kelvin–Voigt constitutive relation, the natural frequencies significantly affect the stochastic stability of the viscoelastic plate. The fractional viscoelastic model arises naturally in the context of systems where integer order model does not match well with practical needs and finds wide applications in engineering reality. However, the research on stochastic dynamic characteristic of the fractional viscoelastic plate is still limited. In this paper, the stochastic stability of a fractional viscoelastic plate under Gaussian white noise is studied by determining the p th moment Lyapunov exponent. Firstly, by introducing the fractional Kelvin–Voigt model to represent the constitutive relation, the fractional stochastic dynamic equations with two degrees of freedom for the viscoelastic plate are established by piston theory and Galerkin approximate method. Thereafter, the first-order approximate analytic results of the p th moment Lyapunov exponent are calculated through utilizing the singular perturbation method, which agree well with the Monte Carlo simulations. Finally, the effects of noise, viscoelastic factors and system parameters on the stochastic stability of the fractional viscoelastic plate are investigated in detail. We show that the natural frequencies carry significant effects on the stochastic stability of the viscoelastic plate.