Effects of Kerr-type viscoelastic coupling layer with different stiffnesses on stochastic stability of Rayleigh double beams

Abstract

This paper discusses the stochastic stability of a double Rayleigh beam system connected by a Kerr-type three-parameter elastic layer with two different stiffnesses, under compressive axial loads. The beams are modeled using the Rayleigh beam theory, and the axial forces consist of a constant component and a time-dependent stochastic function. The study investigates the almost-sure and moment stability of the double beam system subjected to stochastic compressive axial loading, utilizing the Lyapunov exponent and moment Lyapunov exponents. In the case of weak noise excitations, a singular perturbation method is employed to derive second-order expansions of the moment Lyapunov exponent and the Lyapunov exponent. Monte Carlo simulation is included to validate the obtained results. A numerical study is conducted for selected parameters, and the almost-sure and moment stability in the first and second perturbation are graphically presented. The results provide insights into the influences of different stiffnesses, damping, and the shear parameter of the Kerr-type layer on the stochastic stability of the coupled Rayleigh beam mechanical system, considering the effects of rotational inertia. It is quantitatively and qualitatively determined that reducing the stiffness of one part of the Kerr-type layer leads to a decrease in the stable region of stochastic stability, while reducing the shear parameter results in an increase in the stable region of stochastic stability. Furthermore, a quantitative relationship between different dampings of the Kerr-type viscoelastic layer is determined, where increasing either of the two damping parameters leads to an expansion of the stable region of stochastic stability. The inclusion of rotational inertia effects through the Rayleigh beam theory contributes to more accurate approximations of the obtained solutions.