Dynamic stability of nonlocal Voigt–Kelvin viscoelastic Rayleigh beams

The dynamic stability problem of a viscoelastic nanobeam subjected to compressive axial loading, where rotary inertia is taken into account, is investigated. The paper is concerned with the stochastic parametric vibrations of a Voigt–Kelvin nanobeam based on Eringen’s nonlocal elasticity theory of the Helmholtz and bi-Helmholtz type of kernel. The axial force consists of a constant part and a time-dependent stochastic function. By using the direct Liapunov method, bounds of the almost sure asymptotic stability of a viscoelastic nanobeam are obtained as a function of retardation time, variance of the stochastic force, geometric ratio, scale coefficients, and intensity of the deterministic component of axial loading. Numerical calculations were done for the Gaussian and harmonic process. When the excitation is a real noise process, the advanced numerical simulation based on the Monte Carlo method is presented for moment Liapunov exponents numerical determination.