Dynamic instability of coupled nanobeam systems

Abstract

The dynamic instability problem of coupled nanobeam system subjected to compressive axial loading is investigated. The paper is concerned with the stochastic parametric vibrations of nanobeams based on Eringen’s nonlocal elasticity theory of Helmholtz and bi-Helmholtz type of kernel and Euler–Bernoulli beam theory. Each pair of axial forces consists of a constant part and a time-dependent stochastic function. By using the direct Liapunov method, bounds of the almost sure asymptotic instability of a coupled nanobeam system as a function of viscous damping coefficient, stiffness of the coupling elastic medium, variances of the stochastic forces, scale coefficients, and intensity of the deterministic components of axial loading are obtained. Analytical results are verified with the numerical results obtained from the Monte Carlo simulation. Numerical calculations are performed for the Gaussian process with a zero mean as well as a harmonic process with random phase.