Stochastic stability of multi-nanobeam systems

Abstract

The paper analyzes a stochastic stability problem of a multi-nanobeam system subjected to compressive axial loading. It is assumed that each pair of nanobeams is simply supported and continuously joined by a viscoelastic layer. Differential equations of nanobeams are given according to 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 moment Lyapunov exponent method, regions of almost sure stability of a multi-nanobeam system are obtained in a function of different parameters of the viscoelastic medium, axial loadings and number of nanobeams. Using the regular perturbation method, an approximated analytical solution of the moment Lyapunov exponent is obtained for a single nanobeam subjected to the white noise process, where the results are successfully confirmed with numerical results using the Monte Carlo simulation method. Numerical determination of the moment Lyapunov exponents is further performed for a higher number of nanobeams and different models of wideband processes.