Goran Janevski

Moment Lyapunov exponents and stochastic stability of moving narrow bands

Stochastic stability of narrow moving bands under random tension fluctuation is investigated within the concept of the Lyapunov exponent. The moment Lyapunov exponents and Lyapunov exponents are important characteristics determining the moment and almost-sure stability boundaries of a stochastic dynamical system. Galerkin’s method is used to reduce the partial differential equation of motion to a corresponding ordinary differential equation with randomly varying stiffness. We obtain explicit stability conditions based on the asymptotic expansion series for the moment Lyapunov exponent g(p), and the Lyapunov exponent λ for a two-dimensional linear stochastic system.

THERMAL EFFECT ON FREE VIBRATION AND BUCKLING OF A DOUBLE-MICROBEAM SYSTEM

The paper investigates the problem of free vibration and buckling of an Euler-Bernoulli double-microbeam system (EBDMBS) under the compressive axial loading with a temperature change effect. The system is composed of two identical, parallel simply-supported microbeams which are continuously joined by the Pasternak’s elastic layer. Analytical expressions for the critical buckling load, critical buckling temperature, natural frequencies and frequencies of transverse vibration of the EBDMBS represented by the ratios are derived and validated by the results found in the literature. Also analytical expressions are obtained for various buckling states and vibration-phase of the EBDMBS. The temperature change effect is assumed to have an influence on both the microbeams. The length scale parameter, temperature change effect, critical buckling load, thickness/material parameter, Pasternak’s parameter and Poisson’s effect are discussed in detail. Also, as a clearer display of the thermo-mechanical response of EBDMBS, the paper introduces a critical scale load ratio of the modified and the local critical buckling loads in low-temperature environs. Numerical results show that the critical buckling temperatures for classical theories are always higher than the critical buckling temperature for MCST systems.