Dinamička stabilnost viskoelastičnih kontinualnih sistema pod dejstvom slučajnih poremećaja

Abstract

Dynamic stability of elastic and viscoelastic mechanical systems and nanostructures under the influence of axial forces which are represented by time dependent stochastic functions is analyzed in this dissertation. These disturbances can be wideband random processes such as white noise, real noise, bounded noise etc., or regular random processes with known probability density function distribution (Gaussian and harmonic process). Almost sure boundaries for discreetisated stochastic differential equations which contain wideband processes are obtained by maximal Liapunov exponent and moment Liapunov exponent which are determined using the first and second order stochastic averaging method. In case of non white processes stability boundaries are obtained by Liapunov functional method. Influence of different physical and geometric parameters on almost sure stochastic stability regions are analyzed. Numerical verification for analytical results obtained by moment Liapunov exponent method, as well as numerical determination of moment Liapunov exponents were performed using the simulation based on Monte Carlo method.