Dynamic stability and instability of mechanical systems subjected to stochastic excitations

The dynamic stability and instability of discrete and continuous mechanical systems subjected to deterministic and stochastic loading will be examined in this project. As far as continuous systems are concerned, elastic and viscoelastic materials will be studied, whereby special attention will be directed towards composite structures. One of the areas of research within the proposed project will be the study of stability and instability of multiply connected structures. Apart from the classical theory based on the hypotheses of Kirchhoff-Love, the influence of rotary inertia and transverse shear deformations on the region of almost-sure stability and instability of beams, plates, and shells will be considered. In the case when stochastic processes are ergodic and with known probability density functions, the almost-sure stability will be examined. When the type of a stochastic process is that of white noise, real noise, bounded noise, or a combination of periodical and white noise and periodical and real noise, the regions of stability will be determined on the basis of the analysis of the Lyapunov exponent and moment Lyapunov exponents. The verification of the analytically obtained results will be given in comparison to numerically determined values of the Lyapunov exponent and moment Lyapunov exponents using the Monte Carlo method. A part of numerical calculations will be performed by special functions, such as orthogonal polynomials and hypergeometric functions.