Analiza nelinearne dinamike mehaničkih struktura sa prigušenjem frakcionog reda primenom aproksimativnih metoda

Abstract

The thesis investigates dynamical behavior of two different mechanical models, nano-beam on fractional viscoelastic foundation and dynamical mass damper, which can be reduced to the nonlinear fractional differential Duffing-type equation systems. Incremental harmonic balance method with continuation method are used to obtain amplitude-frequency response of the system’s steady state solutions. Stability of periodic orbits is investigated in special cases by using Floquet theory of stability. As comparative methods for models described with fractional differential equations are used among others the perturbation method of multiple time scales and Newmark method. The influence of different system parameters on dynamic behavior is examined.