A Study of A Multi-Degree of Freedom Fractional Order Damped Oscillatory System

Abstract

The fractional calculus is a promising applied mathematical tool to different disciplines. Some dynamic systems can be precisely represented as fractional systems due to their physical properties. A multi-degree of freedom fractional damped oscillatory system is mathematically modeled by means of fractional order differential equation. In this model the damping force acting on the vibrating system is proportional to the fractional derivative of the displacement. The variable-order Caputo fractional derivative and an approximation technique are utilized to obtain the system responses. The approximation is accomplished by using a numerical discretization technique. Based on the definition of variable-order Caputo fractional derivative, the system response is investigated for different system parameters. The approximation of the system response is verified to show the efficiency of the applied techniques.