Dynamics of multi-pendulum systems with fractional order creep elements

Abstract

A survey as a short review of author's research results in area of dynamics of hybrid systems and analytical dynamics of discrete material particle sys- tem containing creep elements described by fractional order derivatives, is presented. Free vibrations of a multi-pendulum system intercoupled by stan- dard light elements and different properties are considered. The correspon- ding system of an ordinary fractional order as well as integro-differential equations, described dynamics of the multi-pendulum system, are derived and analytically solved. For the case of one pendulum and two pendulum systems containing standard light creep elements with the stress-strain con- stitutive relation expressed by a fractional order derivative, ordinary diffe- rential equations are analytically solved. From the analytical solutions, for the case of the homogeneous two-pendulum system, it is visible that free vibrations under arbitrary initial conditions contain three modes, one pure periodic and two aperiodic expressed by time series expansions. The obta- ined analytical solution modes are numerically analysed and characteristic vibration modes for different kinetic parameters are graphically presented.