Dynamics of multi-pendulum systems with fractional order creep elements

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 system containing creep elements described by fractional order derivatives, is presented. Free vibrations of a multi-pendulum system intercoupled by standard light elements and different properties are considered. The corresponding 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 constitutive relation expressed by a fractional order derivative, ordinary differential 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 obtained analytical solution modes are numerically analysed and characteristic vibration modes for different kinetic parameters are graphically presented.