Dynamics of fractional-order multi-beam mass system excited by base motion

Abstract

Vibration of structures induced by some external sources of excitation is a common phenomenon in many engineering fields such as civil engineering, machinery and aerospace. In most cases, it is desirable to suppress such vibrations but lately there are attempts to exploit this phenomenon for the energy harvesting purposes. Multiple connected structures with attached masses are ideal systems for such applications. In this study, we propose a cantilever multi-beam system excited by base motion, with an arbitrary number of attached masses on beams and fractional-order damping considered. The corresponding governing equations with fractional-order derivatives and non-homogeneous boundary conditions are given. These equations are solved by first homogenizing the boundary conditions and applying the Galerkin discretization, and then using the Fourier transform and impulse response methodology. A steady state response of the system is also analysed. In the numerical study, the influence of various system parameters on the dynamic behaviour of the system is investigated, and different beam-mass configurations are examined. The potential application of this type of systems is also commented.