Transverse vibration of a cantilever beam under base excitation using fractional rheological model

Abstract

A cantilever beam with piezoelectric layer/layers and with (or without) tip mass under base excitation is very often applied as the main element in piezoelectric devices for harvesting energy. The energy is gained from transverse vibrations of the beam. In the theoretical description, damping term is usually added to Euler-Bernoulli beam equation to eliminate infinite vibration amplitude at resonance. In this study, the fractional derivatives are used to model both stiffness and damping terms in this equation. Suitable equations for the beam with and without tip mass are formulated and solved. For some parameters of proposed fractional model, resonant characteristics and solutions for a few natural vibration modes are numerically calculated.