Vibration Modeling Of A Bimorph Functional Graded Piezoelectric Energy Harvester Based On The Timoshenko Beam Theory

The goal of this work is the modelization of a clamped-free bimorph Functionally Graded Piezoelectric Energy Harvester (FGPEH) subjected to an electrical voltage. The FGPEH is composed of a mixture of two different materials: ceramic alumina and of aluminum sandwiched by two identical piezoelectric layers. These two layers represent piezoelectric actuators, which are symmetrically and perfectly bonded to the top and bottom surfaces of the FGM substrate layer. The FGPEH is modeled by a rectangular Timoshenko beam considering the physical axis instead of the neutral axis. The position of the physical axis has been determined. Only geometric and material linearities are considered in this study. Power law relations are used to obtain the constituent effective material properties. The lagrangian formalism is adopted to establish the free vibration governing equations of the functionally graded piezoelectric beam. The eigenfrequencies and eigenmodes of the bimorph functionally graded piezoelectric beam are computed analytically. This study showed that there is a critical frequency that delimits two distinct vibratory behaviors. For frequencies below (resp above) the critical frequency there is a generation of two (resp four) traveling waves. The effects of pulsation, volume fraction index, and location of the physical axis on the eigenmodes are also examined.