Electromechanical Modeling and Analysis of a Double-Layer Cantilever Beam Undergoing Combined General Motion

Abstract

Electromechanical modeling and vibration analysis of an inward cantilever beam undergoing translational and rotational motion is carried out based on the Euler-Bernoulli beam theory. The piezoelectric layer is attached to the cantilever beam having a C-shaped cross-section. The equations on motion are derived using the hybrid deformation variable modeling method along with the Rayleigh-Ritz assumed mode method. Spin-up rotational motion and sinusoidal translational motion are simultaneously prescribed for the inward cantilever beam. As a result of the simultaneously prescribed motion, combinatory excitation frequencies are generated. Therefore, resonance occurs at the combinatory frequencies that match the first natural frequency of the inward cantilever beam. Piezoelectric energy harvesters can be effectively designed by changing the specifications of the beam.