A contribution on the optimal design of a vibrating cantilever in a power harvesting application – Optimization of piezoelectric layer distributions in combination with advanced harvesting circuits

•We study the effect of shaped piezoelectric layers for power harvesting.•We investigate the influence of different electric circuits for power harvesting.•Verification of an extended Bernoulli-Euler theory for piezoelectric passive beams.•Recommendation of an optimized beam configuration in power harvesting applications.•Simulation of piezoelastic beams and nonlinear circuits within one environment.

The present paper focuses on the optimization of a vibrating cantilever beam in a power harvesting application studying different distributions of piezoelectric layers and attached electric circuits. In the first part of the contribution, the governing motions of a slender beam with piezoelectric layers are presented. Then the basic equations of three commonly accepted interface circuits are presented: a standard interface circuit, a synchronized switching circuit with inductance (SSHI) and a circuit consuming energy through the synchronous charge extraction technique (SCE). In the case study, a cantilever beam is studied, which is excited by a uniformly distributed quasi-harmonic lateral force. In a first step the presented theory for a laminated piezoelastic Bernoulli–Euler beam is validated by three-dimensional, electromechanically coupled finite element results with ANSYS. Then the verified model is used to compare the dissipated energy for the different layer distributions (discretized by a parabolic, a linear and a constant distribution) and for the three interface circuits. The ratio of the dissipated energy between a beam with parabolically distributed piezoelectric layers and a beam with space-wise constant layers is 2:1. The configuration with the SCE-circuit as the electric network and the layers distributed according to the parabolic function is the most efficient.