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.