A Three-dimensional Piezoelectric Timoshenko Beam Model Including Torsion Warping

EMMANUEL BELTRAMO; BRUNO A. ROCCIA; MARTÍN E. PÉREZ SEGURA; SERGIO PREIDIKMAN

CORDOBA

Simposio; MuSMe 2021 - 7th International Symposium on Multibody Systems and Mechatronics; 2021

International Federation for the Promotion of Mechanism and Machine Science

In this article, the authors present a three-dimensional formulation of a Timoshenko beam element intended for energy harvesting. The beam cross-section is idealized as an arbitrary number of laminate piezoelectric transducers embed-ded within an elastic substrate. In addition, each transducer is connected to three different electronic components: a resistance, a capacitor, and an inductor. Unlike standard Timoshenko-like beam theories, the model presented here is enhanced by including warping displacements due to homogeneous torsion. The resulting gov-erning equations are spatially discretized through the finite element method (FEM) and numerically integrated in the time domain using the ODE solvers available in MATLAB®. The performance, advantages and disadvantages of the proposed model are evaluated by performing a mesh convergence analysis and a shear locking test. Fi-nally, a comparative study between the current model and an Euler-Bernoulli model, in terms of harvested output power, is presented for different beam lengths.