A Three-Dimensional Piezoelectric Timoshenko Beam Model Including Torsion Warping

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 embedded 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 governing equations are spatially discretized through the finite element method (FEM) and numerically integrated in the time domain using the ODE solvers available in MATLAB (R). The performance, advantages and disadvantages of the proposed model are evaluated by performing a mesh convergence analysis and a shear locking test. Finally, a comparative study between the current model and an Euler-Bernoulli model, in terms of harvested output power, is presented for different beam lengths.