A Three-Dimensional Piezoelectric Timoshenko Beam Model Including Torsion Warping

BELTRAMO, EMMANUEL; PREIDIKMAN, SERGIO; PÉREZ SEGURA, MARTÍN EDUARDO; ROCCIA, BRUNO ANTONIO

Multibody Mechatronic Systems

Springer Nature

Año: 2021; p. 143 - 150

In this article, the authors present a three-dimensional formulation of aTimoshenko beam element intended for energy harvesting. The beam cross-sectionis idealized as an arbitrary number of laminate piezoelectric transducers embeddedwithin an elastic substrate. In addition, each transducer is connected to threedifferent electronic components: a resistance, a capacitor, and an inductor. Unlikestandard Timoshenko-like beam theories, the model presented here is enhanced byincluding warping displacements due to homogeneous torsion. The resulting governingequations are spatially discretized through the finite element method (FEM)and numerically integrated in the time domain using the ODE solvers available inMATLAB®. The performance, advantages and disadvantages of the proposed modelare 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.