Analysis of bimorph piezoelectric beam energy harvesters using Timoshenko and Euler–Bernoulli beam theory

• Published in: Journal of intelligent material systems and structures Vol. 24; no. 2; pp. 226 - 239
• Main Author: Wang, Gang
• Format: Journal Article
• Language: English
• Published: London, England SAGE Publications 01-01-2013; Sage Publications
• Subjects: Beams (radiation); Computer simulation; Energy harvesting; Euler-Bernoulli beams; Exact sciences and technology; Finite element method; General equipment and techniques; Harvesters; Instruments, apparatus, components and techniques common to several branches of physics and astronomy; Mathematical analysis; Mathematical models; Physics; Piezoelectricity; Transducers; Energy harvesting; spectral finite element; piezoelectric; Finite element method; Spectral method; Bimorph transducer; Timoshenko beam; Lumped parameter system; Energy recovery; Modelling; Euler equations; Distributed parameter systems
• ISSN: 1045-389X; 1530-8138
• DOI: 10.1177/1045389X12461080

Single-degree-of-freedom lumped parameter model, conventional finite element method, and distributed parameter model have been developed to design, analyze, and predict the performance of piezoelectric energy harvesters with reasonable accuracy. In this article, a spectral finite element method for bimorph piezoelectric beam energy harvesters is developed based on the Timoshenko beam theory and the Euler–Bernoulli beam theory. Linear piezoelectric constitutive and linear elastic stress/strain models are assumed. Both beam theories are considered in order to examine the validation and applicability of each beam theory for a range of harvester sizes. Using spectral finite element method, a minimum number of elements is required because accurate shape functions are derived using the coupled electromechanical governing equations. Numerical simulations are conducted and validated using existing experimental data from the literature. In addition, parametric studies are carried out to predict the performance of a range of harvester sizes using each beam theory. It is concluded that the Euler–Bernoulli beam theory is sufficient enough to predict the performance of slender piezoelectric beams (slenderness ratio > 20, that is, length over thickness ratio > 20). In contrast, the Timoshenko beam theory, including the effects of shear deformation and rotary inertia, must be used for short piezoelectric beams (slenderness ratio < 5).