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Harvesting vibration energy using piezoelectric materials has gained considerable attention over the past few years. Typically, a piezoelectric energy harvester is a unimorph or bimorph cantilevered beam which undergoes base vibration. The focus of this paper is to compare the Euler-Bernoulli model and the Timoshenko model, which are both used for modeling the vibration-based energy harvester. Procedures of deriving the electro-mechanical equation of motion are provided, following exact expressions for the electrical output in two models. Parametric case studies are carried out in order to compare the frequency response of two models. Simulation results show that there is a great difference between Euler-Bernoulli model and Timoshenko model at low length-to-thickness aspect ratio. Such difference diminishes and becomes negligible as aspect ratio increases. It is shown that for the design of piezoelectric energy harvester with small aspect ratio, Timoshenko model can be more accurate than Euler-Bernoulli model in predicting the system behavior.Copyright © 2011 by ASME

In reality, the behavior and nature of nonlinear dynamical systems are ubiquitous in many practical engineering problems. The mathematical models of such problems are often governed by a set of coupled second-order differential equations to form multi-degree-of-freedom (MDOF) nonlinear dynamical systems. It is extremely difficult to find the exact and analytical solutions in general. In this paper, the homotopy analysis method is presented to derive the analytical approximation solutions for MDOF dynamical systems. Four illustrative examples are used to show the validity and accuracy of the homotopy analysis and modified homotopy analysis methods in solving MDOF dynamical systems. Comparisons are conducted between the analytical approximation and exact solutions. The results demonstrate that the HAM is an effective and robust technique for linear and nonlinear MDOF dynamical systems. The proof of convergence theorems for the present method is elucidated as well.Copyright © 2010 by ASME