A Timoshenko like model for piezoelectric energy harvester with shear mode

Abstract

In the present study a fully coupled electromechanical Timoshenko beam theory is developed for modelling an energy harvester operating in d31 (flexural mode with correction due to shear deformation/rotary inertia) and relatively rare d15 (pure shear) mode. The model is developed based on Variational Asymptotic Method (VAM). VAM is a dimensional reduction methodology, which asymptotically approximates the original 3D electromechanical enthalpy into an equivalent 1D electromechanical enthalpy functional, using small parameters present in the system. Firstly, we develop a fully coupled Timoshenko cross sectional model, which provides us a single common platform to analyze both d15 and d31 mode energy harvester. The developed cross sectional model is represented by a 7 × 7 electromechanical stiffness matrix with an additional 1D electrical variable along with 6 1D mechanical degrees of freedom commonly present in Timoshenko type analysis. The cross-sectional model is general enough to accommodate harvesters made of multilayer, arbitrary shaped cross-section, anisotropic material operating in both pure shear as well as in flexure mode. The coupled cross sectional output is fed subsequently into a 1D beam problem for a complete solution.