Analytical Techniques for Broadband Multielectromechanical Piezoelectric Bimorph Beams with Multifrequency Power Harvesting

Abstract

This paper presents the multifrequency responses of multielectromechanical piezoelectric bimorph beams using a novel analytical model based on the closed-form boundary value method reduced from the strong form of Hamiltonian’s principle. The reduced constitutive multielectromechanical dynamic equations for the multiple bimorph beams connected in series, parallel, and mixed series-parallel connections can be further formulated using Laplace transformation to give new formulas for power harvesting multifrequency response functions. The parametric case studies based on the change in geometrical structures of the multiple bimorphs with and without tip masses are discussed to analyze the trend of multifrequency power harvesting optimization under resistive load. Nyquist responses based on varying geometrical structures and load resistances were used to analyze the multifrequency power amplitudes in the complex domain. Overall, the trend of system response using multiple tiers consisting of multiple bimorphs was found to significantly widen the multifrequency band followed by increasing the power amplitudes.