Dynamic Modeling and Performance Analysis of Complex Nonlinear Piezoelectric Energy Harvesting Systems based on Timoshenko Beam Theory

Abstract

This paper establishes a coupled, electromechanical nonlinear model with formulation for a complex piezoelectric energy harvester using Hamilton’s principle based on both Timoshenko and Euler-Bernoulli beam theories. The coupled nonlinear governing equations are derived and it incorporates geometric, inertial, damping, material and electromechanical coupling nonlinearity effects. The Galerkin method is applied to reduce the nonlinear partial differential equations, while the method of multiple scales is used to yield approximate analytical solutions for displacement, output voltage, and power amplitude. Comparison between the two beam theories under varying length-to-thickness ratios reveals that material nonlinearity significantly enhances the system nonlinear dynamic response. Accounting for shear deformation and rotary inertia, the Timoshenko beam theory demonstrates superior accuracy, particularly for short, thick beams with low length-to-thickness ratios. The results show effective reduction of natural frequency and broadening of low-frequency applicability. Additionally, optimizing load resistance matching improves output stability and energy conversion efficiency under low-frequency resonance conditions.