Nonlinear vibration analysis of electret-based energy harvesting beams

This paper investigates the nonlinear dynamics of a capacitive electret-based capacitive energy harvester, focusing on solving the governing equations using semi-analytical methods, particularly the method of multiple scales (MMS). The harvester features a cantilever micro-beam above an electret layer, where surface voltage induces nonlinear electrostatic forces. These forces are simplified using a third-order Taylor expansion to reduce complexity while preserving key nonlinear characteristics. The Galerkin method is used to discretize the governing equations, transforming them into ordinary differential equations based on the system's mode shapes. The method of multiple scales (MMS) is then applied to these reduced equations to obtain approximate analytical solutions for the system’s dynamic response. A comparison between the simplified and original equations confirms the simplified model’s accuracy. The study highlights the value of advanced nonlinear analysis in enhancing the performance of capacitive energy harvesters and proposes a robust framework for their optimization using these combined methods.

Nonlinear vibration analysis of electret-based energy harvesting beams Keywords:

Electret , Method of Multiple Scales , Galerkin Method , Taylor Expansion.