Effect of geometric non-linearity and tip mass on the frequency bandwidth of a cantilever piezoelectric energy harvester under tip excitation

Abstract

The research community is investigating a variety of approaches to convert mechanical energies to useful electrical energy in order to fulfil the ever-increasing demand for energy and fulfil the requirements of the various sectors. In this regard, numerous contributions toward increasing the capacity and efficiency of the various energy harvesting techniques have been proposed in recent times; one such promising technology is piezoelectric-based vibration energy harvesting. In the present work, the effect of geometric nonlinearity and tip mass is investigated on the operational frequency range of a cantilever nonlinear piezoelectric energy harvester. The proposed mathematical model is based on an energy-based variational approach. The methodology is formulated for the piezoelectric patched cantilever beam and, eventually solved using an efficient numerical technique . An amplitude incremental iterative algorithm is used to solve the non-linear governing equations of motion for the proposed non-linear broadband harvester along with the experimental validation. Firstly, a parametric study is performed to determine the optimum piezoelectric patch dimensions. Subsequently, the attempt is made to increase the frequency bandwidth for optimum energy harvesting by taking advantage of geometrically non-linear behaviour. Additionally, a tip mass, appropriate for the excitation level, can be added to the harvester design to make it effective for lower excitation frequency. Increased frequency bandwidth for improved energy harvesting capacity with the hardening type nonlinearity and tip mass is meaningfully shown with the help of frequency-amplitude response. Furthermore, to interpret the efficacy of nonlinear harvesters in terms of frequency band-width, power spectral density plots with improved harvesting capability are presented and compared with the conventional linear vibration energy harvester.