Non-linear dynamics of a vibration energy harvester by means of the homotopy analysis method

This article reports on the modelling and experimental validation of a vibration energy harvesting approach that uses a permanent-magnet/ball-bearing arrangement and a wire-coil transducer. The harvester’s behaviour is modelled using a forced Duffing oscillator modified with quintic non-linearity, and the primary first-order steady-state resonant solutions are found using the homotopy analysis method. These solutions found are shown to compare well with measured ball-bearing displacements and harvested output power and are used to predict the wideband frequency response of this type of vibration energy harvester. A prototype harvester was found to produce a maximum output power of 16.4 mW from a 14.2 Hz, 400 milli-g excitation.