A multiple degree-of-freedom velocity-amplified vibrational energy harvester Part B: modelling

Vibrational energy harvesting has become relevant as a power source for the reduced power requirement of electronics used in wireless sensor networks (WSNs). Vibrational energy harvesters (VEHs) are devices that can convert ambient kinetic energy into electrical energy using three principal transduction mechanisms: piezoelectric, electromagnetic and electrostatic. In this paper, a macroscopic two degree-of-freedom (2Dof) nonlinear energy harvester, which employs velocity amplification to enhance the power scavenged from ambient vibrations, is presented. Velocity amplification is achieved through sequential collisions between free-moving masses, and the final velocity is proportional to the mass ratio and the number of masses. Electromagnetic induction is chosen as the transduction mechanism because it can be readily implemented in a device which uses velocity amplification. The experimental results are presented in Part A of this paper, while in Part B three theoretical models are presented: (1) a coupled model where the two masses of the non-linear oscillator are considered as a coupled harmonic oscillators system; (2) an uncoupled model where the two masses are not linked and collisions between masses can occur; (3) a model that considers both the previous cases. The first two models act as necessary building blocks for the accurate development of the third model. This final model is essential for a better understanding of the dynamics of the 2-Dof device because it can represent the real behaviour of the system and captures the velocity amplification effect which is a key requirement of modelling device of interest in this work. Moreover, this model is essential for a future optimization of geometric and magnetic parameters in order to develop a MEMS scale multi-degree-of-freedom device.