A formulation for modeling levitation based vibration energy harvesters undergoing finite motion

Abstract

This paper presents a geometrically exact formulation for modeling electromagnetic vibration energy harvesters undergoing finite displacements and rotations. The formulation is conceived to model uniaxial harvesters that extract energy from the vibration of flexible multibody systems that are moving arbitrarily in space. The finite rotation framework is based on an updated Lagrangian procedure; the geometrically exact dynamic equilibrium equations of the harvester are written in terms of local director vectors using a material description. The resulting coupled electro-mechanical equations of motion preserve its classical one-dimensional form. Numerical tests are conducted to address the response of the harvester under specific finite displacements-finite rotations excitations.