Design sensitivity analysis of the electromechanical response of piezoelectric energy harvesters under structural vibrations from offshore floating structures

In this paper, we propose to use an innovative multi-scale approach for modeling the frequency and time domain response of piezoelectric energy harvesters (EH) under structural vibrations from offshore floating structures. In doing so, a simplified single degree of freedom (SDOF) model is used to describe the dynamic behaviour of a wave energy converter and/or a floating foundation of offshore wind turbines subjected to flow induced vibrations. The semi-empirical Morison equation is employed to compute the resulting load acting on the structure that is considered as a classically damped linear elastic system. Once the apparatus dynamic response is fully determined, we analyze the energy harvester behaviour which dynamic excitation corresponds to the structural response previously assessed. In practise, the floating device acts as a filter for the wave loads. Furthermore, with the aim to optimize the overall performances, a design sensitivity approach is used for EH modeling and design. The implementation is based on finite element method and automatic differentiation techniques where the overall algorithm is split in two stages: a primal problem and a secondary sensitivity problem.