Design and Optimization of Nature-inspired Piezoelectric Generators: Fractal design

Abstract

A piezoelectric energy harvester or generator is a device with no need for maintenance or external energy being provided since it utilizes vibrations generated by industrial machines to produce an electrical voltage output through a piezoelectric material. The piezoelectric energy harvester can be used to power small Internet of Things (IoT) components, without need for an external battery or connecting cables. The optimization solutions are meant to develop a proof-of-concept for the chosen fractal tree energy harvester design. The aim of this is to investigate if that design can produce a sufficiently high electric output (voltage and power) and a high enough stress in longitudinal branch direction as Frequency Response Functions (FRFs). The chosen material for the overall structure is structural steel, whereas the piezoelectric material for energy harvesting is Polyvinylidene Fluoride (PVDF). The fractal tree design is optimized by running a MATLAB code called SAMO which carries out first a Sensitivity Analysis (SA) followed by a Multi-objective Optimization (MO) using an Elitist Genetic Algorithm (GA). The coupling between MATLAB and the COMSOL Multyphysics fractal tree model is ensured by the COMSOL feature called LiveLink for MATLAB. The optimal design solutions form a set which are referred to as a Pareto set, and they are associated to two minimized objective functions and multiple design variables. In the first phase of the optimization setup (Phase 1), for the minimization of two given objective functions per optimization process, multiple fractal tree geometry design variables are tested. For that first phase, at each optimization procedure iteration, the overall geometry of the fractal design is updated according to the design variables values, and if the geometry is acceptable, a static analysis is computed. Then, if the maximal static load is permissible, a modal analysis (eigenfrequency study) and a frequency domain analysis are also carried out. For the second optimization phase (Phase 2) of the project, two general designs of the fractal tree are chosen, one with and one without proof masses (PM) positioned at the end of the top branches. The piezoelectric material placement is optimized by considering an area coverage variation for each branch of the fractal tree design in order to favour the least negative voltage output generation and maximal branch longitudinal stress in the frequency domain. In the end, the best optimized fractal tree design in terms of calculated longitudinal stress and voltage output will be fabricated after completion of the project. Simulated FRFs responses will then be validated in the MC2 Laboratory by being compared with experimental FRFs obtained by Laser Doppler Vibrometer tests.