Geometric Nonlinear Finite Element and Genetic Algorithm Based Vibration Energy Harvesting from Functionally Graded Nonprismatic Piezolaminated Beams

Abstract

Energy harvesting technology has the ability to create autonomous, self-powered systems which do not rely on the conventional battery for their operation. The term energy harvesting is the process of converting the ambient energy surrounding a system into some useful electrical energy using certain materials. Among several energy conversion techniques, the conversion of ambient vibration energy to electrical energy using piezoelectric materials has great deal of importance which encompasses electromechanical coupling between mechanical and electrical domains. The energy harvesting systems are designed by incorporating the piezoelectric materials in the host structure located in vibration rich environment. The work presented in this dissertation focuses on upgrading the concept of energy harvesting in order to engender more power than conventional energy harvesting designs.
The present work deals with first the finite element (FE) formulation for coupled thermo-electro-mechanical analysis of vibration energy harvesting from an axially functionally graded (FG) non-prismatic piezolaminated cantilever beam. A two noded beam element with two degrees of freedom (DOF) at each node has been used in the FE formulation. The FG material (i.e. non-homogeneity) in the axial direction has been considered which varies (continuously decreasing from root to tip of such cantilever beam) using a proposed power law formula. The various cross section profiles (such as linear, parabolic and cubic) have been modelled using the Euler-Bernoulli beam theory and Hamilton‘s principle is used to solve the governing equation of motion. The simultaneous variation of tapers (both width and height in length directions) is incorporated in the mathematical formulation. The FE formulation developed in the present work has been compared with the analytical solutions subjected to mechanical, electrical, thermal and thermo-electro-mechanical loading. Results obtained from the present work shows that the axially FG nonprismatic beam generates more output power than the conventional energy harvesting systems. Further, the work has been focussed towards the nonlinear vibration energy harvesting from an axially FG non-prismatic piezolaminated cantilever beam. Geometric nonlinear based FE formulation using Newmark method in conjunction with Newton-Raphson method has been formulated to solve the obtained governing equation. Moreover, a real code GA based constrained optimization technique has also been proposed to determine the best possible design variables for optimal power harvesting within the allowable limits of ultimate stress of the beam and voltage of the PZT sensor. It is observed that more output power can be obtained based on the present optimization formulation within the allowable limits of stress and voltage than that of selection of design variables by trial and error in FE modelling.