Optimal vibration energy harvesting from non-prismatic axially functionally graded piezolaminated cantilever beam using genetic algorithm

Optimal vibration-based energy harvesting from the axially functionally graded non-prismatic piezolaminated cantilever beam using finite element and genetic algorithm has been proposed in this article. The functionally graded material (i.e. non-homogeneous) in the axial direction is considered, where the cross section is varied (continuously decreasing from root to tip of such cantilever beam) using a proposed power law formula. The shape variations of piezolaminated cantilever (such as linear, parabolic and cubic) have been modelled using the Euler-Bernoulli beam theory. Hamilton's principle is used in order to derive the governing equation of motion. The governing equation is solved by considering two-noded beam element with 2 degrees of freedom at each node. The responses (such as frequency, voltage and output power) are compared between uniform and the axially functionally graded beam with arbitrary power gradient index. The effects of taper (both in the width and height directions) on output power along with frequency and voltage are analysed for axially functionally graded beam. In order to maximise the output power within the allowable limits of voltage and stresses, a real-coded genetic algorithm-based constrained optimisation technique has been proposed.