Nonlinear dynamics of an enhanced piezoelectric energy harvester composited of bi-directional functional graded materials

Given the energy harvesters in the engineering are often confronted with the possibility of catastrophic failure due to the multi-directional loads induced by the seismical or wind actions, a novel piezoelectric energy harvester made of bi-directional (2D) functional graded materials (FGMs) undergoing the large deformation is presented to resist the 2D loads so that the reliability of harvesting the vibration energy in the environment is enhanced. Taking the material properties continuously and smoothly varying across the axial and thickness directions of the substrate into account, Hamilton's principle is used to establish the electromechanical model of distributed parameters based on the geometric nonlinearity. The Galerkin truncation and the harmonic balance method combined with the arc-length tracking continuation are applied to trace the frequency responses, which are compared with numerical solutions and the excellent agreements are obtained. The stability and bifurcation behaviors on the condition of resonance response interaction are predicted by Floquet's theory. Numerical examples are disclosed that the effects of the excitation amplitude, damping coefficient, load resistance, axial and thickness FGMs indexes on the vibration displacement, output voltage, and power. Notably, the bifurcation behaviors of the proposed energy harvester may be tailored/tuned by multi-directional FGMs to achieve a wider frequency bandwidth and a higher harvesting power.