Effect of asymmetric proof mass and size-dependency in flexoelectric nanoharvester subjected to base and restraint forces

Abstract

The piezoelectric and flexoelectric techniques are of great interest among the scientific fraternity, especially for the design of vibration-based micro/nano energy harvesters. The development of such energy harvesters in the micro/nanoscale has a huge potential, mostly in wireless networks and IoT-based applications. The present work thus formulates novel nanostructure-based analytical models of energy harvesters with asymmetric proof mass considering nonlocal flexoelectricity, geometrical nonlinearity, mid-plane stretching, harmonic base, and axially restraint forces. Using non-classical Euler-Bernoulli nanobeam and Hamilton’s principle, governing differential equation of motion has been derived. Analytical solutions have been obtained to compute the eigenfrequencies and subsequent modes of vibration concerning various systems’ physical and geometric variables. Nonlinear steady-state voltage and power characteristics thereafter have been investigated and studied their local stability and bifurcation for primary and sub-harmonic resonant conditions. The influences of performance factors associated with asymmetrically proof mass, nonlocal elasticity, and time-dependent base and restraint forces on the nonlinear voltage and power output using frequency characteristics criterion. These results have been validated with the findings using COMSOL-2D, and interestingly, mean voltage and power responses from linear models are found to be highly consistent with findings in COMSOL 2D. The present outcome shows how the asymmetric proof mass and nanoscale effect create disparities in harvesting energy performance and, simultaneously, how important their role is to avoid any undesirable structural instability. The present studies together can strengthen the significance of size-dependency and asymmetric proof mass while designing a nanoscale generator in the presence of harmonic excitation.