چكيده به لاتين
Flexoelectricity is a universal phenomenon that has gained significant research interest in recent times owing to its vast range of potential applications in diverse fields, that include actuators and sensors, regulating the properties of ferroelectric thin films, etc. It describes the coupling between the mechanical strain gradient and the electric polarization, known as the direct flexoelectric effect or, conversely, the coupling between the electric field gradient and the mechanical stress, which is known as the converse flexoelectric effect. The main objective of this paper is to elucidate the size-dependent nonlinear dynamics behavior of flexoelectric Nano-energy-harvesters taking strain effect, surface elasticity and thickness stretching effect into account. Considering constitutive relations for a flexoelectric bulk, surface elasticity, Maxwell’s theory and Gauss’s law, Euler-Bernoulli beam theorem together with von-Karman nonlinearity is utilized for mathematical formulation of the problem. The obtained governing motion equations throughout Hamiltonian’s principle are then discretized via single-mode discretization based on Galerkin’s approach. Thereafter, static condensation methodology is employed in order to reduce the number of the acquired time-dependent ordinary equations. The resulted nonlinear equations are then solved analytically employing multiple time scales method as a solution approach. Steady-state solution is considered and as a result a frequency-response is achieved for the system. According to the obtained frequency-response, the maximum amplitude of the generated voltage and power are calculated and corresponding curves are presented. A comprehensive numerical investigation is finally implemented to analyze the size-dependent behavior of the harvested energy against various involved factors namely thickness stretching effect, flexoelectricity and surface effects, load resistance and base excitation, considering energy harvesters with different thicknesses. As a prominent result, it is revealed that the thickness stretching effect exhibits a substantial influence on the Nano-scale energy harvester’s dynamics especially for those with lower thicknesses. It is shown that similar to the flexoelectricity and surface effect, the thickness stretching effect is also size-dependent. The results disclose that in addition to the flexoelectric and surface effects, thickness stretching effect could also be considered in mathematical modeling of Nano-scale energy harvesters to modify the conventional models. This might lead us to reach Nano-energy harvesters with high performance and efficiency.
