On comprehensive nonlinear size-dependent analysis of nano-scale flexoelectric energy harvesters considering strain gradient, surface elasticity and thickness size effect
Noise and Vibration Control Research Laboratory, School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
Accepted: 8 August 2023
Published online: 14 September 2023
Thickness size effect is known as a size-dependent effect which might play an important role in mechanical behavior of nano-sized structures. This effect has not been considered so far for nano-energy harvester’s behavior analysis. This paper aims to elucidate the size-dependent nonlinear vibrational response of flexoelectric nano-energy harvesters considering the effect of strain gradient, surface elasticity and thickness size effect. The fundamental equations are established based on the constitutive relations for a flexoelectric bulk, surface elasticity, Maxwell theory and Gauss law. Also, Euler–Bernoulli beam theorem together with nonlinearity of von-Karman is employed. The obtained governing equations of motion throughout Hamiltonian’s principle are then discretized via single-mode discretization based on Galerkin’s approach. Static condensation methodology is employed to decline the number of the acquired time-dependent equations. The multiple timescales method as a solution approach is hired to solve the resulted nonlinear equations analytically. According to the obtained frequency response, the maximum amplitude of the generated voltage and power is 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 size effect, flexoelectricity and surface effects, load resistance and base excitation, considering energy harvesters with different thicknesses. As a paramount result, it is concluded that the thickness size effect has an essential influence on the nano-scale energy harvester’s dynamics, especially for those with lower thicknesses. It is disclosed that similar to the surface effect and flexoelectric phenomenon, the thickness effect is also size-dependent. The results disclose that in addition to the surface and flexoelectric effects, thickness size effect could also be considered in mathematical formulation of nano-energy harvesters to modify the conventional models. This might lead to reach nano-energy harvesters with higher performance and efficiency.
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