Flexoelectric and surface effects on vibration frequencies of annular nanoplate
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ORIGINAL PAPER
Flexoelectric and surface effects on vibration frequencies of annular nanoplate A Ghorbanpour Arani1,2*, A H Soltan Arani1 and E Haghparast1 1
Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
2
Institute of Nanoscience and Nanotechnology, University of Kashan, Kashan, Iran Received: 25 August 2019 / Accepted: 10 April 2020
Abstract: This research points out the positive results of flexoelectricity and surface effect on the nonlocal vibration of annular nanoplate. First-order shear deformation plate theory is used to formulate the problem. According to the new form of nonlocal elasticity theory, small-scale effects are taken into account. The nanoplate is subjected to a potential electric. The influences of surface stresses and properties including surface residual stresses, surface mass density and surface elasticity are considered. The principle of virtual work is used to derive the governing equations of equilibrium. Finally, differential quadrature method (DQM) in conjunction with the iterative method is utilized to solve equations of motion. Parametric study is done to examine effects of parameters such as radius ratio, nonlocality, thickness-to-radius ratio, different mode numbers, surface properties, normal stress in thickness direction and stretching effect on the size-dependent vibration of flexoelectric nanoplate. The results demonstrate that the consideration of flexoelectric and surface effects leads to significant increase in the natural frequency of flexoelectric nanoplate. The results of this research are utilized in aerospace, military facilities and industries. Keywords: Vibration analysis; Flexoelectric effects; Annular nanoplate; Surface effects; New nonlocal elasticity theory
1. Introduction Due to the high ratio of surface to volume of nanostructures, the surface effects can play a significant role. Hence, taking into account surface effects leads to higher mechanical strength and elastic modulus in comparison with the conventional structures. The Gurtin–Murdoch elasticity theory is commonly applied to characterize the surface effects in the nanostructures. In the last decade, many researchers investigated surface effects and their influence on the behavior of materials in nanostructures. Utilizing principle of minimum potential energy, Ghorbanpour Arani and Haghparast [1] studied the axisymmetric buckling behavior of annular plates reinforced with boron nitride nanotubes (BNNTs). Analytical solution for free vibration analysis of nanoplates with consideration of surface stress based on different theories is developed by Ansari and Sahmani [2]. The influences of nonlocal
*Corresponding author, E-mail: [email protected]; [email protected]
parameter, surface energy, small scale and geometrical nonlinearity on the free vibration of skew nanoplates were studied by Malekzadeh et al. [3]. They found out that the nonlinear vibration of nanoplates is significantly dependent on the small-scale effect and surface energy. Norouzzadeh and Ansari [4] ana
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