flexoelectric and surface effects on vibration frequencies of annular nanoplate

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.