Vibrational analysis of nanoplate with surface irregularity via Kirchhoff plate theory

Abstract

In this work, an attempt is done to apply the Kirchhoff plate theory to find out the vibrational analyses of a nanoplate incorporating surface irregularity effects. The effects of surface irregularity on natural frequency of vibration of nanomaterials, especially for nanoplates, have not been investigated before, and most of the previous research have been carried for regular nanoplates. Therefore, it must be emphasized that the vibrations of irregular nanoplate are novel and applicable for the nanodevices, in which nanoplates act as the main structure of the nanocomposite. The surface irregularity is assumed in the parabolic form at the surface of the nanoplate. A novel equation of motion and frequency equation is derived. The obtained results provide a better representation of the vibration behavior of irregular nanoplates. It has been observed that the presence of surface irregularity affects considerably on the natural frequency of vibrational nanoplates. In addition, it has been seen that the natural frequency of nanoplate decreases with the increase of surface irregularity parameter. Finally, it can be concluded that the present results may serve as useful references for the application and design of nano-oscillators and nanodevices, in which nanoplates act as the most prevalent nanocomposites structural element.

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“…Additionally, the impact of surface effects on the resonant frequency of Timoshenko nanobeams has been studied, considering shear deformation, rotary inertia effects, and surface effects [24]. Furthermore, the vibrational analysis of nanoplates with surface irregularities has revealed the influence of surface irregularity on the natural frequency of vibration, particularly for nanoplates [25]. Research on the surface effects of anti-plane shear waves in magnetoelectro-elastic nanoplates has indicated that surface parameters strongly affect elastic wave propagation and dispersion properties [26].…”