Vibrational analysis of nanoplate with surface irregularity via Kirchhoff plate theory

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 said, the present results may serve as useful references for designing oscillators and nanoscale devices, in which nanoplates act as a structural component for most prevalent nanocomposites structural element.

Automated summary

This work applies Kirchhoff plate theory to investigate the vibrational analyses of nanoplates with surface irregularity, which has not been previously studied. The study reveals that surface irregularity significantly affects the natural frequency of vibrational nanoplates, leading to a decrease in frequency with an increase in irregularity parameter. These findings can be useful for designing oscillators and nanoscale devices where nanoplates serve as a structural component in nanocomposites.