Longitudinal Vibrations of Restrained Irregular Nanoplates

The main purpose of this work is to examine how surface irregularity affects the longitudinal vibration frequency of nanoplates. Based on the Kirchhoff plate model, the boundary conditions and governing equations are developed. The MATLAB R2013a Software is utilized to carry out the numerical solutions, and an accurate solution is shown. We derive a novel equation of motion as well as a new frequency equation. Examined is how several factors, such as thickness, stiffness, and surface irregularity, affect the longitudinal vibration of nanoplates. The studies revealed that from large to small irregularity parameters, the longitudinal natural frequencies of nanoplate increase. Additionally, it has been discovered that increasing the thickness of nanoplates is preferred for enhancing their vibration stability.