Effects of Porosity and Nonlocality on the Low- and High-Frequency Vibration Characteristics of Al/Si 3 N 4 Functionally Graded Nanoplates Using Quasi-3D Theory

This study explores the effects of porosity as well as nonlocal parameter on both low- and high-frequency free vibration behaviors of functionally graded nanoplates for the first times. Three distinct models are used to describe porosity distribution. A combination of the six-unknown quasi-3D theory is utilized to define the displacement field of the nanoplates. The Hamilton’s principle is exploited in combination with the nonlocal elasticity theory to establish the governing equations of the motion of the functionally graded nanoplates. The influence of some parameters such as geometric, power-law index, porosity, and nonlocal parameter on the free vibration behaviors of the functionally graded porous nanoplates is explored in detail. This pioneering study unveils a wealth of numerical findings that, for the first time, shed light on the intricate high-frequency behaviors exhibited by these nanoplates. These insights not only expand the scientific understanding of functionally graded porous nanoplates but also offer valuable knowledge that can empower scientists and engineers in their pursuit of designing and optimizing nanostructures in this domain. This research marks a significant milestone in the study of nanoplates, bridging the gap between low- and high-frequency vibration analyses and opening new avenues for future research and practical applications.