Refined plate theory for free vibration analysis of FG nanoplates using the nonlocal continuum plate model

Document Type: Research Paper

Authors

1 Department of Mechanical Engineering, Islamic Azad University, Branch of Ahvaz, Ahvaz, Iran

2 Department of Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

3 Department of Mechanical Engineering at University of South Carolina

Abstract

In this article, the free vibration behavior of nanoscale FG rectangular plates is studied within the framework of the refined plate theory (RPT) and small-scale effects are taken into account. Using the nonlocal elasticity theory, the governing equations are derived for single-layered FG nanoplate. The Navier’s method is employed to obtain closed-form solutions for rectangular nanoplates assuming that all edges are simply supported. The results are subsequently compared with valid results reported in the literature. The effects of the small scale on natural frequencies are investigated considering various parameters such as aspect ratio, thickness ratio, and mode numbers. It is shown that the RPT is an accurate and simple theory for the vibration analysis of nanoplates, which does not require a shear correction factor.

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