Free vibration of rectangular nanoplates using Rayleigh–Ritz method

• We study vibration of rectangular nanoplates using Rayleigh-Ritz method.
• We examine the effect of nonlocal parameter, length of nanoplates and aspect ratio on the frequency parameters.
• Frequency parameters increase by increasing aspect ratio and the same trends are also seen by increasing the length of nanoplates.
• Increasing nonlocal parameter will decrease frequency parameters.
• We plot three dimensional mode shapes for two types of boundary conditions.

Vibration analysis of isotropic rectangular nanoplates based on the classical plate theory in conjunction with Eringen's nonlocal elasticity theory is considered. Nanoplates are one of the structural units that are used in nanoscale applications. In this study, Rayleigh–Ritz method with algebraic polynomial displacement function is used to solve the vibration problem of isotropic rectangular nanoplates subjected to different boundary conditions. The advantage of the method is that one can easily handle the specified boundary conditions at the edges. A comparison of the results with those available in the literature has been made. The proposed method is also validated by convergence studies. Frequency parameters are given for different nonlocality parameters, length of nanoplates and boundary conditions. The study highlights that nonlocality effects increase with the increase in mode number and the influence of nonlocal effects becomes increasingly pronounced for higher order vibration modes. Three-dimensional mode shapes for the specified nanoplates have also been presented.

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