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Effect of the thickness to length ratio on the frequency ratio of nanobeams and nanoplates

Bahrami Arian, Shiri Hamidreza, Khosravi Nima

Journal of Theoretical and Applied Mechanics

2020

Vol. 58 nr 1

87--96

This communication presents the effect of thickness on the frequency ratio of nanobeams and nanoplates using Eringen’s nonlocal theory. Although there exist numerous works regarding the effects of thickness and small scale on the frequency ratio of nanobeams and nanoplates, none has captured and reported the true effects. The main intention of this communication is to correct the misunderstanding regarding this issue. It was found that the frequency ratio is indeed dependent on the thickness to length ratio and its variation with respect to thickness to length ratio is highly dependent on the mode number, combination of boundary conditions, plate aspect ratio, and the nonlocal parameter.

Free vibration analysis of functionally graded rectangular nanoplates considering spatial variation of the nonlocal parameter

Alipour Ghassabi A., Dag S., Cigeroglu E.

Archives of Mechanics

2017

Vol. 69, nr 2

105--130

We present a new nonlocal elasticity-based analysis method for free vibrations of functionally graded rectangular nanoplates. The introduced method allows taking into account spatial variation of the nonlocal parameter. Governing partial differential equations and associated boundary conditions are derived by employing the variational approach and applying Hamilton’s principle. Displacement field is expressed in a unified way to be able to produce numerical results pertaining to three different plate theories, namely Kirchhoff, Mindlin, and third-order shear deformation theories. The equations are solved numerically by means of the generalized differentia quadrature method. Numerical results are generated by considering simply-supported and cantilever nanoplates undergoing free vibrations. These findings demonstrate the influences of factors such as dimensionless plate length, plate theory, power-law index, and nonlocal parameter ratio upon vibration behavior.