Torsional vibration of simply supported nanoplate using nonlocal mathematical model

Abstract

Present article is promoted to analyze the torsional vibration of simply supported nanoplate using nonlocal elasticity model. The equations motion of the nonlocal nanoplate are evaluated by rewriting the classical Hooke’s law through Eringen‘s model. Then, the numerical calculations are carried out to examine the reactions of the natural frequency of considered nanoplate to change of small-scale‘s coefficient, nanoplate‘s thickness, and torsional stiffness‘s parameter. The results reported that, any increase in the small-scale‘s parameter leads to a decrease in the natural frequency of nonlocal simply-supported nanoplate, while any increase of torsional stiffness‘s parameter leads to an increase of natural frequency. Additionally, the natural frequency of nonlocal nanoplates noticeably decreases as nanoplate thickness increases. Moreover, the torsional vibration analysis of nanoplates is significantly important in modelling real cases such as the nanodevices, which the nanoplates are common structural components in its designs. As a result, the findings of this investigation may be helpful in understanding torsional vibrations in nanostructures and nanodevices.

Keywords

• Torsional vibration
• Simply supported
• Nanoplate
• Nonlocal mathematical model
• Eringen's model