A Kirchhoff Plate Model for Longitudinal Vibration Analysis of Restrained Nanoplate Including Thermal Effects

This work attempts to apply the Kirchhoff plate theory to find out the vibrational analyses of a nanoplate incorporating thermal effects. The effects of thermal environments on the natural frequency of longitudinal vibration of restrained nanomaterials, especially for restrained nanoplates, have not been investigated, and most of the previous research has been carried out for unrestrained nanoplates. Therefore, it must be emphasized that the vibrations of restrained nanoplate, including thermal effects, are novel and applicable to the nanodevices, in which nanoplates act as the main structure of the nanocomposite. A novel motion and frequency equation are derived using the Kirchhoff plate model. The present study illustrates that a nanoplate’s longitudinal vibration characteristics strongly depend on the temperature change and stiffness coefficients. The numerical results clearly show that the longitudinal natural frequencies of the nanoplate are less than unity for both cases of low and high temperatures. This means that applying the Kirchhoff plate model for restrained nanoplate analysis would lead to an over-prediction of the frequency if the small thermal stress effect is neglected. Finally, the investigation of the restrained and thermal impact on longitudinal vibration of nanoplates may be used as a valuable reference for the application and the design of nanoelectronics and nano-drives devices, nano-oscillators, and nano-sensors, in which nanoplates act as essential elements.