On the High-Frequency Analysis of Exponentially Graded Nanobeams Resting on Winkler–Pasternak Foundations

The main aim of the present study is to analyze the high-frequency behaviors of the exponentially graded nanobeams resting on the Winkler–Pasternak foundations. This work provides new insights into the high-frequency behaviors of exponentially graded nanobeams through a comprehensive parametric study. Eringen’s nonlocal elasticity theory is applied to consider the small effects on the behaviors of the nanobeams. The governing equations of motion of the nanobeams are established via higher-order shear deformation theory and Hamilton’s principle. A close-form solution of Navier’s technique is used to achieve the free vibration behaviors of the exponentially graded nanobeams. The influence of some parameters, such as geometric parameters, material gradient, and elastic foundations’ parameters, on the free vibration behaviors of nanobeams is presented. Some new numerical results on the high-frequency behaviors of the exponentially graded nanobeams are demonstrated in the current study. The outcomes of the parametric study shows that the nonlocal parameter plays a significant role in the high-frequency vibration of the nanobeams. The high-frequency vibration of the exponentially graded nanobeams was extensively investigated. The outcomes of this study are expected to contribute to the understanding of nanobeam dynamics under high-frequency conditions and offer valuable information for the design and optimization of nanoscale devices and systems. Furthermore, the insights gained from this research could potentially have implications for a wide range of applications, spanning from MEMS to nanoscale sensors and actuators. By addressing the scientific gap in high-frequency nanobeam analysis, this study provides researchers and readers with a sound basis for further exploration and innovation in the field of nanotechnology.