Thermal vibration analysis of double-layer graphene embedded in elastic medium based on nonlocal continuum mechanics

Document Type : Reasearch Paper


1 Department of Aerospace Engineering, PVP Siddartha Engineering College, Vijayawada 520 007, India.

2 Defence Research and Development Laboratory, Kanchanbagh, Hyderabad 500 058, India.

3 4Computational Wave Mechanics Laboratory, Department of Aerospace Engineering, Indian Institute of Science, Bangalore 560 012, India.



This paper presents the thermal vibration analysis of double-layer graphene sheet embedded in polymer elastic medium, using the plate theory and nonlocal continuum mechanics for small scale effects. The graphene is modeled based on continuum plate theory and the axial stress caused by the thermal effects is also considered. Nonlocal governing equations of motion for this double-layer graphene sheet system are derived from the principle of virtual displacements. The closed form solution for thermal-vibration frequencies of a simply supported rectangular nanoplate has been obtained by using the Navier’s method of solution. Numerical results obtained by the present theory are compared with available solutions in the literature and the molecular dynamics results. The influences of the small scale coefficient, the room or low temperature, the high temperature, the half wave number and the aspect ratio of nanoplate on the natural frequencies are considered and discussed in detail. The thermal vibration analysis of single- and double-layer graphene sheets are considered for the analysis. The mode shapes of the respective graphene system are also captured in this work. The present analysis results can be used for the design of the next generation of nanodevices that make use of the thermal vibration properties of the double-layer graphene system.