Effects of eccentric circular perforation on thermal vibration of circular graphene sheets using translational addition theorem

• Thermal effect on free vibration of eccentric circular graphene sheet is considered.
• The translational addition theorem for Bessel functions is used.
• Comparison studies showed good reliability and accuracy of the present method.
• The temperature change and eccentricity play an important role.

In this article, nonlocal thin plate theory of Eringen is employed to investigate effects of thermal environment on behavior of freely vibrating circular single layer graphene sheet containing a circular perforation of arbitrary size and location. In order to analytically solve equation of motion, the separation of variables method in conjunction with the translational addition theorem for Bessel functions is used. Accuracy and stability of results are verified by the literature. The behavior of sheets in low and high temperature conditions is considered. The influences of temperature change and various geometrical parameters on the natural frequencies are investigated by considering size-dependent material properties. In some cases, thermal buckling phenomenon was observed. Results show that the temperature changes play an important role in free vibration behavior of eccentric circular graphene sheets.