تحلیل ارتعاشات آزاد نانولوله‌های کربنی با مدل پوسته‎های نازک و تئوری غیرمحلی ارینگن

In this paper, the free vibration natural frequencies and mode shapes of nanotubes embedded in an elastic medium are investigated. The Love’s thin shell theory is employed to model the mechanical behavior of the nanotube and the small scale effect is modeled by Eringen’s nonlocal elasticity theory. The governing equations of the nanotube are obtained as a set of three partial differential equations in terms of the three displacement components of the nanotube. Navier’s method is employed for solving the governing equations of the nanotube for simply supported boundary conditions and the natural frequencies of the nanotube are obtained. The validation of numerical predictions are investigated and good results are achieved. In the numerical results, the natural frequencies of the nanotube for different circumferential and bending modes are studied. The effects of various parameters such as nonlocal parameter, mode numbers and geometrical parameters on the natural frequencies of nanotube are investigated.