[01] Vebil Yıldırım, Mechanical Engineering Department, University of Çukurova, Adana, Turkey.

The principal purpose of the present study is to introduce the transfer matrix method, which is an efficacious and accurate analytical/numerical method developed based on the initial value problem (IVP), to analytical evaluation of the longitudinal natural frequencies of a single-walled carbon nanotube (SWCNT) based on Eringen’s nonlocal elasticity theory under classical boundary conditions. After validation of the results, it is graphically shown that there is an upper bound (cut-off/corner/break frequency) for the non-local natural frequencies contrary to the local ones. The numerical value of this bound depends on the geometrical and material properties together with the boundary conditions. The effects of vibrational parameters on the natural frequencies are also investigated.

Transfer Matrix Approach, Exact Solution, Initial Value Problem, Free Longitudinal Vibration, Nonlocal Elasticity Theory

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