Vibrational analysis of carbon nanocones under different boundary conditions: An analytical approach

• Developing a nonlocal shell model for the free vibrations of carbon nanocones.
• Conducting an analytical solution capable of treating different end conditions.
• Studying geometrical parameters and nonlocal parameter on the vibrational behavior.

The purpose of this study is to analytically investigate the free vibration of carbon nanocones (CNCs) under different types of boundary conditions. The Donnell shell theory and nonlocal elasticity are used to derive the governing equations of motion. The analytical Galerkin method together with beam mode shapes as weighting functions is employed to solve the problem. Making use of the beam modal functions enables us to examine the role of boundary condition in the vibrational behavior of CNCs. The effects of boundary conditions, semivertex angle and nonlocal parameter on the response of CNCs are explored.