Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method

The small scale effect on the axial vibration of a tapered nanorod is studied employing nonlocal elasticity theory. The nonlocal elasticity theory is used to analyze the mechanical behavior of nanoscale materials. Differential quadrature method (DQM) is applied to solve the governing equations of the nanorod for clamped–clamped (C–C), clamped–free (C–F) and fixed-attached spring boundary conditions. It is shown that the nonlocal effect plays an important role in the axial vibration of nanorods. Also, the nonlocal frequencies are always smaller than their local counterparts. Further, it is concluded that the percentage difference in frequency ratio (nonlocal natural frequency/local natural frequency) between tapered and uniform nanorod is significant at small values of the length of rod and for C–C boundary condition.

► Axial vibration analysis of tapered nanorods.
► Small scale effects are taken into consideration using nonlocal elasticity theory.
► Natural frequencies are obtained by employing differential quadrature method.
► A new boundary condition (elastically restrained end condition) is presented.