Size-dependent free vibration of axially functionally graded tapered nanorods having nonlinear spring constraint with a tip nanoparticle

Abstract

According to the present literature review, the axial vibration of the axially functionally graded (FG) tapered nanorod with attached nonlinear spring has not been addressed so far. In this study, the axial vibration of the FG tapered nanorod is studied based on Eringen’s nonlocal theory, in which one end of the nanorod is clamped and the other end is attached to a nonlinear spring and a nanoparticle. The influence of different parameters such as the nonlinear spring constant, mass of the nanoparticle, and the nonlocal parameter on the natural frequencies is presented in detail. The solutions via Tables can be utilized as a reliable reference for evaluating the validity of future researches. The presented nonlocal solutions can be helpful for those who are interested in designing micro/nano electromechanical systems.

Moving axial load on dynamic response of single-walled carbon nanotubes using classical, Rayleigh and Bishop rod models based on Eringen’s theory

“…Bahrami et al (2019) employed Eringen’s nonlocal elasticity theory to study the axial response of the axially functionally graded (AFG) nanorod, subjected to a nonlinear spring and a nanoparticle at one of the ends of the nanorod, while the other side was clamped. Bahrami (2017) studied the vibrational behavior, wave power transmission, and reflection of the multi-cracked nanorods based on the wave propagation method and differential constitutive law consequent for two different boundary conditions.…”