Stochastic Longitudinal Vibration of Single Walled Carbon Nanorods—A Non Local Elasticity Approach

Abstract

The present study deals with stochastic nonlocal non-dimensional natural frequencies of single walled carbon nanorods and rotating cantilever beam. In this study, the chordwise bending–vibration behavior of nanocantilever is analyzed. The nonlocal parameter focused on the small-size effects when dealing with nanosize structures such as single-walled carbon nanotubes (SWCNTs). The Eringen’s nonlocal elasticity theory in conjunction to the governing differential equations are utilized to solve the problem. The stochastic nonlocal natural frequencies for rotating nano cantilever are observed by employing the differential quadrature method (DQM). The effects of the scale is computationally analyzed based on Monte Carlo simulation (MCS). In another case free longitudinal frequency of a nanorods considering two types of boundary condition is observed, namely, clamped-clamped and clamped-free. The longitudinal vibration of the system are described by a set of partial differential equations, derived by using D’Alembert’s principle and using by employing Fourier infinite series in conjunction to separation of variables. The nanoscale effects implement a important role on the frequency response of nanorods subjected to rotation. The statistical analysis are carried out based on stochastic input parameters such as material properties (elastic modulus, density) and geometric properties (length).