Hygro-Magnetic Vibration of the Single-Walled Carbon Nanotube with Nonlinear Temperature Distribution Based on a Modified Beam Theory and Nonlocal Strain Gradient Model

Abstract

In this study, vibration analysis of single-walled carbon nanotube (SWCNT) has been carried out by using a refined beam theory, namely one variable shear deformation beam theory. This approach has one variable lesser than a contractual shear deformation theory such as first-order shear deformation theory (FSDT) and acts like classical beam approach but with considering shear deformations. The SWCNT has been placed in an axial or longitudinal magnetic field which is also exposed to both the hygroscopic as well as thermal environments. The thermal environment is considered as nonlinear thermal stress field based on the Murnaghan’s model whereas the hygroscopic environment is assumed as a linear stress field. The size effect of the SWCNT has been captured by both the nonlocal and gradient parameters by employing the Nonlocal Strain Gradient Theory (NSGT). Governing equation of motion of the proposed model has been developed by utilizing the extended Hamilton’s principle and the non-dimensional frequency parameters have been computed by incorporating the Navier’s approach for Hinged–Hinged (HH) boundary condition. The proposed model is validated with the existing model in special cases, by comparing the non-dimensional frequency parameters, displaying an excellent agreement. Further, a parametric study has been conducted to analyze the impact of nonlocal parameter, gradient parameter, thermal environment, hygroscopic environment, and magnetic field intensity on the non-dimensional frequency parameters. Also, results for some other theories like Classical Elasticity Theory (CET), Nonlocal Elasticity Theory (NET), and Strain Gradient Theory (SGT) have been presented along with the NSGT.