Nonlinear dynamic response analysis of a pressurized carbon nanotube resting on winklerpasternak foundation using multi-dimensional differential transform method

Abstract

The tremendous strength and light weight properties of Carbon nanotubes (CNTs) have fascinated the interest of researchers and scientists towards using CNTs for thermal, chemical, optical, electrical, structural and mechanical applications. This paper presents analytical solutions to the nonlinear dynamic response, shear force and bending moment of such CNTs. The CNT is modeled via thermal elasticity mechanics and Euler-Bernoulli theories. Without linearization, series expansion or omission of any independent variable, the developed nonlinear model that governs the physics of the behaviour of the CNT when excited by the aforementioned external agents is solved using transient differential transform method (TDTM) and verified with an inbuilt numerical scheme in MAPLE16. The results of the generated close form solution in this work are also compared with those of past works and excellent agreements are achieved. The parametric studies revealed that an increase in pressure term increases CNT deflection for any mode while a corresponding increase in the temperature and foundation parameters have an attenuating impact on deflection. Finally, the dynamic study reveals that locations with maximum bending moments are observed to possess minimum shear forces. It is envisaged that this work will enhance the use of CNTs for structural, electrical and mechanical applications.