Nonlinear Vibration of Single-Walled Carbon Nanotubes on Winkler and Pasternak Foundations in a Magneto-Thermal Environment Under the Influence of Casimir Force

Nanotubes are known to have the strongest and stiffest fibers with exceptional tensile strength and higher modulus of elasticity, researchers have been very interested in studying their nonlinear vibrations. Nonetheless, using nanotubes to partially substitute reinforcing material has emerged as a revolutionary approach for applications of the future. This work examines the nonlinear vibration study of single-walled carbon (NTs) with geometric imperfection supported on linear and nonlinear Winkler and Pasternak Foundations in a thermal-magnetic-electrostatic environment under the influence of Casimir Force. The nonlinear mathematical model for this work is formulated using the Hamiliton principle, Euler-Bernoulli elasticity theory, and non-local elasticity beam theory. The Galerkin decomposition approach is used directly to break down the nonlinear partial differential equation of motions into two separate components, that is spatial and temporal parts of nonlinear duffing equations of motions. An approximate analytical expression of the fundamental natural frequency is presented by modern asymptotic approach namely Iteration Perturbation Method (IPM). The method is used to solve the resulting nonlinear mathematical model and the following solutions were obtained that is the natural frequency of vibration, nonlinear frequency ratio and dynamic response analysis. Moreso, parametric study was conducted on the obtained semi-analytical solutions and the effects of the following parameters such as magnetic, thermal, electrostatic force, Van der Waals force, Casimir force, linear foundation, nonlinear foundation, Pasternak foundation and mass on stability and dynamic responses on four different boundary conditions considered. Afterwards, the outcomes are then compared with existing literature and found to be completely consistent.