Analytical investigation of nonlinear response of single-walled carbon nanotube resting on elastic foundation subjected to casimir-electrostatic-van der waals forces

This paper presents analytical investigation into the nonlinear dynamic response of single-walled carbon nanotube (SWCNT) resting on elastic foundation and subjected to magneto-thermal and electrostatic environment under the influence of Casimir and intermolecular forces. The Euler-Bernoulli beam theory, the nonlocal elasticity theory and Hamilton’s principle of nonlinear mechanistic motion are applied in the theoretical formulation of the governing differential equation and the Galerkin decomposition technique is used to decompose the formulated equation of motion into spatial and temporal parts. The duffing equation which describes the temporal part of the equation of motion of the SWCNT is then solved analytically. Subsequently, the frequency ratios of the nanotube for end conditions including simple-simple, clamped-clamped, clamped-simple, and clamped-free are obtained. Furthermore, parametric study is carried out to show the influences of Casimir force, intermolecular force, electrostatic force, magnetic term, elastic foundation and thermal term on the nanotube’s stability. The stability response solution obtained from the parametric study reveals that an increase in Casimir force enables CNTs to experience an additional attractive pressure that decreases their stability and may result in buckling or collapse. Meanwhile, increase in Van der Waals force reduces critical buckling load. Additionally, increasing the electrostatic force results in an increased frequency ratio and vibration amplitude. These parameters need to be carefully monitored or controlled to prevent instabilities due to their sensitivities.