Nonlinear coupled mechanics of nanotubes incorporating both nonlocal and strain gradient effects

The coupled nonlinear mechanical behavior of nonlocal strain gradient nanotubes subject to distributed excitation forcing is investigated for the first time. Both longitudinal displacements and transverse deflection are taken into consideration in both the continuum-based formulation and the numerical solution. The influences of being at the nanoscale level are modeled with the use of the nonlocal strain gradient theory. The coupled large amplitude motion characteristics are extracted via Galerkin's approach and a continuation method. The influences of scale coefficients, the slenderness ratio, and the force amplitude of the external forcing on the motion are examined.