Nonlinear mechanics of nanoscale tubes via nonlocal strain gradient theory

A size-dependent nonlinear nonlocal strain gradient model for nanoscale tubes is proposed in this investigation and the forced mechanical behaviour is examined. This continuum model is better capable of incorporating size effects as it includes two independent length-scale parameters. The scale-dependent elastic energy and motion energy as well as the work carried out by the excitation load are formulated. The non-classical nonlinear differential equation of motion of the nanoscale tube is obtained using Hamilton's work/energy principle together with the nonlocal strain gradient elasticity. A precise numerical solution is presented for the nonlinear dynamic characteristics within the framework of Galerkin's scheme in conjunction with a continuation approach. The influences of nanosystem parameters such as the scale parameters, the length-to-gyration-radius ratio as well as the amplitude of the excitation force on the frequency/force responses are explored and discussed in details.