Dynamics of nonlocal strain gradient nanobeams with longitudinal magnetic field

Flexural dynamics of carbon nanotubes under the longitudinal magnetic field have been investigated in the paper. Carbon nanotube has been assumed as a hollow beam with circular cross section. Nonlocal strain gradient model has been employed in the modeling of nanobeam. Transverse component of Lorentz force, which occurs with longitudinal magnetic field, has been considered as an external force on nanobeam. Stress and strain energy functionals have been defined for the nonlocal strain gradient model using Hamilton principle. Higher-order governing differential equation of motion for the present problem has been solved with Differential Quadrature Method. Lorentz force and nonlocal strain gradient parameters have been considered in the standard and nonstandard boundary conditions in the present model formulation. Length scale and magnetic field parameters effect on the flexural vibration response of nanobeam have been investigated. Mode shapes of nonlocal strain gradient nanobeam have been depicted on various cases. Softening nonlocal strain gradient model gives physically consistent results and should be used in the analysis. Magnetic field effect shifts the mode shapes of clamped-free nanobeam. Present study could give useful results for designing of magnetically actuated nanomotors.