Forced torsional vibration of nanobeam via nonlocal strain gradient theory and surface energy effects under moving harmonic torque

Abstract

The forced torsional vibration of a nanobeam by using the nonlocal strain gradient theory and incorporating the surface effects is investigated in the current work. The aim of this paper was to analyze the surface effect on the forced torsional vibration of a nanobeam. The simulated nanobeam is under the distributed external torque and moving external harmonic torque. The governing equations are derived by employing the Hamilton principle. The extracted partial differential equation is converted to ordinary differential equation by deploying the Assumed Modes method. The dynamic torsion of clamped–clamped end supports of nanobeam is determined by using the Convolution integral. The effect of nondimensional material length scale parameter, the nondimensional nonlocal parameter, the velocity parameter and the nondimensional moment, on the maximum nondimensional dynamic torsion of nanobeam are studied. Eventually, the effect of residual surface torsion and surface shear modulus on the maximum nondimensional dynamic torsion of nanobeam, which is obtained from the nonlocal strain gradient theory under the distributed torsional and moving harmonic dynamic moments, is studied.