Torsional vibration analysis of nanorods with elastic torsional restraints using non-local elasticity theory

In this work, torsional vibration of nanorods with torsional elastic boundary conditions is presented via non-local elasticity theory. The present model developed based on non-local elasticity theory gives the opportunity to interpret size effect. Two torsional elastic springs are attached to a nanorod at both ends. A mathematical transformation known as Stoke transformation' is utilised to work out the Fourier series for the nanorods with torsional restraints. A coefficient matrix including torsional coefficients is determined by using non-local boundary conditions. A comparison is performed to validate numerical simulations with those given in the literature and the results agree with each other exactly. The non-local effects of torsional end restraints on the free torsional vibration response are investigated for both deformable and rigid boundary conditions.