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.