Abstract The torsional free vibration of the nano-shaft embedded in an elastic medium is investigated based on the nonlocal strain gradient theory. Firstly, the governing equations and boundary conditions are derived by Hamilton principle. Then the discrete form of the governing equations and boundary conditions are obtained by the differential quadrature method. Finally the torsional vibration characteristics are analyzed from the numerical results. The influence of two small-scale parameters and the stiffness of elastic media on vibration frequency are discussed. The coupling effect of the two scale parameters on vibration frequency is reflected through the influence of the scale parameter ratio. The results show that the torsional free vibration frequency decreases due to the increase of non-local parameters, and increases when the strain gradient scale parameter or elastic medium stiffness increase. When the non-local parameter is larger, the scale utility is reflected as a non-local effect , on the contrary, it is reflected as a strain gradient effect.
Received: 10 November 2020
Published: 21 October 2021
2021, Vol. 42 
