Torsional and axial vibration of restrained saturated nanorods via strain gradient elasticity

Abstract

Size-dependent torsional and longitudinal free vibrations of restrained saturated porous nanorods are studied by a higher-order elasticity theory. The strain gradient elasticity model is used in this study able to overcome inconsistencies of classical elasticity model. The presented higher-order model leads to well-posed boundary value problem for arbitrary value of the small size parameter. Two elastic springs in torsional and axial directions are attached to saturated porous nanorods at two boundary points. Angular rotation and axial deflection functions based on the strain gradient elasticity model are represented by two Fourier sine series. The difference of this proposed solution is that it does not impose a limitation on the support conditions and allows the frequencies to be obtained with a single solution. Two coefficient matrices including torsional or axial effects are obtained by using Stokes' transformation and non-classical boundary conditions. Free vibration frequencies of saturated nanorods are calculated by an effective eigen-value solution strategy. It is shown clearly that elastic spring coefficients, small-scale parameter and saturation a notable impact on the dynamic response of nanorods.