Size-dependent vibration of porous bishop nanorod with arbitrary boundary conditions and nonlocal elasticity effects

Abstract

This study investigates the size-dependent free axial vibration of a nanorod made of porous material. In this context, nonlocal elasticity theory for size dependence and Bishop rod theory are used in the study. The porous nanorod is considered in arbitrary boundary conditions and for this purpose, it is modeled with elastic springs at both ends. A method based on the combination of Fourier sine series and Stokes' transform is presented to realize the solution. Thanks to the presented approach, an eigenvalue problem is established to find the frequencies of a porous Bishop nanorods in general boundary conditions. Finally, the axial vibration frequencies of the porous Bishop nanorod based on the nonlocal elasticity theory are obtained depending on various parameters and the effects of these parameters are discussed.