On the torsional vibration of a porous nanorod with arbitrary boundary conditions considering nonlocal lam strain gradient theory

Porous materials are an important type of advanced materials due to their excellent properties, with one of the most notable being their lightweight nature. It is also important to accurately understand the mechanical response of nanorods, one of the components of nano-electro-mechanical systems. Therefore, a porous material is considered for the nanorod and elastic boundary conditions are considered, which presents a more realistic model. In order to provide a general eigenvalue solution based on these boundary conditions, an approach based on Fourier sine series and Stokes’ transform is considered. The main novelty of this eigenvalue solution, which calculates the torsional frequencies of the porous nanorod, lies in its ability to analyze both rigid and deformable boundary conditions. Although the analysis of other types of rods under arbitrary boundary conditions has been performed in the literature, the torsional vibration of porous nanorods based on nonlocal Lam strain gradient theory presented in this work is the first. To summarize the key findings of the study, it can be said that an increase in the nonlocal parameter and the porosity parameter which affects the shear modulus, cause a decrease in the torsional vibrations of the porous nanorod. On the other hand, an increase in the material length scale parameters, the spring stiffnesses at the ends and the porosity parameter, which causes the alters the mass density, results in an increase in the vibration frequencies.