بررسی تحلیلی ارتعاشات طولی نانومیله های نسبتا ضخیم با استفاده از تئوری الاستیسیته دوفازی

The aim of this article is to investigate the free vibrations of relatively thick nanorods based on the two-phase elasticity theory. The relatively thick nanorod is modeled using Rayleigh's theory. The main subject investigated in this article is how to solve the equation of motion of longitudinal free vibrations of nanorods in two-phase elasticity space. Because the transformation of the equations of motion from local space to local-non-local (two-phase) space increases the order of the derivative in the equations of motion. Therefore, the number of boundary conditions required for an analytical or exact solution is greater in the two-phase elasticity space than in the local space. Usually, the theory of two-phase elasticity suggests more boundary conditions, and the number of boundary conditions is sufficient in addition to the boundary conditions obtained from the local theory. However, it has been seen in the articles that local boundary conditions have not been used in solving the equations of motion, and this has caused researchers to use numerical methods to solve the equation of motion. Another problem caused by the non-use of local boundary conditions is the impossibility of providing solutions for different boundary conditions simply by using the boundary conditions obtained from the two-phase theory. The mentioned subject has also been observed in relation to the behavior of longitudinal free vibrations of relatively thick nanorods. Therefore, the author tries to determine the effect of these factors on the behavior of longitudinal free vibrations of relatively thick nanorods.