Abstract
In this paper, nonlocal free vibration of axial rods embedded in elastic medium is examined by utilizing Love–Bishop rod theory with finite element method for the first time in the literature. Firstly, kinematic relations and dynamic equilibrium of this rod formulation are constituted. Equation of motion and boundary conditions are attained with the help of first variation of total potential of nano rod and solved using separation of variables. The frequency equations of four different nanorod types are obtained. On the other hand, a size–dependent finite element formulation is presented based on Weighted Residual Method. The nondimensional frequency parameters of nanorods are calculated by using analytical and finite element methods for different parameters such as mode number, nonlocal parameter, rod length, length–to–diameter ratio, finite element number and a detailed discussion is performed in the numerical results. In order to understand the characteristics of this rod theory, several comparative results that include nonlocal simple rod formulation are given as well.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
