حل دقیق ارتعاشات آزاد محوری نانومیله‌های دوفازی

One of the important behaviors of structures is their vibration behavior. Among different structures and different vibration behaviors, rods are considered a one-dimensional system and their axial vibration behavior is of great importance. On the other hand, the difference in the behavior of structures at the nano scale and the macro scale causes researchers to pay more attention to the nano field. For this reason, the aim of this article is to investigate the axial free vibrations of nanorods. Nanorods are modeled in a simple theory and two-phase elasticity theory is used to investigate the effect of scale. In this article, it has been tried to present the equation of motion in the two-dimensional elasticity space using a new method. Then, the equation of motion has been solved accurately and analytically, and the natural frequencies and mode shapes have been extracted. To check the correctness of equations and results, a comparison has been made between the results of this research and previous researches. The result of this comparison shows the high accuracy and accuracy of the solution method and obtained equations. It has also been tried to provide new results that have not been presented before for the use of researchers.