Amirkabir University of Technology Amirkabir Journal of Mechanical Engineering 2008-6032 53 Issue 2 (Special Issue) 2021 04 21 Investigation of the effect of longitudinal grading of material on vibrations of axially moving systems Investigation of the effect of longitudinal grading of material on vibrations of axially moving systems 1197 1210 3863 10.22060/mej.2020.17295.6567 FA Ali Forooghi Department of Mechanical Engineering, Faculty of Engineering, Tarbiat Modares University, Tehran, Iran Mehran Safarpour Department of Mechanical Engineering, Faculty of Engineering, Tarbiat Modares University, Tehran, Iran Akbar Ali Beigloo Department of Mechanical Engineering, Faculty of Engineering, Tarbiat Modares University, Tehran, Iran Journal Article 2019 10 30 For the first time, vibrations of the axially graded Rayleigh moving beams are studied. It is supposed that the material characteristics of the system change linearly or exponentially in a longitudinal direction continuously. By using the Galerkin method and eigenvalue problem, the natural frequencies and divergence of the system are computed numerically. Also, the analytical relations are extracted for the critical velocity of the system. Essential contours of velocity and stability maps are investigated for different distributions of material. As indicated, exponential and linear changes lead to more stable operation in the variable state of density and elastic modulus, respectively. Also, the results showed that increasing the elastic modulus gradient parameter or decreasing the density gradient parameter results in an increase in the natural frequency of the system and a development in stability. Hence, alteration in the density and elastic modulus gradient parameters has a different role in the dynamic behavior of the system. The results of this study can be useful for designing and optimizing high-speed non-homogeneous axial movable structures. For the first time, vibrations of the axially graded Rayleigh moving beams are studied. It is supposed that the material characteristics of the system change linearly or exponentially in a longitudinal direction continuously. By using the Galerkin method and eigenvalue problem, the natural frequencies and divergence of the system are computed numerically. Also, the analytical relations are extracted for the critical velocity of the system. Essential contours of velocity and stability maps are investigated for different distributions of material. As indicated, exponential and linear changes lead to more stable operation in the variable state of density and elastic modulus, respectively. Also, the results showed that increasing the elastic modulus gradient parameter or decreasing the density gradient parameter results in an increase in the natural frequency of the system and a development in stability. Hence, alteration in the density and elastic modulus gradient parameters has a different role in the dynamic behavior of the system. The results of this study can be useful for designing and optimizing high-speed non-homogeneous axial movable structures. https://mej.aut.ac.ir/article_3863_c4d2ce3f3ebb5393a77c33c0cd95dc93.pdf