Investigation of the effect of longitudinal grading of material on vibrations of axially moving systems

For the first time, in this work, 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 longitudinal direction continuously. By using Galerkin method and eigenvalue problem, the natural frequencies and divergence of the system are computed numerically. In addition, the analytical relations are extracted for the critical velocity of the system. Critical velocity contours and stability maps are investigated for different distributions of material. As indicated, exponential and linear changes lead to a more stable system in the variable state of density and elastic modulus, respectively. Also, the results indicated 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 the stability. Hence, alteration in the density and elastic modulus gradient parameters has an opposite 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.