Investigation of dynamics and stability behavior of axially moving micro-beams with functionally graded property in the longitudinal direction

In this paper, in order to improve the efficiency of the moving systems, vibrations and stability of axially functionally graded Rayleigh moving micro-beams are studied. Also, to clarify the influences of various parameters such as axially functionally graded, the length of the material characteristics, and the whirling inertia on the stability boundaries of Rayleigh and Euler-Bernoulli beams, a detailed parametric study is done. It is assumed that the material characteristics of the system change linearly or exponentially in longitudinal direction continuously. To calculate the natural frequencies, dynamics configuration, and divergence and flutter instability thresholds of the system, the strain gradient theory, Galerkin discretization method, and an eigenvalue problem are utilized. In addition, the analytical relations are extracted for the critical velocity of the system. Critical velocity contours and stability maps are examined for different distributions. It is demonstrated that the 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 regions. Hence, the alteration in the density and elastic modulus gradient parameters has an opposite role in the dynamic behavior of the system.