Application of Interpolating Matrix Method to Study Dynamics of Axially Moving Beams Made of Functionally Graded Materials

Abstract

In this paper, the divergent instability and coupled flutter characteristics of axially moving beams made of functionally graded materials (FGM) are studied using the interpolation matrix method. The material property of the beam is designed to change smoothly and continuously along the thickness direction. In considering the Euler-Bernoulli beam theory, Hamilton’s principle is used to derive the differential equation of the transverse vibration kinematics of axially moving FGM beams. In addition, the calculation model for solving the complex frequency of the beam based on the interpolation matrix method has been established. The presented solutions are compared with those in the literature to illustrate the effectiveness of the interpolation matrix method. The results show that the divergence and flutter velocities of axially moving FGM beams tend to decrease with the increase of the material gradient index, and there is a very narrow stability region between the first static instability region (divergence) and the first dynamic instability region (first- and second-order coupled flutter).