Dynamic analysis of rotating curved beams by using Absolute Nodal Coordinate Formulation based on radial point interpolation method

Abstract

It is well known that rotating beams are stretched due to centrifugal forces. Accordingly, it can be speculated that the stretching effect for rotating curved beams leads to changes of the curvature. But this speculation has been not verified and reported in existing literatures. In this paper, a dynamic model of curved beams is derived by using the Absolute Nodal Coordinate Formulation based on radial point interpolation method (ANCF/RPIM), and the transient analysis of curved beams rotating at the steady state angular speed are especially performed by using the ANCF/RPIM. The results show that the curvature of curved beams is reduced due to centrifugal forces. These configuration changes have an important influence on frequency characteristics. Thus, modal analysis should take account of the configuration changes by using steady states which can be obtained in a manner of static analysis. The “static external force” for steady states is a non-zero centrifugal force, while centrifugal forces are identically equal to zero in the original ANCF. To this end, this paper uses a floating frame to describe overall rotations of beams, and defines the nodal coordinates located on the floating frame to describe configurations of beam. Based on this description, new ANCF dynamic equations can be easily obtained by using coordinate transformation of the original ANCF dynamic equations, in which the centrifugal forces are not equal to zero. The results show that the configurations in steady and transient states are very close, and transient states are almost located in both sides of the steady state. Therefore, steady states can be regarded approximately as equilibrium positions of vibrational curved beams. By using steady states, the new ANCF dynamic equations can be linearized to determine frequencies of curved beams. Finally, the effects of curvature changes on the frequencies of curved beams, especially “dynamic softening” effect, are investigated, and the reason that these effects are caused in curved beams is explained in detail.