In-plane Vibration Analysis of Rotating Cantilever Curved Beams

Equations of motion of rotating cantilever curved beams are derived based on a dynamic modeling method developed in this paper. The Kane's method is employed to derive the equations of motion. Different from the classical linear modeling method which employs two cylindrical deformation variables, the present modeling method employs a non-cylindrical variable along with a cylindrical variable to describe the elastic deformation. The derived equations (governing the stretching and the bending motions) are coupled but linear. So they can be directly used for the vibration analysis. The coupling effect between the stretching and the bending motions which could not be considered in the conventional modeling method is considered in this modeling method. The natural frequencies of the rotating curved beams versus the rotating speed are calculated for various radii of curvature and hub radius ratios.