In-plane vibration analysis of cantilevered circular arc beams undergoing rotational motion

Equations of motion of cantilevered circular arc beams undergoing rotational motion are derived based on a dynamic modeling method developed in this paper. 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 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 effects of rotational speed, arc angle, and hub radius ratio on the natural frequencies of the rotating circular arc beam are investigated through numerical analysis.