Stability analysis of a rotating multi-layer annular plate with a stationary frictional follower load

This paper is concerned with examining the critical rotational speeds of a annular laminated disk and instability due to the existence of a stationary frictional follower load. A refined higher order layerwise zigzag theory (RHOT) is used to derive the governing equations of motion of a laminated disk. A four-node sector finite element incorporating RHOT is developed and applied for the stability analysis of a rotating multi-layer disk. The critical rotational speeds of a laminated disk made of isotropic layers and a laminated disk made of polar-orthotropic layers are calculated using the state-space method with respect to a moving frame and an inertial frame. The effect of a frictional follower load on the system stability is investigated using the frequency-speed diagram and the state-space method. It is found that the frictional follower load makes all forward modes with nodal diameters unstable over the entire relational speed range. Total Lagrangian kinematics with the modified Newton method is used in the solution finding procedure. (C) 1997 Published by Elsevier Science Ltd.