A study on the dynamic stability of plates under a follower force

In this study, a dynamic stability analysis of a plate under a follower force was performed through the finite element method based on the Kirchhoff–Love plate theory and Mindlin plate theory. Four-, nine- and 16-node quadrilateral elements were used. Through the dynamic stability analysis of a thin plate under an in-plane force and a follower force, the calculation results of these elements were compared with the analytical solutions. It is concluded from these observations that the 16-node Mindlin plate element is the best element for the dynamic stability analysis of a shear deformable plate. The dynamic stability analysis was performed for an isotropic, orthotropic and a symmetrically laminated composite plate under a pure follower force using 16-node Mindlin plate element. The effects of shear deformation and rotary inertia were investigated.