Effect of ribs on vibration characteristics of cantilever plate

Abstract

Analytical solution for the vibration response results of the ribbed rectangular cantilever plate using the Kirchhoff plate theory is presented in this paper. The validity of the analytical solution is verified by comparison with the results of finite element analysis. The analytical model is then used to study the effect of the single rib, periodic ribs and orthogonal ribs on the modal vibration of the cantilever plate. According to the minimum inertia axis and torsion center line of the cantilever plate, the modal vibration shapes generated by the cantilever plate are divided into flexural and torsional vibration mode. The effect of the insertion of single rib on the modal vibration of the cantilever plate and the curvature of the insertion position are analyzed. It can be found that the effect of single rib on modal vibration of cantilever plate depends on the vibration mode and the location of the rib insertion, where a rib can be used as a mass loading, a stiffness attachment, or a combination of both. And the effect of periodic ribs on the vibration characteristics of the cantilever plate is further investigated. When periodically ribbed, the effect of the periodic ribs on the modal vibration of the cantilever plate depends on the dominant of the total of the mass loading or the stiffness enhancement played by each of these ribs. However, when another rib is added to the torsion center line of the periodic ribbed cantilever plate, it shows stiffness enhancement in both flexural and torsional vibration.