Vibration Equations of Thick Rectangular Plates Using Mindlin Plate Theory

Problem statement: Rectangular steel plates are widely used in various steel structures and steel industries. For a proper design of steel plate structures and efficient use of material, the behavior, strength, buckling and post-buckling characteristics of plates should be accurately determined. Approach: Considering the significance of this matter, lateral vibration of thick rectangular plates was studied on the basis of mindlin plate theory. The exact characteristic equations for a plate which is single supported in two opposite edges are available in the literature. S-C-S-F boundary condition which covers all possible situations is selected in this study. Results: The plate frequencies were calculated for this boundary condition for a wide range of plate sizes and thicknesses. The plate mode shapes were obtained for different cases and the effect of changes in boundary conditions; size ratio and thickness on the vibration behavior of rectangular steel plates are studied. Conclusion/Recommendations: Since the results of this study is exact and without any approximation, the presented values can be used as a proper criteria to evaluate the error value of approximate methods which are used by engineers for design of steel plates. These results can provide a good gridline for efficient design and prevention of using high safety factors. Considering the wide range of steel rectangular plates, more sizes and thicknesses of plates can be studied. The behavior of plates with other boundary conditions can also be studied for future research.