Free Vibration Analysis of an Integrally Stiffened Plate with Plate-Strip Stiffeners using a Set of Static Timoshenko Beam Functions

摘要

We investigated the natural frequencies and mode shapes of a freely vibrating, integrally stiffened and/or stepped plate. The stiffeners used here, were plate-strip stiffeners as opposed to rib stiffeners. Both plate and stiffeners were analyzed using the first order shear deformation theory (FSDT), which employs the transverse shear deformation and rotary inertias as well as the longitudinal displacements. The deflections and rotations were assumed as a product of Timoshenko beam functions, chosen appropriately according to the given boundary conditions. Unlike Navier and Levy solution techniques, the approach used in this paper can also solve for fully clamped and free stiffened plates. The governing differential equations were solved using Rayleigh-Ritz method. Stiffened plates were considered in the study with simply-supported, fixed and free boundary conditions. The procedure adopted in this paper can analyze plates with centrically and non-centrically placed stiffeners. Moreover, the development of the stiffness and the mass matrices in the Ritz analysis consumes huge amount of CPU time due to recursive integration of Timoshenko beam functions, which include sets of trigonometric functions. A technique is used to greatly decrease the amount of CPU time, by replacing the recursive symbolic integration in a loop structure in the computer program, with the solution of the integrand in the loop. The numerical results were compared with the exact solutions available in the literature and the commercially available finite element software ABAQUS~®, and the results were found to be highly satisfactory. Some parametric studies were carried out to exhibit the influence of certain important parameters on the natural frequencies of the stiffened plate. Finally, a plate with end viscous dampers was studied and some conclusions were drawn about the mode shapes of the plate.