Free Vibration Analysis of Integrally Stiffened Plates with Plate-Strip Stiffeners

Abstract

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 the normally employed rib stiffeners. Both the plate and stiffeners were analyzed using the first-order shear deformation theory. The deflections and rotations were assumed as a tensor 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 be applied to fully clamped, free, and cantilever supported stiffened plates. The governing differential equations were solved using the Rayleigh–Ritz method. The development of the stiffness and the mass matrices in the Ritz analysis was found to consume a huge amount of CPU time due to recursive integration of Timoshenko beam functions. An approach is suggested to greatly decrease this amount of CPU time, by replacing the recursive integration in a loop structure in the computer program, with the analytical integration of the integrand in the loop. The numerical results were compared with the solutions available in the literature as well as the commercially available finite-element software ABAQUS®, and the results were found to be highly satisfactory.