Free Vibration of Stiffened Plate with Cracked Stiffeners (Advances in Applied Mathematics and Mechanics, 2023)
In this paper, a new cracked stiffener model for the stiffener with a part-through and open crack is proposed, considering the compatibility condition of displacements between the plate and the stiffener. Based on the first-order shear deformation theory, the free vibration of stiffened isotropic plates with cracked stiffenersare investigated for the first time. The description of the crack parameters is based onthe continuous equivalent bending stiffness and equivalent depth of the cracked beam,and it takes into consideration of shear deformation, bending-extensional coupling vibration, and eccentricity between the stiffeners and the plate. The stiffened plates withsingle or multiple cracked stiffeners are formulated and discussed. The Ritz methodwith the modified characteristic functions is applied to demonstrate the effects of crackparameters (crack depth and location) coupling with the position and number of thecracked stiffeners on the vibration frequencies and modes of the stiffened plate. Thevalidity and accuracy of the present solutions are verified through convergence studiesand compared with the finite element results.