(untitled) (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 stiffeners are investigated for the first time. The description of the crack parameters is based on the 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 with single or multiple cracked stiffeners are formulated and discussed. The Ritz method with the modified characteristic functions is applied to demonstrate the effects of crack parameters (crack depth and location) coupling with the position and number of the cracked stiffeners on the vibration frequencies and modes of the stiffened plate. The validity and accuracy of the present solutions are verified through convergence studies and compared with the finite element results.