Using a Multi Domain Generalized Differential Quadrature Method to Study the Effect of Crack on the Vibrational Behavior of Composite Cylindrical Shell

In this study, the vibration of a composite cylindrical shell in the presence of a longitudinal and circumferential crack was investigated. The governing equations were derived based on the first-order shear deformation theory and could be converted to Donnell’s, Love’s, and Sanders’ theories by selecting proper parameters. A multi-domain generalized differential quadrature method was used to solve the problem. In this technique, a physical domain was decomposed into several elements. Then, a generalized differential quadrature method was employed to discretize the governing equations, boundary conditions at shell edges, and the compatibility conditions at the interface boundaries of adjacent elements in both longitudinal and circumferential directions. Assembling these discretized equations led to a system of algebraic equations, which could be solved through an eigenvalue solution to calculate the natural frequency of the shell. This procedure was coded in Matlab environment. Numerical results obtained by the presented method were compared with Abaqus results and those available in the literature. After verifying the accuracy and precision of the proposed method, it was employed to study the effect of different parameters on the vibrational behavior of cracked composite shells. The obtained results can be used as a benchmark for further studies.