Effects of local thinning defects and stepped thickness for free vibration of cylindrical shells using a symplectic exact solution approach

Based on the Reissner shell theory and a new symplectic method, an analytical exact solution approach is presented in this paper to deal with free vibration of stepped cylindrical shells with thickness variations in both the axial and circumferential directions. Such cylindrical shells are often applied for designing aeronautics and space structures and hence any local defects and local geometric variations will result in significant design consequences. For this reason, this paper intends to establish a cylindrical shell model with local wall defects including local wall thinning and wall thickness stepped variations. A new exact solution approach for free vibration of the model are obtained by superposing the eigensolutions of the perfect shell. To ensure validity of the present result and the universality of the method, the solutions for three forms of stepped shells are compared with published data and finite element analysis. The effects of geometric parameters of the local thinning defect on free vibration characteristics are also investigated and presented.