Wave based method (WBM) is presented to analyze the free and forced vibration of cylindrical shells with discontinuity in thickness. The hull is first divided into multiple segments according to the locations of thickness discontinuity and/or driving points, and then the Fl€ ugge theory is adopted to describe the motion of cylindrical segments. The dynamic field variables in each segment are expressed as wave function expansions, which accurately satisfy the equations of motion and can be used to analyze arbitrary boundary conditions, e.g., classical or elastic boundary conditions. Finally, the boundary conditions and interface continuity conditions between adjacent segments are used to assemble the final governing equation to obtain the free and forced vibration results. By comparing with the results existing in open literate and calculated by finite element method (FEM), the present method WBM is verified. Furthermore, the influences of the boundary conditions and the locations of thickness discontinuity on the beam mode frequency and fundamental frequency are discussed. The effects of the direction of external force, location of external point force, and the structural damping on the forced vibration are also analyzed.
Wave based method (WBM) is presented to analysis the free vibration characteristics of cylindrical shells with nonuniform stiffener distributions for arbitrary boundary conditions. The stiffeners are treated as discrete elements. The equations of motion of annular circular plate are used to describe the motion of stiffeners. Instead of expanding the dynamic field variables in terms of polynomial approximation in element based method (finite element method etc), the ring-stiffened cylindrical shell is divided into several substructures and the dynamic field variables in each substructure are expressed as wave function expansions. Boundary conditions and continuity conditions between adjacent substructures are used to form the final matrix to be solved. Natural frequencies of cylindrical shells with uniform rings spacing and eccentricity distributions for shear diaphragm-shear diaphragm boundary conditions have been calculated by WBM model which shows good agreement with the experimental results and the analytical results of other researchers. Natural frequencies of cylindrical shells with other boundary conditions have also been calculated and the results are compared with the finite element method which also shows good agreement. Effects of the nonuniform rings spacing and nonuniform eccentricity and effects of boundary conditions on the fundamental frequencies and the beam mode frequencies have been studied. Different stiffener distributions are needed to increase the fundamental frequencies and beam mode frequencies for different boundary conditions. WBM model presented in this paper can be recognized as a semianalytical and seminumerical method which is quite useful in analyzing the vibration characteristics of cylindrical shells with nonuniform rings spacing and eccentricity distributions.
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