A Vectorial-Wave Method for free and forced vibration analysis of extra thin cylindrical shells with boundary discrete damping

The Vectorial-wave method (VWM) is developed to study free and forced vibrations of cylindrical shells in the presence of dampers at supports. In modeling the issue, a circular cylindrical shell is considered with two ended supports, including separate springs and viscous dampers in the possible directions. Accordingly, based on Flügge thin shell theory and by considering the wave vectors going in the opposite direction along with the shell axis, reflection and transmission matrices are determined to satisfy the shell continuity as well as the boundary conditions. The proposed method is verified through comparing its results with the available literature and the numerical results calculated by Finite element method (FEM). Employing VWM, the viscous characteristics of the applied supports on natural frequencies of the shell are investigated. Furthermore, frequency responses of the shell, which are affected by point-load excitation, are obtained. Finally, the results show that several tandem resonance picks can be eliminated via accurate setting of the support damping.