Vibration and damping analysis of cylindrical shell treated with viscoelastic damping materials under elastic boundary conditions via a unified Rayleigh-Ritz method

The present article presents an improved unified approach of Rayleigh-Ritz method to investigate the vibration and damping behavior of thin short cylindrical shell with viscoelastic damping materials treatment under arbitrary elastic edges. In the frame of the Donnell's thin shell application, the governing equation of dynamic of shell treated with the constrained layer damping (CLD) is established, in which the effects of shear stress due to viscoelastic damping material layer are considered. Then, the formulation of the CLD shell with traditional boundary supports is derived according to the Rayleigh-Ritz method being unified with expanding a serious of orthogonal polynomials as the admissible displacement functions. Next, a set of artificial springs are imported on the free edges of the shell to simulate the possible elastic supports of the CLD shell. Further, the convergence of the presented method in dealing with CLD shell with various boundary supports are confirmed by presenting an experiment and some numerical comparisons. Finally, some further numerical investigations are carried out to illustrate the influence of the variations of boundaries stiffness values on the vibration frequencies and model loss factors of constrain layer damping shell.