Modal Analyses of a Thin Shell with Constrained Layer Damping (CLD) Based on Rayleigh-Ritz Method - Song, Xu-Yuan; Ren, Hong-Jun; Zhai, Jing-Yu; Han, Qing-Kai (Journal of Applied Nonlinear Dynamics, 2026)
Foreign Object Debris (FOD) is debris or article alien, which may This paper presents analytical results of natural frequencies and loss factors of node-diameter and node-circumferential modes of a thin shell treated with constrained layer damping (CLD) based on Rayleigh-Ritz method. General differential equations of motion of the thin CLD shell are derived firstly by following the Donnell-Mushtari shell theory. By taking the beam characteristic functions as the admissible functions, the Rayleigh-Ritz method is employed to deduce the higher degree equations of natural frequencies of the thin CLD shell under different boundary conditions. It is confirmed that the present method is accurate and convenient so that it is applicable to the thin CLD shell compared with classic analytic method or transfer matrix method. Several examples are achieved and compared to illustrate the effects of the viscoelastic material (VEM) and constrain layer’s thickness ratios on the natural frequencies and modal loss factors, besides the effect of boundary conditions. The results show that the thickness ratio of VEM affects sensitively the modal frequencies and the total damping capacity of the thin CLD shell.