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A cantilever thin rotating circular cylindrical shell is investigated in this paper. The precession factor of vibrating shape is obtained by an energy approach, with damping and geometric nonlinearity considered. Donnell's shallow-shell theory is used, the non-linear equations of motion are discretized by Galerkin method, in which geometric nonlinearity and precession of vibrating shape are taken into account. The non-linear mode equations are studied by using Runge-Kutta method and harmonic balance method, and the stability of analytical solutions is studied. The results show that geometric nonlinearity does not influence the precession factor of vibrating shape but causes multi-value and leap characteristics. [ABSTRACT FROM AUTHOR]

Based on the linear theories of thin cylindrical shells and viscoelastic materials, the governing equation generally describing vibration of a sandwich circular cylindrical shell with partially constrained layer damping treatment under harmonic excitation, which can be written in a matrix differential equation of first order, is derived by considering the energy dissipation due to the shear deformation of the viscoelastic layer and the interaction between all layers. After that a semi-analytical and semi-numerical method for solving this governing equation is presented by means of the extended homogeneous capacity precision integration approach. Its essential difference from the recent works on transfer matrix method is that the state vector in governing equation is composed of the twelve displacements and internal forces of the sandwich shell rather than of the displacements and their derivatives. As a result, the present method can be applied to solve the dynamic problems of the kind of sandwich shell with various boundary conditions and partially constrained layer damping. Numerical examples show that the proposed approach is very effective and reliable, compared with the existing analytical solutions. Furthermore, the effects of PCLD coverage percents and locations on FRF are then discussed. [ABSTRACT FROM AUTHOR]