CHAOTIC BEHAVIOR OF VISCOELASTIC CYLINDRICAL SHELL UNDER AXIAL PERIODIC EXCITATION

Based on Donnell-Kármán theory of a thin shell with a large deflection and Kelvin-Voigt constitutive relation, the chaotic motion of a viscoelastic cylindrical shell under axial pressure and transverse periodic excitation was investigated. The governing equations for the deflection and stress function are derived, in addition, by utilizing the method of Galerkin, the governing equations of the viscoelastic cylindrical shell are transformed into the square-order and a cubic nonlinear differential dynamic system. With the assumption of the material parameter a > 0 , the critical conditions of horseshoe-type chaos are obtained by using Melnikov function, and the influences of axial pressures and viscous damper coefficients upon chaotic motion of the system are analyzed by numerical calculation. Furthermore, the motion behaviors of the system are described through the bifurcation diagrams, the time-history curve, phase portrait and Poincaré map were given by means of Runge-Kutta method. At the same time, the results indicate the characteristics of steady motion and chaotic motion when a > 0 and a < 0 .