Dynamics Of Cylindrical Shells Research Articles

The generalized Schamel equation in nonlinear wave dynamics of cylindrical shells

The axisymmetric propagation of longitudinal waves in an integrally stiffened physically and geometrically nonlinear cylindrical shell is studied. The case is considered when the parameters characterizing nonlinearity, dispersion and thickness–radius ratio are the same order. Using the multiscale asymptotic method, the generalized Schamel equation is derived from the equations of motion of the shell. This equation contains an additional term with the fifth derivative with respect to the spatial coordinate which characterizes the high-frequency dispersion. It is shown that the derived equation does not pass the Painleve test and therefore is not integrated by the inverse scattering transform. The geometric series method using Pade approximants is applied to construct exact solitary-wave solution of the equation. It has been established that for the existence of an exact bounded amplitude solution a “soft” type of physical nonlinearity is necessary. The Schamel–Kawahara equation containing the combined nonlinearity is considered; its exact soliton-like solution is given. Numerical simulation confirmed that the initial perturbation in the form of the exact solution generates a persistently propagating solitary wave.

Nonlinear Oscillations and Stability of Parametrically Excited Cylindrical Shells

Based on Donnell shallow shell equations, the nonlinear vibrations and dynamic instability of axially loaded circular cylindrical shells under both static and harmonic forces is theoretically analyzed. First the problem is reduced to a finite degree-of-freedom one by using the Galerkin method; then the resulting set of coupled nonlinear ordinary differential equations of motion are solved by the Runge-Kutta method. To study the nonlinear behavior of the shell, several numerical strategies were used to obtain Poincare maps, Lyapunov exponents, stable and unstable fixed points, bifurcation diagrams, and basins of attraction. Particular attention is paid to two dynamic instability phenomena that may arise under these loading conditions: parametric excitation of flexural modes and escape from the pre-buckling potential well. Calculations are carried out for the principal and secondary instability regions associated with the lowest natural frequency of the shell. Special attention is given to the determination of the instability boundaries in control space and the identification of the bifurcational events connected with these boundaries. The results clarify the importance of modal coupling in the post-buckling solution and the strong role of nonlinearities on the dynamics of cylindrical shells.

Dynamics of cylindrical shells containing fluid flows with a developing boundary layer

This paper deals with the dynamics and stability of a thin cylindrical shell, with clamped ends, conveying incompressible viscous fluid. In particular, the case of a developing boundary layer is considered. It is shown that the main unsteady fluid-dynamic terms influencing the dynamics of the system are 1) the unsteady pressure associated with shell oscillations and 2) the unsteady circumferential component of the skin friction stress, coupled with circumferential movements of the shell, expressions for which are obtained for both a laminar and a turbulent boundary layer. The problem is formulated in terms of a unique equation of motion obtained from Flugge's set of three equations, without the intercession of additional simplifications or assumptions, such as those utilized by Donnell and Kempner, for instance. It is shown that the unsteady viscous effects on the dynamics of the problem are generally small and stabilizing. The effect of some system parameters on stability is also investigated.

Dynamics of cylindrical shells with variable curvature

The transfer matrix method is extended to the analysis of non-circular cylindrical panels. The exact solution for the transfer matrix of a panel with exponential curvature is obtained by solving exactly the variable coefficient differential equations of motion of the shell using a Laplace transform—difference equation technique. The results are compared with respect to accuracy and computer time with various approximate methods of computing the transfer matrix for the same panel. Natural frequencies and mode shapes for typical non-circular panels are computed and compared with a constant curvature panel to show the effects of variable curvature.