Nonlinear Traveling-Wave Vibration of a Ring-Stringer Stiffened Cylindrical Shell

Abstract

The nonlinear traveling-wave vibration of a ring-stringer stiffened cylindrical shell is analyzed. Using Donnell’s nonlinear shell theory and Lagrange equations, the nonlinear dynamic model of the ring-stringer stiffened cylindrical shell is derived. Galerkin’s method based on multi-mode instead of single-mode approximation is used to discretize the shell’s displacements. Two types of orthogonal circumferential modes with same frequency are used and the interaction between them is considered in the analysis of the shell’s nonlinear traveling-wave vibration. The harmonic balance (HB) method, along with the pseudo-arc length continuation algorithm, is adopted to solve the forced vibration responses of the shell. The stability of the solution is determined by the Floquet theory. Through comparison with the results available in the literature, the correctness of the present nonlinear dynamic model and its solution process are validated first. Next, the mode selection rules are determined through a convergence study. Finally, the nonlinear traveling-wave vibration of the ring-stringer stiffened cylindrical shell is studied. Also, the paper investigates, in detail, the effects of stiffener parameters on the nonlinear dynamic characteristics of the stiffened shell.