Structural Vibration Analysis For Elastic Axially Traveling Cables

Elastic, axially traveling cables are special suspension cables that transport themselves longitudinally. Many applications of these cables can be found in transportation, aerospace and national defense industries. With the rapid development of cable carriages, space structures and helicopter transmission cables, the vibration of traveling cables has become an important interest to both domestic and foreign researchers. It has been realized that the cable's vibration is governed by a second-order partial differential equation which contains partial derivatives with respect to both time and space variables, and it will be difficult to solve the modal response by using traditional methods. To this end, the dual formulation based on the Hamiltonian dynamics can be used, leading to a concise and efficient dynamical system that can be easily solved either analytically or numerically.The main issue in vibration analysis of traveling cables can be summarized as follows: modeling the structural system properly and solving the natural frequencies and modal functions. Also, the periodic responses of the free vibrations, forced vibration and the self-excited vibrations should be investigated. Additionally, the stability of equilibrium configuration, resonance and bifurcation has to be studied.In this dissertation, some fundamental issues are investigated in the frameworks of Lagrangian dynamics and Hamiltonian dynamics, respectively, including(l).The development of dynamic modeling of traveling, elastic cables.(2).The exact solutions of natural frequencies, modal functions and the free vibration response. The Hamiltonian dual equations of motion are developed through variable principle, and the conjugated pairs of eigenvalues and eigenvectors are determined in closed form. The exact displacement is obtained from the theorem of expansion.(3).The exact solution of linear, undamped forced vibration response is developed, and the damped forced vibration as well as the self-excited oscillation are obtained numerically. For nonlinear vibration, the equilibrium is solved and its stability is analysed for a traveling cable excited by a loading of nonlinear function of displacement.(4).The response of a traveling cable under the action of air-elastic force is solved approximately through the Method of Multiscale Scale. The expression of air-induced damping is used and the equation of motion is developed. A nonlinear, second-order ordinary equation of motion is obtained through the Galerkin's method for modal coordinates, and the steady-state vibration is solved approximately. The stability of the equilibrium configuration is investigated by using Lyapunov's theory. The critical translation speed and stable region are determined by means of the Routh-Hurwitz criterion.This dissertation is funded by "Theory and Numerical Method for Multidisciplinary Optimization Design of Couple Systems", a Key Project of the Natural Science Foundation of China under contract number 10032030.