| Elastic, axially traveling cables are special suspension cables that transport themselves longitudinally in operations. Many applications of these cables can be found in transportation, aerospace and national defense industries. The traveling cables belong to gyroscopic continuous systems with infinite degrees of freedoms. As nonlinearities are concerned, complex dynamical characteristics may show up under circumstance of damping, wind, snow, gravitational force etc. 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. In this dissertation, some fundamental issues are investigated respectively based on previous researches, including:(1). Derivations of exact solutions of natural frequencies and modal functions of the damped vibration response. It is pointed out with the eigenvalue-bifurcation analysis that the period varies with the damping coefficient and transport speed. Discussion is made about the orthogonality conditions of the modal functions.(2). Development of dynamic modeling of traveling, elastic cables considering geometric nonlinearity. The approximate solution of the equation and its stability property are obtained by using the method of multiple scales. The vibration of a damped traveling cable is compared with the undamped one.(3). Approximate solution of response under aerodynamic damping modeled as nonlinear function of velocity. The governing equation of motion is developed and solved through the method of multiple scales. The stability of equilibrium configuration is discussed with varying parameters.(4). The development of dynamic modeling of traveling, elastic cables under the influence of initial tension. The static configuration is obtained with initial distribution of cable tension computed numerically. Analyses are provided for effects of the tension amplitude as well as the uniformity of tension distribution on the vibration response. Comparison is made between the response and the one with uniformly distributed tension.This dissertation is funded by the Natural Science Foundation of China under contract numbers 10472021 and 10421202 and the SRF for ROCS and the Program for Changjiang Scholars and Innovative Research Team in University of China (PCSIRT). |
