Active Vibration Control for Nonlinear Axially Translating Cable Systems of Multi-Dimensions

Abstract

Cables, s trings, and highly flexible slender structures moving relative to fixed material constraints, known as axially translating cable systems, are commonly seen in engineering applications. In many cases, such cable systems may be generated with vibrations which need to be controlled properly. Strictly speaking, such vibrations are nonlinear. If the nonlinear vibrations of the systems are to be considered, effective and reliable control of such vibrations can be a challenge to the researchers and engineers. Conventionally, control strategies are applied for linear axially translating cable systems or the systems linearized or simplified, though nonlinear systems or models of the axially translating cable systems are more representative to the systems in real world and can be used to accurately describe the responses of the systems. In the past years, some control strategy was developed for controlling one-dimensional nonlinear axially translating cable systems. However, an effective and reliable control strategy for controlling the nonlinear vibrations of axially translating cable systems of multi-dimensions is not seen in the current literature. In this chapter, a newly developed active control strategy is to be introduced for quantitatively controlling the vibrations of nonlinear axially translating cable systems of multi-dimensions. The modeling and governing equation development for such cable systems are to be presented with the solutions developed for the systems. The detailed establishment of the active vibration control strategy will be provided in this chapter. The application of the control strategy is also to be demonstrated in a few cases of chaotic vibration controls for a nonlinear axially translating cable system.