Active Nonlinear Vibration Control of Engineering Structures of Multiple Dimensions

Abstract

An active nonlinear mechanical vibration control strategy is developed in the research of the author’s PhD program for the nonlinear vibration control of engineering structures of multiple dimensions. The proposed control strategy has been applied in several wildly applied typical engineering structures, including Euler-Bernoulli beams and axially moving structures. Nonlinear vibrations wildly exist in engineering structures, such as bridge, aircrafts, micro-electro-mechanical devices, and elevator cables. Comparing to linear vibrations, nonlinear vibrations may lead structure failures in short time, and chaotic vibrations among the nonlinear vibrations features unpredictability. Considering the damage and unpredictability of nonlinear vibrations, nonlinear vibrations is ought to be controlled. However, most of the existing active nonlinear vibration control strategies can only be applied to the nonlinear dynamic system of single dimension, while multi- dimensional dynamic systems show the advantages over those of single dimension in dynamic analysis. Therefore, an active nonlinear control strategy has been proposed based on the existing control strategy the Fuzzy Sliding Mode Control (FSMC) strategy, and has been applied in the vibration control of the following engineering structures: Euler-Bernoulli beams subject to external excitation; axially moving Euler-Bernoulli beam without external excitation; retracting Euler-Bernoulli beam without external excitation; axially translating cable; extending nonlinear elastic cable. First of all, the nonlinear vibration and control of an Euler-Bernoulli beam subjected to a periodic external excitation is given as an example to demonstrate how the active nonlinear control strategy is developed and applied for a multi-dimensional nonlinear dynamic system. Then, considering the two typical engineering structures modeled with Euler-Bernoulli beams, the control strategy is applied in the nonlinear vibration control of a micro-electro-mechanical system (MEMS) beam and a fluttering beam. After that, corresponding to the attentions paid to the axially translating materials, the control strategy is applied in the nonlinear vibration control of four typical axially moving structures. Applications of the proposed control strategy evidently show effectiveness and efficiency of the active control strategy in controlling the nonlinear vibrations of typical engineering structures.