| In order to satisfy the practical engineering requirement, diferent control measures invibration control of the flexible structure have been adopted in the fields of civil engineering,ocean engineering and aerospace engineering. However, a fixed time delay existing due tothe online data acquisition, filtering, manipulation of the digital data inside the controlprocessor, calculation of the required control action and the signal transmission from thecomputer to the actuator. Small as the time delay is in reality control system, but it maycause a detrimental efect on the stability of the controlled structure. So time delay dynamicsis very important to optimize the design of the control system. Moreover, the time delayproblem is an important part of the dynamic response and design of controlled structures.To make a further address the mechanisms of the time delay in the controlled flex-ible structure, representative flexible engineering structure (cable, beam and cable-beamstructure) are investigated. Based on the Hamilton principle, the continuous dynamicalmodel of cable, beam and cable-beam structure are derived by considering the time delayfactors in the MR damper-stay cable control system, and by using delayed feedback con-trol strategy, and introducing the basic theory of delay diferential equation (DDE). Thenthe control system are investigated by combined the quantitative analysis method (multiplescales method) and qualitative analysis method (center manifold method and normal formtheory). We study the efectiveness of the time delay in the control system, and based onthe theoretical analysis and numerical computing, and analyze the influence of parameters(such as time delay, control gain) on the control efect, and provide a theoretical bases forthe optimized design of the control system. The contents of this thesis are as follows:1. Based on the extensively reviewing literatures, the nonlinear dynamics and it’s vibra-tion control studies of cable, beam and cable-beam structure (the representative of theflexible engineering structure) are stated, and the delay problem in the control systemare highlighted, respectively.2. In order to study the efectiveness of the time delay in the MR damper-stay cablecontrol system and explore the nonlinear response of the structure, based on theHamilton principle, a dynamical model of the MR damper-stay cable system is derivedand the Galerkin method is used to obtain the time delay dynamics system. By usingthe multiple scales method, the in-plane and out-of-plane1:1internal resonance andthe bifurcation of the control system are studied. Moreover, the numerical results areobtained by using the shooting method and arc-length continuation method. 3. By choosing a more precise description of the cables vibration mode function in theMR dampers, the MR damper-cable stayed control system model and the equationsof motion are derived and the Galerkin method is used to obtain the time delaydynamics system, and the center manifold method and normal form theory are used toa high dimensional nonlinear systems with unequal frequency conversion from infinitedimensional space to low dimensional space. Then, based on amplitude truncatedequation after dimensionality reduction, nonlinear dynamical behavior of the originalsystem are studied, and the averaging equations under external loads are obtained bysing the average method.4. Based on acceleration delayed feedback control strategy and Euler-Bernoulli beamtheory, the nonlinear dynamic model of the elastic support axial force piezoelectriccoupling beam are obtained. Via conducing the modal analysis and linear stabilityanalysis, the stability conditions of system under piezoelectric coupling and delayedfeedback are obtained. The Galerkin method and multiple scale method are used tostudy the bifurcation response of the time delay system.5. Based on the Hamilton principle, the connection and boundary conditions of the cable-beam structure are investigated by using the statics and dynamics method, and thein-plane motion equations are derived. Moreover, the large amplitude vibration ofcable-beam structure are controlled by using the delayed feedback control. The studyprovide an idea for the vibration control of the cable-beam structure by focused onthe influence of the time delay in the controlled system.The results show that: the time delay is an important unignorable factor in the vibrationcontrol system with robust under the small time delay efect. As the time delay increas-ing, the system may exhibit complex nonlinear dynamics behavior (such as quasi-periodicmotion, Hopf-Hopf bifurcation and chaos, etc) or even lead to instability of structural. Byadjusting the control system parameters, instability and complex movement of the systemcan be avoided, and the control performance can be improved. This study can be theoreticalbasis in practical engineering applications, and the design method is also be recommendedas a useful supplement to improve the performance of the control system. |
