Rigid-Flexible Dynamics Modeling And Vibration Control Of Rotating Cantilever Plate With ACLD Treatments

Vibration analysis and control of rotating cantilever plates is an important subject in the mechanical engineering. Many aeronautic and astronautic structures can be simplified as rotating cantilever plate models, such as blades of helicopters, turbines as well as turbo-machines, satellite antennae and solar energy panels. For thin plate structures, ACLD (Active Constrained Layer Damping) is a typical hybrid vibration control method, involving active and passive damping and consequently being of smartness and robustness. As for rotating cantilever plates with ACLD treatments, the dynamic characteristics will change with different rotating speeds, generating the phenomena of"motion-induced stiffness". Moreover, shear modulus of viscoelastic material (VEM) can also vary with temperature and frequency. Piezoelectric material has the electromechanical coupling effects. Therefore, in this dissertation, accurate and rational equations for the coupled rigid-flexible dynamics are first developed to reveal dynamic characteristics of rotating flexible plates with ACLD treatments. On the basis of modal identification technique (i.e. the state subspace identification / SSID) and control theory, mathematical modeling, simulation as well as real-time vibration control are conducted to investigate dynamic behavior of ACLD treated rotating flexible plates.Dynamics modeling and vibration control of rotating rectangular cantilever plates treated with ACLD have been investigated theoretically and experimentally, the relevant research results are summarized as follows:1. A large amount of literature on rigid-flexible dynamics modeling and ACLD are reviewed with focus on current status of research in the world, solved and open problems in this area. Based on this review, rigid-flexible dynamics modeling and passive/active vibration control of rotating plates with ACLD treatments are investigated completely.2. Based on the existing references, the rigid-flexible dynamics equations of a rectangular plate in free motion are deduced by combining the second kind of Lagrange formulation with the finite element method. Numerical simulation is conducted to exhibit dynamic characteristics of the rotating rectangular (composite) plate and how these characteristics are affected by rotating speeds, aspect ratios as well as fiber orientation. Effectiveness of the theoretical model is also validated.3. The GHM model of viscoelastic material is combined with the finite element method, rendering unnecessary the iterations for calculating modal parameters and responses as usually done in common methods. Parameters of the GHM model are obtained by nonlinear curve fitting in the complex frequency domain, which makes the modeling become a nonlinear optimization problem. Simulation results show that the GHM model can be used effectively in dynamic characteristics analysis.4. The coupled rigid-flexible dynamics model of a rotating cantilever plate treated with ACLD treatments is established. The model takes into account the rigid-flexible coupling, the mechanical and piezoelectric coupling of piezoelectrical material and the constitutive relationship of viscoelastic material of the ACLD plate. The established finite element model of the ACLD treated rotating cantilever plate sets a base for experimental study.5. The stochastic subspace identification method using output only is employed to identify modal parameters of systems with closely spaced natural frequencies. Also used is the improved stabilization diagram, which indicates the variation of estimates to fitting data, to increase the identifiability of modal parameters. Component energy index is given as well to evaluate the contribution of each mode. Modal parameters of a system with closely spaced frequencies are given by simulation and compared with the FEM results, indicating that the SSID has sufficient accuracy in identification. As a result, modal parameters by SSID can indicate the natural characteristics of a system.6. The model of the rotating ACLD cantilever plate is identified by the state subspace identification method and its order is reduced by the balanced model reduction method. Therefore, the controllable and observable model can be used directly in the design of controllers. Simulation results have demonstrated the effectiveness and reliability of SSID.7. In order to validate the coupled rigid-flexible dynamics equations, an experimental test rig was established to conduct motion and vibration control (This work was supported by the NSFC project 10672099). The motion control subsystem is used to simulate motion of the cantilever plate at different rotating speeds. The vibration control subsystem is used to suppress vibration. Experimental results show that the test rig can validate the modeling of rotating structures at different speeds. Moreover, PID can be applied to control vibration of the rotating cantilever plate with ACLD treatments.For the first time, investigated thoroughly are the coupled rigid-flexible dynamics modeling and vibration control of the rotating rectangular plates with ACLD treatments. The finite element model of the composite plate is established and reduced to a controllable and observable minimal realization by the identification technique and model reduction method. To validate the proposed modeling, the experimental setup for motion control and vibration suppression is designed with a servo-electric motor and a DSP controller. Frequency responses and vibration control of the ACLD treated rotating rectangular plate at different speeds are carried out. Experimental results have demonstrated the coupled rigid-flexible dynamics modeling is suitable for engineering application, and active constrained layer damping can suppress effectively the vibration of rotating structures.