Research On Dynamic Modeling Theory For Rigid-Flexible Coupled Composite Structures

Many engineering and aerospace structures, such as wind turbine blades, robotic manipulators, helicopter rotor blades, aircraft engine blades, satellite antennae, solar energy panels, etc., are rigid-flexible coupled structures that contain the flexible appendages attached to a rigid body, and can be modeled as rotating hub-beam systems or rotating cantilever plate systems to study their dynamic characteristics. The working tasks of these structures take on are very complex, and the corresponding flexible appendages are often under extreme environments such as high temperatures or high loads. In order to meet the demands of practical engineering applications, new functional composite materials and intelligent materials have gradually replaced traditional materials and become the first choice of the structural designers. The study of dynamics modeling theory and control design of flexible composite structures which include geometric nonlinear, material nonlinearity and intelligent materials are one of the key problems.In this dissertation, based on the rigid-flexible coupled dynamic theory of multibody system, the dynamic modeling theory and numerical simulation of composite and intelligent beam/plate structures that include functionally graded materials (FGM), piezoelectric materials and active constrained layer damping (ACLD) with large overall rotating motion are studied. The main research work and achievement are as follows:1. A review of the research background of the flexible multibody systems, the advances in the research of FGM, piezoelectric materials and ACLD as well as curve veering problem is presented.2. The rigid-flexible dynamic modeling theory for the rotating hub-composite/intelligent beam systems is studied. The high-order rigid-flexible coupled dynamic equations of a hub-FGM beam system with the thickness-wise material gradation of the beam are established. Based on the high-order rigid-flexible coupled dynamic modeling theory, the model is extended to the intelligent hub-FGM beam system with piezoelectric materials included and the hub-ACLD beam system.3. Based on the high-order rigid-flexible coupled dynamic modeling theory, the dynamic simulation softwares for the rotating hub-intelligent and composite beam systems are developed. Dynamic behaviors of the composite beams are investigated. Free vibration characteristics of a hub-FGM system with constant rotating speeds are analyzed and the frequency and modal properties of the beam with the stretching and bending coupling effect included are studied extensively. Using the ACLD hybrid control technology, intelligent vibration control of the hub-ACLD beam system is realized through the design of feedback control gains.4. Another new rigid-flexible coupled dynamic modeling method of a planar rotating hub-beam system based on a description using the slope angle and stretch strain of the beam is proposed. The nonlinear partial differential equations of the system and associated boundary conditions are derived using Hamilton’s principle. Four corresponding spatially discretized models are obtained based on the new modeling method:(1) the spatially discretized exact slope angle model that considers the stretch strain of the beam by using the finite element method; (2) the spatially discretized fourth-order slope angle model by neglecting the fifth- and higher-order nonlinear terms from a quadratic Taylor series expansion of the slope angle by using the method of assumed modes; (3) the second-order slope angle model by neglecting the third- and higher-order nonlinear terms in the fourth-order slope angle model; and (4) the simplified second-order slope angle model without considering the stretch of the beam. The dynamic equations of a second order slope angle model of a rotating hub-axially functionally graded tapered beam system are derived.5. Dynamic behaviors of the rotating hub-beam system are studied based on the new slope angle modeling theory. Dynamic responses from the four nonlinear slope angle models and the first-order approximate coupled model as well as the high-order coupled model are compared, and the accuracy of the slope angle modeling method is proved. Comparisons of the four different slope angle models are made to show the differences of computational efficiency and precision among them. Dynamic characteristics of rotating hub-axially functionally graded tapered beams are studied based on the efficient second-order slope angle modeling theory.6. The rigid-flexible coupled dynamics modeling theory for a rectangular FGM thin plate undergoing large overall motion is studied. The free vibration characteristics of a rotating cantilever FGM plate at constant speeds are investigated. Curve veering phenomena of the system are analyzed intuitively by drawing mode shapes of the rotating plate.