Flexible Multibody Dynamics Research And Application Based On The Absolute Nodal Coordinate Method

The theory for multi-rigid-body system dynamics has been very perfect. With the development of technology, many modern high-speed, light flexible multiody systems such as flexible aircraft, flexible thin and long manipulator, train pantograph/catenary system, etc are used in many areas. When these systems are working, the dynamics charactericstics often show the large rigid body motion as well as large structure deformation. Previous researches have indicated that the traditional modeling method based on the small deformation and small rotation assumptions can not lead to accurate results for these flexible multibody systems. The multiobdy dynamics research has entered a new era since the appearance of the absolute nodal coordinate (ANC) method, which also further makes the unity of the multibody system theory and the finite element theory. The ANC-based beam, plate and shell elments are isoparametric elements. Within the system equations of motion, the system mass matrix remains constant and the centrifugal and Coriolis forces vanish. The rigid body motion of the system can be describled exactly. All the above characteristics can assure the ANC method leads to more accurate results than the traditional methods for the multibody systems, especially for the flexile multibody systems undergoing large deformation and rotation. The ANC method has been considered a benchmark in multibody sytem dynamics research field and has always been a hot research topic since its appearance. In this dissertation, based on the previous multibody dynamics researches based on the ANC method, the following further unique and creative researches on ANC-based multibody dynamics theory and applications are carried out.1) Many classic algorithms for system dynamics differential algebraic equations (DAEs) are applied to solve the DAEs based on the ANC method. Detail results comparisons are made in terms of constraints violation, system energy dissipation and the total cost CPU time. The Bathe integration is firstly applied to solve the DAEs based on the ANC method. An efficient hybrid method to solve the equations of motion is proposed based on the Augmented Lagrange Formulation (ALF) and the ANC methods, which is further used to solve the dynamics probems for large deformation flexible multibody system with nonlinear constraints. 2) By the ANC method, the dynamics for the multibody systems with fractional derivative damper is investigated. The mathematical model for the damper is expressed by the three-parameter fractional derivative model. Furtherly, the equations of motions for viscoelastic flexible multbody system are derived based on the ANC method; The effects of the different parameters within the fractional derivative model on the viscoelasticflexible multibody system dynamics characteristics are also studied.3) The dynamics characteristics of the planar and spatial multibody systems with planar revolute clearance joint and spatial spherical clearance joint are investigated by the ANC method. The kinetic model for the planar revolute clearane joint and the spherical clearance is expressed by the ANC method, the equations of motion are also derived and the friction effects are also considered. The effects of the element number used and the material Young's modulus on the responses for on the dry impact models of the multibody systems with clearance joint are studied. Based on the dry impact researches, for the planar revolute clearance joint a squeeze lubrication force model which can consider the cavity effects is adopted to model the lubrication condition. While for the spatial spherical clearance joint the squeeze lubrication force model is directy ducted by using the lubricant's Reynolds equation. With or without the lubricaiotion condition, the dynamics characteristics of the planar and spatial multibody systems with planar revolute clearance joint and spatial spherical clearance joint are compared, which indicates the great significance of joint lubrication.4) Based on the ANC method, the model for the two-link flexible manipulator is derived. The tip square and circle trajectory are successfully tracked by using PID control scheme.