| Summary: | 碩士 === 中華大學 === 機械與航太工程研究所 === 92 === The main objective of this study relies on the stability of numerical method to the multi-body flexible mechanical system. Due to the flexible kinematic constrain, the governing equation is derived by Lagrange multiplier formulation to form a set of differential-algebraic equation (DAE). The Lagrange multiplier represents the joint reaction forces which is an important factor in the mechanical design, such as bearing. Form previous documented, the consideration of joint reaction forces combined to the flexible dynamic system is rarely investigated which initiates the motivation of the study. The application of different numerical methods is well established to the multi-body rigid body mechanical system. However, the capability of each numerical method to the high stiffen flexible mechanical system is an important topic in order to accurately simulate the flexible mechanical. Two dynamic models of a flexible rotating beam and four-bar linkage have been considered to investigate the dynamic behavior including the joint forces. The flexible rotating beam dynamic model is based on a beam with steel beam subjected to small linear deformation and geometric nonlinearity. The flexible mechanism dynamic model is based on the coupler with flexibility subjected to small linear deformation. Lagrange multiplier method is used to derive the governing equation of the flexible system the includes the coupled rigid and flexible generalized coordinates and multiplier force parameters. A continuous system is considered in the analytical approach. The axial deformation and the transverse deformation are included and represented by the mode shape functions of the beam. The coupled effect between the rigid body motion and the flexible motion is also considered. The forward dynamic simulation is performed by a prescided driving troque in the numerical simulation.
Direct integration method, QR decomposition method and acceleration projection method well be used to derive the numerical solution which may not satisfy the constraint. A projection process well be taken after every time step to ensure the numerical solution to satisfy the constraint.
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