Flexible Multibody System Dynamics Considering Geometric Nonlinear And Thermal Effect

In this dissertation, dynamic modeling theory of flexible multibody system considering geometric nonlinear and thermal effect is investigated. Based on nonlinear elastic theory, heat conduction equations of a planar beam and dynamic equations of hub-beam system are derived, and then the modeling theory of rigid-flexible coupling system considering thermal effect is extended to flexible multibody system. The main contents are described as follows:In chapter 1, according to the survey of corresponding literatures, the previous research of thermal coupled dynamics and rigid-flexible dynamics are summarized. The objective of the dissertation is put forward.In chapter 2, based on precise nonlinear strain-displacement relationship, rigid-flexible coupling dynamic equations of a hub-beam system are established using virtual work approach and finite element method in case that the time history of the temperature is prescribed. Since the high-order terms of the stiffness matrix are included, such nonlinear formulation is suitable for large deformation problem as well as small deformation problem. In order to avoid repeated symbolic integration and to improve computational efficiency, each element of the nonlinear stiffness matrix is expressed as product of constant matrices and deformation matrices. Firstly, simulation of a flexible single pendulum is carried out to verify the correctness and efficiency of the present nonlinear formulation and then the effect of geometric nonlinearity on rigid-flexible coupling dynamics in case of the variation of temperature and hub rotary inertia is investigated. Spectrum analysis method is used to investigate the characteristics of the natural frequencies of the hub and simply-supported beam system to reveal the softening effect in case of temperature increase. Furthermore, heat conduction and dynamic equations of a flexible beam and dynamic equations of hub-beam system are derived using virtual work approach, and then the coupling equations are solved and the temperature variables as well as the variables related to rigid body motion and elastic deformation are calculated simultaneously. Rigid-flexible coupling dynamic performance of a hub cantilevered beam system applied with heat flux is investigated to show the effect of the transverse temperature gradient on the elastic deformation and rigid body rotation. Significant effect of the geometric nonlinear terms in case of large deformation is revealed. Rigid-flexible coupling theory considering thermal effect is extended to flexible multibody system in chapter 3. Firstly, variational equations of each flexible beam are derived by using virtual work approach, and then according to the kinematic relation among flexible beams, equations of motion of open-loop hub-beams system are obtained. In addition, heat conduction equations are assembled and the coupled heat conduction and dynamic equations of flexible multibody system are derived. By leading into the constraint equation of the cut joint and Lagrange multiplier, the equations of motion of close-loop flexible multibody system are established and the module chart of simulation of flexible multibody system is designed. Finally, dynamic performance of planar four-bar mechanism and hub-beams system is investigated and the effect of thermal expansion and thermal bending is revealed.In chapter 4, the present research work is summarized and the prospect of the future research is proposed.