Dynamics of deformable multibody systems

This thesis presents an investigation of the nonlinear dynamics of arbitrary deformable multibody systems that undergo large translation and rotation movements and small elastic deformations. The objective of this study is to develop an accurate and efficient modeling method to meet the requirements in system design and control.; A general implicit formulation based on the joint coordinate method for arbitrary tree or closed-loop deformable multibody systems (MBS) is developed by defining a new topological matrix The newly-developed formulation and code have been verified numerically by investigating the total energies and strain energies of two different conservative rigid-flexible systems. The absolute error of the total energy should be several orders smaller than the strain energy to ensure the validity of the small elastic deformations. An experiment study on the dynamic responses of a 3-D test rig with both joint and link flexibility was conducted to verify the simulations. The results of the simulation and experiment show good agreement in both the time and frequency domains.; A simulation comparison amongst the joint coordinate method, Order N method and absolute coordinate method was performed. It was shown that the Order N formulation method may induce chaotic behavior in nonchaotic systems due to the propagation and enlargement of numerical errors. The commercial software ADAMS was used as a representative of the absolute coordinate method. The results demonstrate that the newly-developed implicit formulation has some advantages compared with other methods.; Two geometrical nonlinear effects are discussed in this thesis. The simulation an experimental results of the test rig show that the formulation including the foreshortening effect overestimates the nonlinearity. The thesis also presents simulations of modal expression, nonlinear coupling effects and chaos.