Flexible Multi-body Coupling Time-varying System Frequency And Modal Perturbation Analysis

In this dissertation the coupling dynamical modeling theory and discrete method of flexible multibody system are studied. For fully appreciating the dynamical response numerical solution of the system, a flexible cantilever beam, as an example, is investigated. After Kane proposed the concept of Dynamic Stiffing, the coupling dynamical modeling theory of flexible multibody system has been deeply developed. However, the discrete method about that has still barely been studied.In the first part of this thesis various theoretic of modeling is presented, then based on the modeling theory of literature, the exact coupling dynamical model of elastic beam in large overall motion and its dynamical equation are established. Then the strict mathematics theory is used to solve for the exact frequencies and mode shapes of this model. These exact solutions will be used to compare with other approximate solutions with discrete method in the following parts.The second part of this thesis is devoted to establish the high-order perturbation theory based on the low-order perturbation theory. Then this high-order perturbation theory is employed to solve the vibration frequencies and mode shapes of time-varying flexible multibody system with coupling dynamical model. By the solutions of MATLAB, the results of the high-order perturbation theory are of high accuracy compare with the exact solutions in the case of high rotating angular velocity, which solves the questions that the low-order perturbation solutions are of poor accuracy as rotating angular velocity increase. In the solving process, the coupling deformation items of middle line of the coupling model, which exist in the process of FEM disperse of flexible component with large overall motion, is improved.Due to the cumbersome process and a large amount of computer time-consuming of high-order perturbation solutions, in last part of this thesis the standard first-order perturbation method is improved and the Rayleigh- perturbation theory of solving vibration frequencies and mode shapes of time-varying coupling flexible multibody system is established, and then, with the help of MATLAB, the Rayleigh-perturbation solutions are obtained. Compared to the high-order perturbation solutions, Rayleigh-perturbation solutions are accurate enough, and also have compacter process and less computer time-consuming...