Dynamic modeling of multibody flexible structures

Xu, Jiechi
Major Professor
J. R. Baumgarten
D. R. Flugrad, Jr.
Committee Member
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Mechanical Engineering
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Mechanical Engineering

This dissertation presents research work on the dynamic modeling of a three-dimensional, multibody, flexible, structural system with mutually coupled multicoordinates of unknown large overall rigid body motion. The study includes theory development and mathematical modeling, time integration numerical technique investigation, computer simulation and results, and experimental measurements and verification. The specific structure under consideration is characterized as an open loop system with spherical unconstrained chains capable of three-dimensional rotation motion. The elastic deflections and rotations change the instantaneous body shape and energy level of each individual flexible member and consequently affect the rigid body motion of the system. In return, rigid body motion induces passive inertial forces resulting from tangential, centrifugal, and Coriolis accelerations and therefore influence the elastic deformation. In addition, an elastic-to-elastic coupling phenomenon, an effect of elastic deformation in succeeding links on the current link, is also involved during the motion of the system. All of these strongly nonlinear coupling terms are accounted for and are derived exactly in the dynamic modeling of the structure. The Lagrangian approach associated with a conventional stiffness finite element method is adopted in the derivation of the dynamic equations of motion and in the space discretization of the flexible members. Some hypotheses are made in the modeling of three-dimensional elastic deformations using finite element analysis in order to reduce the total elastic degrees of freedom and to simplify the procedure of space discretization with only minor loss of exactness. A special numerical technique, a sequential implicit-explicit time integration method with predictor-corrector schemes (20) (21) (96), is developed to solve a second-order, nonlinear, ordinary differential equation system with time-varying coefficient matrices. The numerical algorithms are capable of handling the dynamic equation systems with inherent characteristics involving the variables of large overall nonlinear rigid body motion and the variables of small linear vibration. A general purpose computer code is developed with the implementation of the numerical technique presented in this work. Multiple finite elements of beam type are selected for each flexible member in order to increase accuracy where concerned. Extensive computer simulation of the dynamic response of the system is performed for several cases with different conditions and numerical parameters. The measurement instrumentation and computerized data acquisition system are set up to measure structural deflections at different locations. The most significant deformation, the overall deflection at the end of the chain accounting for all the possible elastic deflections and rotations preceding that location, is also calculated and the result is compared with experimental data. Good agreement between the analytical and experimental results in terms of overall radial deflection at the tank center is achieved.