Efficient Modeling of a Flexible Beam in Dymola using Coupled Substructures in a Floating Frame of Reference Formulation

Abstract

In this Master Thesis a three dimensional Euler-Bernoulli beam model was implemented in the simulation software Dymola. The beam model is based on the Floating Frame of Reference formulation combined with the Craig-Bampton method. The theory is developed with the scope to capture the dynamic and static responses of a beam model in a compact and computer efficient implementation. The Thesis includes derivation of kinematic description, mass matrix, stiffness matrix and force vectors of an Euler-Bernoulli beam in three-dimensional space. Two one-dimensional models have been derived as well. The implementation in Dymola is described together with validation of the model, discussion and conclusions. The validation of the model shows great accuracy in static loading both in elongation, torsion and bending. Excitation of eigenfrequencies is possible but the results slightly differs from the analytical solutions. Dynamic tests of the beam model shows realistic responses but further testing on this subject is recommended. Compatibility with other components in Dymola works fine. However there are some minor issues that should be solved to enhance the efficiency. Overall the static and dynamic responses of the beam model works sufficiently well

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