Dynamics modeling for a rigid-flexible coupling system with nonlinear deformation field |
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Authors: | Fengyan Deng Xingsuo He Liang Li Juan Zhang |
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Affiliation: | (1) Department of Engineering Mechanics, Northwestern Polytechnical University, Xi’an, 710072, China |
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Abstract: | In this paper, a moving flexible beam, which incorporates the effect of the geometrically nonlinear kinematics of deformation,
is investigated. Considering the second-order coupling terms of deformation in the longitudinal and transverse deflections,
the exact nonlinear strain-displacement relations for a beam element are described. The shear strains formulated by the present
modeling method in this paper are zero, so it is reasonable to use geometrically nonlinear deformation fields to demonstrate
and simplify a flexible beam undergoing large overall motions. Then, considering the coupling terms of deformation in two
dimensions, finite element shape functions of a beam element and Lagrange’s equations are employed for deriving the coupling
dynamical formulations. The complete expression of the stiffness matrix and all coupling terms are included in the formulations.
A model consisting of a rotating planar flexible beam is presented. Then the frequency and dynamical response are studied,
and the differences among the zero-order model, first-order coupling model and the new present model are discussed. Numerical
examples demonstrate that a ‘stiffening beam’ can be obtained, when more coupling terms of deformation are added to the longitudinal
and transverse deformation field. It is shown that the traditional zero-order and first-order coupling models may not provide
an exact dynamic model in some cases. |
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Keywords: | Flexible beam Coupling terms Nonlinear deformation |
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