Control-oriented Study On Rigid-flexible Coupling Dynamic Modeling Method Of Flexible Beams

The flexible beam is not only the most widely used basic structure in mechanical,aerospace and other fields,but also the most typical kind of research object in flexible multi-body system dynamics.With the development of modern industrial technology,more and more new materials continue to emerge and light weight has become one of the main trends.Besides,in order to meet the demands of modern industry,the working conditions of these light flexible beams need to undergoing great changes,especially the operating speed raising a lot.The light structures in these working conditions show some different mechanical behaviors,such as the coupling between rigid motion and elastic motion,which leads to significant change in the dynamic characteristics of light structures,which brings great difficulties to motion vibration control system design.Therefore,it is very important to study the theory of rigid-flexible coupling dynamics of flexible beam undergoing large overall motions.The first-order approximation model,as a kind of rigid-flexible coupling model,is widely applied in the field of flexible multi-body system dynamics.It introduces the "Foreshortening Effect" caused by transverse bending deformation into longitudinal deformation,and gets the dynamic stiffening term to demonstrate rigid-flexible coupling effect.Strategy that choosing floating reference frame can decompose the structure's motion straightly,which brings great convenience to motion and vibration control system design.Dynamic modeling of on-orbit maneuvering large beam-like space truss structure is studied.And the first-order approximation model of beam-like truss is built to analyze dynamic characteristics.Although first-order approximation model includes the dynamic stiffening term,it lacks deeper discussion of the coupling between axial motion and transverse motion.It's well known that axial centrifugal load resulting from rigid rotation motion has certain effect on axial deformation.Once lose sight of the complex links between axial motion and transverse motion,some possible rigid-flexible coupling effects would be overlooked.Based on the principle of continuum mechanics,comparison is carried out between several modeling methods that adopt floating reference frame.Further more,in order to give better expression to rigid-flexible coupling effect,the more comprehensive rigid-flexible coupling dynamic model for flexible beam is established through combining the advantages of these modeling methods mentioned above.The main research is described as follows:(1)Dynamic modeling of on-orbit maneuvering beam-like space truss is studied.In the previous studies,dynamic modeling is too simplistic to describe the coupling between rigid motion and elastic motion.Based on the first order approximation model,"foreshortening effect"is considered to obtain rigid-flexible coupling dynamic model considering dynamic stiffening effect.In the process of dynamic modeling,combing the characteristics of structure itself,a special floating reference frame was chosen as local reference frame,whose origin is consistent with the instantaneous center of mass.The additional two constraints with the reference frame not only greatly simplifies the deriving process of dynamical equations but also weakens coupling effect between translational motion and elastic motion.(2)The nature vibration characteristics of on-orbit maneuvering beam-like space truss is studied.Rayleigh-Ritz method is applied to discretizing displacement variables in the equations of transverse motion for the generalized characteristic equations of transverse motion.Compared with previous models,the present model shows the effect of coupling effect on transverse bending frequencies and mode shapes.(3)Rigid-flexible coupling dynamic model of planar rotating cantilever beam is established.During the modeling process,fully nonlinear Green strain-displacement relationship is considered.The coupling dynamic model is obtained by reserving the coupling terms which demonstrates the axial deformation and transverse bending deformation in strain energy.In addition,the relationship between axial steady-state deformation and rotational speed is deduced through decomposing axial motion.Afterword,the modified dynamic stiffening term is obtained by introducing axial steady-state deformation into transverse vibration equations.Compared with the absolute nodal coordinate formulation,the effect of steady-state axial deformation on the transverse bending frequencies is discussed to verify the effectiveness and rationality of the present model.(4)Rigid-flexible coupling dynamic model of rotational three-dimensional cantilever beam is studied,which takes axial motion,chord-wise bending motion and flap-wise bending motion into account.Rotational speed limit is determined through the analysis of axial steady-state deformation.Decompose equation of axial motion to get equation of axial stretching vibration motion including the effect of axial steady-state deformation.Further more,the modified dynamic stiffening term is derived by introducing axial steady-state deformation into chord-wise and flap-wise vibration model.In the range of rotational speed limit,some work is performed to analyse the effect of axial steady-state deformation on axial stretching vibration,the effect of axial steady-state deformation and axial vibration on chord-wise bending vibration and the effect of axial steady-state deformation on flap-wise bending vibration.