Dynamic Modeling And Simulation Of Functionally Graded Flexible Beam With Circular Section

The manipulator in the field of mechanical engineering,the helicopter rotor and the space manipulator in the field of aerospace all have large motion,and most of them are composed of rigid and flexible bodies.Dynamics of flexible attachments of multibody systems with large overall motions are very complicated due to the coupling effect between the rigid motion and elastic deformation of the flexible body.A rotating hub-beam system can be used to do modeling and dynamic analysis of space manipulators or slender rotor blades,which are usually made of advanced composite materials.For such a rigid-flexible coupled system,there are also complicated coupling effect between different vibrations modes of the flexible beam moving in the three-dimensional space,and the vibration characteristics of the flexible beam structures should be well examined.In addition,traditional isotropic materials and composite materials gradually cannot work normally long times in bad conditions,so functional gradient materials begin to replace these traditional materials.In this paper,dynamic modeling and analysis of FGM beams with rotating circular cross-section are studied.In this paper,based on the floating coordinate system method,the dynamic model of rotating FGM beam with hollow circular cross-section is established,where the materials properties are assumed to vary along radial direction.In order to capture the additional dynamic stiffening terms,the axial shrinkage of the beam caused by the transverse displacement is considered.The three-dimensional dynamic equations of the system governing stretching motion,flapwise bending motion,and chordwise bending motion are derived via employing assumed modes method and The second Lagrange’s equations.Based on the first order approximate coupling(FOAC)dynamic model,natural frequencies and mode shapes of the beam system are calculated by solving eigenvalue problem of the deduced dimensionless vibration equations.Influences of the angular speed,the hub radius,the slenderness ratio,the ratio of hollow radius to the root radius,the taper ratio,and the functional gradient index on natural frequencies are studied.Frequency veering and mode shape interaction are discussed when the bending-stretching mode coupling effect of the beam is considered.In addition,considering the influence of temperature,based on the system dynamics equation,by selecting the specific geometric parameters and considering the influence of the temperature field,the dynamic behavior of the rotating FGM beam in a wide range of unknown and known motion laws is discussed,and the free vibration of the system is analyzed briefly.