Dynamics Of The Large-scale Movement Of The Flexible Beam

With the development of science and technology, in aerospace, robotics, more and moreareas are using lightweight flexible materials, These flexible structure has weak low stiffness,structural damping. Especially when these structures do high-speed movement, traditionalstructural dynamics has been unable to accurately describe the dynamics characteristics.Therefore, there is an urgent need for flexible structural dynamics research.In this paper, we take a large-scale movement of the flexible beam as the research object.Main research is when the beam has a wide range of movement, geometric stiffness force onthe impact of the rigid body mode and the elastic body mode stability. First, we use theprinciple of virtual work to derive the kinetic equation when flexible beam has a wide rangeof rotational motion. Then consider the effect of geometric non-linear term on the rotatingflexible beam model. Divided into four cases. One of these models is a linear model in whichthe effect of longitudinal displacement due to bending is neglected in formulating the inertiaforces, but this effect is considered when the elastic forces are formulated. Simulation resultsshow that when the beam has a high-speed rotation, this model showed an unstable state. Inorder to study the influence of the axial displacement, three different models are discussed.The first model is called consistent complete model, in this model, the effect of longitudinaldisplacement caused by bending is included in formulating both the inertia and elastic forces.The second model is called consistent incomplete model, in this model, the effect oflongitudinal displacement due to bending is neglected in formulating both the elastic andinertia forces. The third model is called second inconsistent model, in this model, the effect oflongitudinal displacement due to bending is included in formulating the inertia forces, but thiseffect is neglected when the elastic forces are formulated. The numerical simulation resultsfound that the beam has a stable state when move at a high speed in these three models. Thisshows that including the effect of longitudinal displacement due to bending in the inertiaforces is not the only way that can be used to maintain the beam stability at high values ofangular velocity. At the same time, have a study about the effect of stiffness on the stability ofrigid body modes of a translating and rotating beam model and the relationship between thecritical angular velocity of the rotation of the beam and the beam length.Then, has a study onconsideration the unconstrained rigid-flexible coupling beam bending vibration modes andwithout considering unconstrained rigid-flexible coupling beam bending vibration modes. The results show that there are some different on mode shape and phase. Odd-order modes has areciprocating vibration around the central axis, while, Even-order vibration mode has areciprocating vibration around the central axis, but at an angle between the vibration centeraxis and the neutral axis of the beam.