| In recent years,flexible multi-body system dynamics has become a hot spot in the academic community.It is an important theoretical tool for studying the development of complex multi-body systems in the direction of lightness,high speed and high precision.The flexible hub-beam is a typical multi-body dynamic system model.It is a simplified model of multi-body dynamics and control problems.It has a close connection with aerospace,robotics and other high-tech fields.For example,the spin deployment process of the IKAROS solar sail in the first phase of orbit can be simplified to a strongly coupled dynamic model described by the flexible hub-beam system.First of all,based on the deformation theory of elastic beam in continuum mechanics,by establishing a local coordinate system on the inertial coordinate system,a simplified model of the flexible hub-beam system is established.The quadratic nonlinear coupling term of deformation and displacement of flexible beam neglected in structural dynamics is found.Based on the Hamilton variational principle,the first-order approximate dynamic equations of the rigid-flexible coupling of the system are derived.And a set of nonlinear partial differential-integral equations that can fully consider the coupling between rigid body motion and flexible deformation is obtained.And considering that the mass of the beam is comparable to the mass of the hub,the dynamic behavior of the flexible hub-beam coupling dynamic model is analyzed.The analysis results found that the root shear force generated by the beam bending has a non-negligible influence on the plane motion law of the entire system.In the second place,taking the flexible hub-beam that rotates in the horizontal plane as the research object,by dividing the flexible beam into finite beam elements,a finite element discrete model based on the consideration of nonlinear coupling deformation is obtained.Using the Newmark method for numerical simulation,the dynamic response of the flexible hub-beam system under the action of external torque is obtained.The main conclusion:when the ratio of the mass of the flexible beam to the hub increases,the amplitude and period of the lateral vibration at the end of the flexible beam will also increase.The reason for this phenomenon is that as the mass of the flexible beam increases,the natural frequency of the system decreases,which increases the vibration period of the system;the rotation speed of the hub also increases with the increase of the mass of the flexible beam,because the root shear force generated by the bending deformation of the beam accelerates the rotation of the central rigid body.Finally,taking the flexible hub-beam rotating in the horizontal plane as the research object,the analytical solutions of the constrained mode and the unconstrained mode are obtained respectively.The assumed modes method is used to modal discretize the dynamic equations of the flexible hub-beam system,and realized the relevant numerical simulations.The main conclusion:when the ratio of the mass of the flexible beam to the mass of the hub increases,the lateral response at the end of the flexible beam increases,which is similar to the harmonic vibration,and the extreme value of the rotational speed of the hub also increases.Compared with the results of the finite element method,it is found that the amplitude of the vibration response at the top of the flexible beam and the rotation speed of the hub obtained by the assumed mode method are smaller than those calculated by the finite element method.The main reason is that in the process of large-scale movement of the system,it is assumed that the modal method model will produce divergent calculation results when the system makes a large-scale high-speed movement.After comparing with the related literature,the results obtained by the finite element method are in better agreement with the reported research results. |
PDF Full Text Request