空间运动体上梁的三维动力学建模和仿真

对附着在空间运动体上梁的动力学问题进行了研究,运用Lagrange方法建立了中心刚体作任意三维运动时,梁作横向振动和纵向振动的动力学方程,考虑了柔性梁的横向弯曲变形所带来的纵向位移,这种耦合变形使所得到的振动方程包含了动力刚化效应,这是与传统的梁振动模型的不同之处,最后通过仿真算例验证了该方法.

Three-Dimensional Dynamic Modeling and Simulation of a Beam Attached to a Spatially Moving Base

The three-dimensional dynamics of a flexible cantilever beam attached to a moving rigid body undergoing an arbitrarily three-dimensional large overall motion is investigated in this paper. A set of dynamic equations for two-dimensional transverse and one-dimensional longitudinal vibrations of the flexible beam is established by using Lagrange's dynamic method. In the construction of the governing equations of motions the coupling effects of the so called transverse deformation-induced longitudinal deformation is included, which leads to the consideration of the dynamic stiffening effects in the obtained dynamic equations. An example is given to show the validity of the method presented in this paper and also the significant effects of the dynamic stiffening terms on the deformation and the dynamic characteristic of the flexible beam, and the difference between the present modeling theory and the traditional vibration theory as well. The traditional vibration theory of flexible beam will produce large error when the flexible beam itself is at higher speed large overall motion. Once the speed reaches at a critical value, the traditional dynamic system will diverge. Whereas the present model has high precision and the dynamic system converges even if the flexible beam undergoes higher speed large overall motion.