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 governing equations of motions the coupling effects of dynamic method. In the construction of the 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.