Application of Distributed System Concepts to Analysis of Bending Vibration

As an alternative to the normal mode approach to the dynamics and controls analysis of flexible aerospace vehicles, the analysis of bending vibration is being studied in terms of the distributed system concepts of propagation and reflection. A relationship is developed between the vibration equation of motion and the propagating wave equation. Transmission matrices, including the effects of shear compliance and rotary inertia, are developed for uniform beam segments. Through a transformation technique, the local state variables are changed to characteristic variables of the beam permitting factorization of the solution into propagation and end-effect matrices. The technique is applied to a cascaded or step beam structure and a beam structure combined with a damped spring mass sloshing model. The advantages and disadvantages of the distributed parameter transmission matrix approach are investigated and the use of this approach for the dynamic analysis of aerospace vehicles is evaluated.