Derivation of Equations of Motion of a Free Rigid Body Steam Generator Supported by Vertical Elastic Rods

摘要

Linear equations were derived for the motion of a steam generator supported by a number of vertical elastic rods attached to a fixed support. These derivations were performed because current computer codes do not account for the potential energy encountered in this type of setup. Three dimensional motions and gravity were considered. Vertical rods were treated as pin-ended with different lengths and axial spring constants. The arrangement of the supporting points in the plane of the top fixed support was arbitrary. The free motion of the rigid body was that of a complex pendulum-bifilar type. The principal thrust concerned deriving equations to calculate the potential energy (V) in terms of the three components of the linear motion of the mass center (G) and three components of rigid body rotation. These six coordinates were assumed to be small. Geometry of motion was considered in detail since customary first order analysis proved inadequate in obtaining the potential energy (V). Results were applied to TVA unit no. 3, a 1200 MW coal-fired steam generator in Paradise, Kentucky.