The dynamic equation of the plate which can freely rotate around the UMP can be obtained by a typical mass-spring-damper system and be presented as
where [L.sub.feature] is the feature length of the UMP and plate, [L.sub.feature] = 1 m; [[rho].sub.plate] is the density of the plate; h is the height of the plate; [L.sub.a] represents the distance between the root of the plate and the center of the UMP; [L.sub.p] represents the length of the plate; [[rho].sub.water] is the density of the water.
The vibration equation (1-dof) of the UMP only in the transverse direction can be obtained by the mass-spring stiffness system and be presented as
where M is the total mass of the UMP which is sum of the total mass of the UMP ([M.sub.1]) and the total mass of the plate ([M.sub.2]).
where [L.sub.feature] is the feature length of the UMP and plate, [L.sub.feature] = 1 m; [[rho].sub.water] is density of the water, [[rho].sub.water] = 1000 kg/[m.sup.3]; [C.sub.p] is an additional mass factor, [C.sub.p] = 1; [[rho].sub.Al] is the density of the plate, [[rho].sub.Al] = 2700 kg/[m.sup.3].
As shown in Figure 3, it can be seen from the figure that the center of UMP is placed at a distance from the left boundary of the computational domain to 15D and on the symmetry axis of the of the top and bottom boundary.
It is worth nothing here that the rigid boundary layer must be added to the surface of the UMP and plate which the boundary layer grid moves with the UMP and plate and is stable and the shape no longer changes to provide sufficient precision.
It is suggested from (7) that SAGE will induce a DC UMP component and pulsating UMP components at 2f.
The UMP amplitudes with respect to different SAGE cases are indicated in Table 1.
As is shown in Table 1, no matter what kind of SAGE happens in the generator, the UMP amplitudes are always related to the SAGE degrees and the exciting current value.
In the case of rotor offset, the UMP formula is relatively simple, as indicated in (7).
Differently, in the case of stator deformation, it is possible that the UMP is zero.
The rotor UMP formulas for the stator concave ([[delta]'.sub.sn]) condition and the convex (-[[delta]'.sub.sn]) condition when [[theta].sub.1] = 0[degrees], respectively, reduce to
Whenever there is a flyball along the foul lines and the umps
call, "infield fly if fair," there should always be an attempt to catch the ball or touch the ball in fair territory, since that will always result in the batter-runner being called out.
Improper or unclear signs by ump
can lead to confusion