Chief Researcher, Vehicle Dynamics Lab.

  From the vibration data obrained simultaneously on several cars in the same
Shinkansen train, it was observed that the vibration amplitude of the tail
car is greater than those of the other cars in a train (Fig.1). Our analysis 
arrived at the conclusion that the vibration mode of a train has a tendency 
for the tail car to vibrate more than the others when the carbody hunting 
characteristics of the train for the yawing mode are likely to emerge, and 
when aerodynamic forces work in tunnel section. Referring to these results,
it was found by simulation analysis, etc. that two car end yaw dampers 
longitudinally and parallel installed between car ends (Fig.2) in proportion
to the angular velocity, are effective to decrease the train vibration 
including the tail car's vibration. However, this method has not so far been
used for the Shinkansen train of the type having two bogies per each carbody. 
A prototype of the car end yaw damper for Shinkansen was designed with the
proper damping coefficient obtained through simulation analysis. In order to
keep the damping coefficient satisfactorily even in small stroke area of 1
or 2mm, corresponding to p-p 2m/s2 car body lateral vibration, a doulbe rod
type damper (fig.3) was adopted. The maximum of about 35% decrease of yawing
vibration due to this damper was verified (Fig.4) in tests up to 310km/h on
Shinkansen train. However, it is found that the effectiveness to decrease
train vibration with the car end yaw damper differs depending on the location 
in a train, the train speed, the vibration amplitude and the phase between
cars etc., as well as on the damper's coefficient. In order to find out the
reason, we analyze the relations between the effectiveness and the factors
using a simplified analysis model. From the analysis, it is seen that 180
degrees phase difference (reverse phase) between cars is important, and this
is actually realized for primary vibration. On the contrary, in the section
(tunnel section etc.,) with high frequency vibration it seems that the
effectiveness of vibration reduction drops. The reason is considered as
follows:
(1) An elasticity develops in the damper is series due to the oil
compressibility and the flexibility of attachment.
(2) An equivalent damping coefficient ceq is expressed as
ceq  = k2c/(k2+(c omega)2)(k:elasticity, c:damp.coef. omega:vibration
freq.). And the larger omega is, the smaller ceq becomes. 
  Our research deals with the lateral vibration data collected mainly from
the tail car of Shinkansen train, the inference of the reason for the greater
tail car's vibration, the computer simulation analysis for decrease of train
vibration by means of the car end yaw damper, the result of running test, and
the analysis for the effectiveness of damper using a simplified analysis
model.