Page 426 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Chap. 12 Problems 413

12-25 Determine the natural frequencies and mode shapes of the three-story building of
Fig. P12-25 by using Holzer’s method for all = m and all = k.

^3
Figure P12-25.

12-26 Repeat Prob. 12-25 when = m, = 2m, = 3m, /cj = /c, k2 = k, and /C3 =
2k.
12-27 Compare the equations of motion for the linear spring-mass system versus the
torsional system with the same mass and stiffness distribution. Show that they are
similar.
12-28 Determine the natural frequencies and mode shapes of the spring-mass system of Fig.
P12-28 by the Holzcr method when all masses arc equal and all stiffnesses are equal.

12-29 A fighter-plane wing is reduced to a scries of disks and shafts for Holzcr’s analysis, as
shown in Fig. PI2-29. Determine the hrst two natural frequencies for symmetric and
antisymmetric torsional oscillations of the wings, and plot the torsional mode corre­
sponding to each.

n J lb in. • s“ K lb • in./rad
1 50 15 X 10^’
2 138 30
3 145 22
4 181 36
5 260 120
6 ^ X 140,000