Page 177 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

164 Systems with Two or More Degrees of Freedom Chap. 5

5-27 To justify the 2-DOF simplified model of the automobile in Example 5.3-2, assume the
weight of each wheel, hub, and tire to be approximately 80 lb, and the tire stiffness per
wheel to be 22,000 Ib/ft. Determine the natural frequency of its wheel-tire system, and
explain why the simplified model is adequate.
5-28 An airfoil section to be tested in a wind tunnel is supported by a linear spring k and a
torsional spring K, as shown in Fig. P5-28. If the center of gravity of the section is a
distance e ahead of the point of support, determine the differential equations of
motion of the system.

Figure P5-28.
5-29 Determine the natural frequencies and normal modes of the system shown in Fig.
P5-29 when
gmj = 3.86 lb /cj = 20 Ib/in.
gm2 = 1.93 lb k2 = 10 Ib/in.

When forced by F, = Fqsin wt, determine the equations for the amplitudes and plot
them against

Figure P5-29.
5-30 A rotor is mounted in bearings that are free to move in a single plane, as shown in Fig.
P5-30. The rotor is symmetrical about 0 with total mass M and moment of inertia / q

Figure P5-30.