Page 179 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

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

for the rotational stiffness. If the ground is now given a harmonic motion,
sin (ot, set up the equations of motion in terms of the coordinates shown in
Fig. P5-36.
5-37 Solve the equations of Prob. 5-36 by letting
,2 _ Kh
M
O o ] ”
Kr
MPÌ

The first natural frequency and mode shape are

- = 0.734 and ■ ¡-^= -1.14

which indicate a motion that is predominantly translational. Establish the second

natural frequency and its mode (Y^ = To - 21q6q= displacement of top).
5-38 The response and mode configuration for Probs. 5-36 and 5-37 are shown in Fig.
P5-38. Verify the mode shapes for several values of the frequency ratio.

3.0

5-39 The expansion joints of a concrete highway are 45 ft apart. These joints cause a series
of impulses at equal intervals to affect cars traveling at a constant speed. Determine
the speeds at which pitching motion and up-and-down motion are most apt to arise for
the automobile of Prob. 5-24.