Page 178 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Chap. 5 Problems 165

about an axis perpendicular to the shaft. If a small unbalance mr acts at an axial
distance b from its center 0, determine the equations of motion for a rotational
speed 0).
5-31 A two-story building is represented in Fig. P5-31 by a lumped mass system in which
mj = {ni2 and /c, = \k 2. Show that its normal modes are

X, ' 1 k,
co \ 1
) =2
(x)\
X2 /

Figure P5-31.
5-32 In Prob. 5-31, if a force is applied to to deflect it by unity and the system is
released from this position, determine the equation of motion of each mass by the
normal mode summation method.
5-33 In Prob. 5-32, determine the ratio of the maximum shear in the first and second
stories.
5-34 Repeat Prob. 5-32 if the load is applied to m2, displacing it by unity.
5-35 Assume in Prob. 5-31 that an earthquake causes the ground to oscillate in the
horizontal direction according to the equation sin wt. Determine the re­
sponse of the building and plot it against io/w,.
5-36 To simulate the effect of an earthquake on a rigid building, the base is assumed to be
connected to the ground through two springs: for the translational stiffness, and

Figure P5-36.