Page 219 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

206 Properties of Vibrating Systems Chap. 6

If the system is started from zero displacement and an arbitrary distribution of velocity
^ (0), determine the coefficients ^4, and
6-41 Figure P6-41 shows a shaft supported by a bearing that has translational and rotational
flexibility. Show that the left side of the shaft flexibility Eq. (6.1-1) or (6.1-2) of
Example 6.1-4 should now be replaced by
V
d - p
From the relationship between rj,p,y,6, and loads P and M, determine the new
flexibility equation

Figure P6-41.
6-42 Set up the matrix equation of motion for the 3-DOF system of Fig. P6-18 in terms of
stiffness. Transform it to the standard eigen-problem form, where A is symmetric.
6-43 In Example 6.10-1 for the forced vibration of a 10-story building, the equation of
motion for the first mode was given as
/I. ; + 0.02235-^1 = -1.2672«o(0
+ 0.299
Assume the values yjk/m = 3.0 and ¿'j = 0.10, and solve for the time response using
RUNGA when the ground acceleration is given by Fig. P6-43.

/ 0 0.1 0.2 0.3 04 0.5 0.6 0.7 0.8 0.9 1.0 1.2
f{t) 0 1.0 0-0.7 0 0.5 0-0.3 0 0.2 0 0 Figure P6-43.