Page 99 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

86 Harmonically Excited Vibration Chap. 3

trial weight of 2.0 oz is added at the rim in a position 91.5° cw from the reference
mark and run at the same speed. If now the new unbalance is 6.0 mm at 80° cw from
the reference mark, determine the position and weight necessary to balance the
original disk.
3-10 If for the same disk of Prob. 3-9, the trial weight of 2 oz is placed at 135° cw from the
reference mark, the new unbalance is found to be 4.3 mm at 111° cw. Show that the
correct balance weight is unchanged.
3-11 If the wheel of Prob. 3-9 shov/s resonance at 900 rpm with damping of ^ = 0.10,
determine the phase lag of the original unbalance and check the vector diagrams of
Probs. 3-9 and 3-10.
3-12 Prove that a long rotor can be balanced by adding or removing weights in any two
parallel planes, and modify the single disk method to balance the long rotor.
3-13 A counterrotating eccentric mass exciter shown in Fig. P3-13 is used to determine the
vibrational characteristics of a structure of mass 181.4 kg. At a speed of 900 rpm, a
stroboscope shows the eccentric masses to be at the top at the instant the structure is
moving upward through its static equilibrium position, and the corresponding ampli­
tude is 21.6 mm. If the unbalance of each wheel of the exciter is 0.0921 kg • m,
determine (a) the natural frequency of the structure, (b) the damping factor of the
structure, (c) the amplitude at 1200 rpm, and (d) the angular position of the eccentrics
at the instant the structure is moving upward through its equilibrium position.

/ / / / / / / > / / / / / / / /V777/ / / 7 7 / / / /V/, Figure P3-13.
3-14 Solve Eq. (3.2-1) for the complex amplitude, i.e., let {meo)^)sm (ot = and
jc = = Xe^^\
3-15 A balanced wheel supported on springs, as shown in Fig. P3-15, is rotating at 1200
rpm. If a bolt weighing 15 g and located 5 cm from center suddenly comes loose and

Figure P3-15.