Page 181 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

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

of diameter r/2 within two larger holes of equal diameters d^. With respect to the
crank, the counterweight has a motion of curvilinear translation with each point
moving in a circular path of radius r = r/, - ^2- Prove that the U-shaped weight does
indeed move in a circular path of r = —<^2-

5-44 A bifilar-type centrifugal pendulum is proposed to eliminate a torsional disturbance of
frequency equal to four times the rotational speed. If the distance R to the center of
gravity of the pendulum mass is 4.0 in. and d^ = ^ in., what must be the diameter d2
of the pins?
5-45 A jig used to size coal contains a screen that reciprocates with a frequency of 600 cpm.
The jig weighs 500 lb and has a fundamental frequency of 400 cpm. If an absorber
weighing 125 lb is to be installed to eliminate the vibration of the jig frame, determine
the absorber spring stiffness. What will be the resulting two natural frequencies of the
system?
5-46 In a certain refrigeration plant, a section of pipe carrying the refrigerant vibrated
violently at a compressor speed of 232 rpm. To eliminate this difficulty, it was
proposed to clamp a spring-mass system to the pipe to act as an absorber. For a trial
test, a 2.0-lb absorber tuned to 232 cpm resulted in two natural frequencies of 198 and
272 cpm. If the absorber system is to be designed so that the natural frequencies lie
outside the region 160 to 320 cpm, what must be the weight and spring stiffness?
5-47 A type of damper frequently used on automobile crankshafts is shown in Fig. P5-47. J
represents a solid disk free to spin on the shaft, and the space between the disk and
case is filled with a silicone oil of coefficient of viscosity /x. The damping action results
from any relative motion between the two. Derive an equation for the damping torque
exerted by the disk on the case due to a relative velocity of o).

Figure P5-47.

5-48 For the Houdaille viscous damper with mass ratio jx = 0.25, determine the optimum
damping Co and the frequency at which the damper is most effective.
5-49 If the damping for the viscous damper of Prob. 5-48 is equal to = 0.10, determine
the peak amplitude as compared to the optimum.
5-50 Establish the relationships given by Eqs. (5.8-7) and (5.8-6).