A Sample Set of Questions for Principles of Vibration Control

1. What is Strouhal Number? Explain briefly with sketches how Karman vortices are formed. Provide four different strategies used for controlling Vortex induced vibration.

2. What is relaxation time constant? How is it related to the damping ratio? What are the basic concepts of free and constrained layer damping? For a free layer damping, how the loss factor varies with the thickness of the treatment?

3. A manometer is a device used for measuring gas or liquid pressure. Sketch of a manometer is given below. Consider the density of the liquid be ρ, the cross-sectional area – A and the total length of the column L. Show that the equation of motion of the system will be

+ (2g/L) x = 0. What is the time period of the system? If the system is now placed over a viscoelastic base (model it as a combination of spring of stiffness ‘k’ and damper (‘c’) in parallel), what will be the new governing equation of motion and how the time period of oscillation of the liquid column will be changed?

4. What is the speciality of linear hysteretic damping? A structural damping material with linear hysteretic damping and damping coefficient ‘h’ is represented in Fig. 1, where the damper c1

( )tjFtF ωexp~)( = is represented by an equivalent

viscous damper. Assuming harmonic excitation , find out the transmissibility of the excitation force to the base of the system in terms of ‘h’ and frequency ratio ‘Ω’.

Figure 1

x

x

5. Find out the loss-factor and the logarithmic damping coefficient for the following system assuming small motion of the translating body and the mass. The system contains a rotary two-disc pulley of mass m1 and m2, a horizontally translating body of mass m3

with a spring and a damper associated with it, and two rigid mass-less rods, the vertical one has a spring connected to it.

6. Consider a Type 1, three pole system, with other two poles placed initially at -2 and -6. Draw the root locus for the system. Next, find out the settling time corresponding to a damping ratio of 0.5. Design a suitable compensator to reduce the settling time by 50%.

7. Obtain the state space representation of the system:

uydtdy

dtyd

dtyd

=+++ 2

2

3

33

Find out the control gains corresponding to full-state feedback; the damping factor for the dominant second order poles is 0.707 and the settling time is less than or equal to 1 second. The 3rd pole may be kept five times away from the real part of the pair of dominant poles.

8. Verify the following comments - (True or False showing reasons)

• Half power band width is based on two frequencies on either sides of a resonating frequency where the amplitude of response is half of the resonating amplitude.

• Linear hysteretic damping shows a linear fit between the logarithm of energy dissipated per unit volume per cycle and the logarithm of the stress amplitude.

• The damping capacity of a low–damping material could be enhanced by inserting annular inserts of high damping material.

• System model is not necessary in Feed-forward control due to the automatic balancing of secondary and primary sources of disturbance

• Stockbridge damper is used to control vortex induced vibrations. 9. Answer the following (i) How can one use self tuned pendulum neutralizer for vibration control? (ii) What are parallel anti-vibartion mounts? Why they are better than single

material based damper? (iii) What are the different steady state specifications and how can you obtain them against unit step and ramp input?