B.Tech VI (Sixth) Semester Examination 2012-13
Course Code: EME603 Paper ID: 0966124
Mechanical Vibrations
Time: 3 Hours Max. Marks: 70 Max Marks: 75
Note: Attempt six questions in all. Q. No. 1 is compulsory.
1. Answer any five of the following (limit your answer to 50 words). (4x5=20)
a) Is the motion of a piston in a reciprocating engine a simple harmonic motion? Explain clearly.
b) What are the main causes of vibration and how the undesirable vibrations can be eliminated or reduced?
c) A spring-mass-dashpot system has a static deflection 1 cm. Would the natural frequency obtained from this static deflection be the undamped natural frequency? Give reasons.
d) Why is the use of an inertial block beneficial in the problems of transmissibility?
e) When a mass-spring system is in a free oscillation, what is the rate at which the potential or kinetic energy varies? why?
f) For coulomb friction what are the various parameters and variables the equivalent viscous damping coefficient depend upon? Are you surprised anything in this?
g) Define the term “whirling speed of shaft”. Also, briefly explain the phenomena of whirling.
h) How does damping alter the performance of the dynamic vibration absorber?
2. a) How the dampings has been classified in vibrating system? Discuss about the coulomb damping. (5)
b) A unknown mass ‘m’ is attached to one end of a spring stiffness ‘K’ having natural frequency of 6 Hz. When 1kg of mass is attached with the ‘m’, the natural frequency is lowered by 20%. Determine the value of unknown mass ‘m’ and stiffness ‘K’. (5)
3. a) Explain the working of fluid dashpot viscous damper with neat sketch. (5)
b) A mass of 10 kg is supported by a steel wire 1m in diameter and 3 meters long. The system is made to move upwards with a uniform velocity of 10 cm/sec when the upper end is suddenly stopped. Determine the frequency and the amplitude of the resulting vibrations of the mass and the maximum stress in the wire. (5)
4. A vibratory body of mass 150 kg supported on springs of total stiffness 1050 kN/m has a rotating unbalance force of 525 N at a speed of 6000 r.p.m. If the damping factor is 0.3, determine the amplitude caused by the unbalance and its phase angle. (10)
5. In a two mass torsional system two wheels are mounted 0.15 m apart on a shaft 40mm diameter. If the moments of inertial of the two wheels are J1 = 1.2 kg-m2 and J2=2.0 kg-m2, find the position of the node and the frequency of the free torsional oscillations.
If both the rotors are coupled to the shaft through similar torsional spring couplings, find the torsional stiffness of these couplings so as to reduce to half the natural frequency of the complete system in torsion. (10)
6. Find the lowest natural frequency of transverse vibrations for the system shown schematically in Fig. 1 by Rayleigh’s method. E = 1.96x1011 N/m2, I = 10-6 m4. (10)
Figures…..
7. For the system shown in Fig.2 , (a) Find flexibility matrix and write the differential equation of motion in terms of flexibility matrix. (b) Show that the product of stiffness matrix and flexibility matrix is a unit matrix. (10)
Figure……………….
8. Write short notes on the following: (2.5x4=10)
a) Degree of Freedom
b) Beats Phenomenon
c) Vibration Measuring Instruments
d) Influence Numbers