Mechanical Vibrations - Dec 2015
Mechanical Engineering (Semester 6)
TOTAL MARKS: 100
TOTAL TIME: 3 HOURS (1) Question 1 is compulsory.
(2) Attempt any four from the remaining questions.
(3) Assume data wherever required.
(4) Figures to the right indicate full marks. 1 (a) Find the natural frequency of a half solid cylinder of a mass 'm' and radius 'r' when it is displaced from the equilibrium position and released as shown in Fig. 1.
i) Peak Amplitude
ii) Peak Frequency(3 marks) 3 (a) All the natural of the system shown in Fig. 3, exist below 2 rad/sec. Find all the natural frequencies and draw mode shapes. m=1kg, K=1N/m (14 marks) 3 (b) How is the critical speed of the shaft determined.(6 marks) 4 (a) How do you find the response of a viscously damped system under rotating unbalanced?(10 marks) 4 (b) A machine of mass 50 kg operates at 1200 rpm. Find the maximum stiffness of an isolator that provides 75 percent isolation. Assume that damping ratio of the isolator is 7 percent.(10 marks) 5 (a) A spring mass damper system, having an undamped natural frequency of 100 Hz and a damping constant of 20 N-s/m, is used as an accelerometer to measure the vibration of a machine operating at a speed of 3000 rpm. If the actual acceleration is 10 m/s2 and the recorded acceleration is 9 m/s2, find the mass and the spring constant of accelerometer.(10 marks) 5 (b) Use Lagrange's equation to derive the differential equations governing the motion of the system, using x1 and x2 as generalised coordinates. Assume the disc of mass m and radius r rolls without slip. (10 marks) 6 (a) Four pulleys are equally spaced along a shaft and each has an out of balance mass at the same radius. The out of balance mass in second pulley is 3 kg and third and fourth out of balance masses are at 72° and 220° to it. Determine the masses in the first, third and fourth pulleys and also the angle of the first mass relative to second. If the complete balance is to be obtained.(10 marks) 6 (b) Explain vibration based condition monitoring and fault diagnosis in rotating machine.(5 marks) 6 (c) Explain the balancing of V-engine.(5 marks)