GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER- VI (New) EXAMINATION - WINTER 2019
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Subject Code: 2160109
Subject Name: Theory of Vibration
Time: 02:30 PM TO 05:00 PM
Date: 09/12/2019
Total Marks: 70
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Instructions:
- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
Q1
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(a) Define Vibration. Which organs of human body are having low frequency oscillations? Which organs of human body are having high frequency oscillations? MARKS 03
(b) Derive the equation to calculate natural frequency of Simple pendulum. MARKS 04
(c) Find the sum of two harmonic motions of equal amplitude but of slightly different frequencies. Discuss the beats phenomenon that results from this sum. MARKS 07
Q2
(a) Define: Degree of freedom. What is DOF for cantilever beam? Why? MARKS 03
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(b) Derive the equation of natural frequency for a disc of mass moment of inertia I suspended on shaft of length L with diameter d, when the disc is given an angular twist of ©. MARKS 04
(c) Show that for finding natural frequency of a spring mass system, the mass of the spring can be taken into account by adding one-third its mass to the main mass. MARKS 07
OR
(c) A vibrating system consists of a mass of 50 kg, a spring of stiffness of 30 kN/m and a damper. The damping provided is only 20 % of the critical value. Determine: i) Damping factor ii) Critical damping coefficient iii) Natural frequency of damped vibration iv) Logarithmic decay v) Ratio of two consecutive amplitudes MARKS 07
Q3
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(a) Why are soldiers ordered to break their marching steps while crossing a bridge? MARKS 03
(b) Explain vibration isolation. Name the various materials for the same. MARKS 04
(c) Write down the equation of motion for damped free vibration. Derive the solution for that equation. MARKS 07
OR
(a) Represent 3+ 16 in exponential form. MARKS 03
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(b) Define Transmissibility. Briefly explain the concept of support motion. MARKS 04
(c) Derive the solution: m¥ + cx + kx = F sin ot. MARKS 07
Q4
(a) Define: Overshooting. Why guns are designed based on critical damping? MARKS 03
(c) Write a short note on Lagrange’s equation. MARKS 07
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OR
Q.4 (a) Give the difference between vibration isolation & vibration absorber. MARKS 03
(b) A vibrometer indicates 2% error n measurement and its natural frequency is 5 Hz. If the frequency that can be measured is 40 Hz. Find the value of damping factor. MARKS 04
(c) For Two rotor system prove that angular displacements of the rotors are inversely proportional to their moment of inertia with neat sketch. MARKS 07
Q.5
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(a) Define: MARKS 03
- Fundamental mode of vibration
- Principal mode of vibration
- Normal mode of vibration
(b) Define: Whirling Speed of shaft. Explain critical speed of shaft carrying single rotor (Without damping). MARKS 04
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(c) What is the working principle of vibration measuring instruments? Explain the working of anyone instrument designed on low natural frequency. MARKS 07
OR
(a) Define: Multi degree of freedom system. Name the various methods used to analyze these systems. MARKS 03
(b) Explain the working of vibration absorber with respect to electricity transmission lines. MARKS 04
(c) What is the working principle of Frequency measuring instruments? With neat sketch explain working of Frahm tachometer. MARKS 07
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