Download GTU BE/B.Tech 2019 Summer 6th Sem New 2160109 Theory Of Vibration Question Paper

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Subject Code: 2160109

GUJARAT TECHNOLOGICAL UNIVERSITY

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SEMESTER-VI(NEW) — EXAMINATION - SUMMER 2019

Date: 16/05/2019

Subject Name: Theory of Vibration

Time: 10:30 AM TO 01:00 PM

Total Marks: 70

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Instructions:

1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks

Q.1

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1. (a) Explain Simple Harmonic Motion with an example. [03]
2. (b) Explain the Energy method for vibration analysis. [04]
3. (c) Define the following terms: [07]
   Degrees of Freedom, Natural Frequency, Node, Damping Ratio, Resonance, Time Period, Damped natural frequency

Q.2

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1. (a) Define Damping. Explain Damped and Undamped Vibration. [03]
2. (b) Explain series and parallel spring connections. [04]
3. (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. [07]

OR

1. (a) Determine the natural frequency of torsional pendulum having following characteristics: [07]
   

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   Length of the rod: 1 m
   Diameter of the rod (d): 5 mm
   Diameter of the rotor (D): 0.2 m
   Mass of the rotor: 2 kg
   Modulus of rigidity (G): 0.83 x 10¹¹ N/m²

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Q.3

1. (a) How many ways you can control the vibration? [03]
2. (b) Show that in case of a Coloumb damping the reduction in amplitude takes place by an amount of 4F/k in one complete cycle. [04]
3. (c) Conclude the response of Overdamped, Underdamped and Critically damped system by solving differential equation of undamped free vibration with neat sketches. [07]

OR

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1. (a) State the applications of critical damping in real life examples. [03]
2. (b) Explain Logarithmic decrement. [04]
3. (c) An electric motor is supported on a spring and a dashpot. The spring has stiffness of 6400 N/m and a dashpot offers resistance of 500 N at a velocity of 4 cm/sec. The unbalanced mass of 0.5 kg rotates at 5 cm radius and the total mass of vibratory system is 20 kg. The motor runs at 400 rpm. Determine: Damping factor, amplitude of vibration and phase angle, resonant speed and resonant amplitude, forces exerted by the spring and dashpot on the motor. [07]

Q.4

1. (a) State the role of spring mass and damper in any vibratory system. [03]

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2. (b) Discuss working of a Vibrometer. [04]
3. (c) Derive the solution of equation of motion for forced vibration for spring mass damper system under the influence of harmonic force. [07]

OR

1. (a) Show the response of transient and steady state vibration. [03]
2. (b) Explain the torsional vibration of two rotor system. Determine the natural frequencies and mode shapes. [07]

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Q.5

1. (a) State the importance of Vibration isolation. Explain different materials used for vibration isolation. [03]
2. (b) Explain the working of Vibration absorber with neat sketch. [04]
3. (c) Using Lagrange’s equation, determine the natural frequency of the system shown in fig. 1. [07]

OR

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1. (a) Compare the vibration absorber with vibration isolator. [03]
2. (b) Explain Rayleigh’s method for finding natural frequency of transverse vibration of beams. [04]
3. (c) Determine the two natural frequencies of vibration and the ratio of amplitudes of motion m1 & m2 for the two mode of vibration for the system shown in fig.2 Take m1= 1.5 kg , m2= 0.80 kg, k1=k2= 40 N/m. [07]

fig.1

fig.2

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