Download JNTUK M-Tech 2020 R19 ME Mechanical Vibrations Model Question Paper

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[M19CAD1105]

I M. Tech I Semester (R19) Regular Examinations

MECHANICAL VIBRATIONS

Department of Mechanical Engineering

MODEL QUESTION PAPER

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Answer ONE Question from EACH UNIT.

All questions carry equal marks.

Max. Marks: 75

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UNIT-I

1. a) Determine the differential equation of a spring mass system (shown in the figure below) and its natural frequency by using (i). D’ Alembert’s principle and (ii). Rayleigh’s method. (15M)
   b) Explain the classifications of vibration with examples.



OR

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2. a) Write short notes on vibration isolation and transmissibility (15M)
   b) Derive the expression for vibration response of a single degree of freedom system if the damping provided is under damped system.

UNIT-II

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1. Write short notes on convolution integral and shock spectrum. (15M)



OR



2. Obtain the response equation for a system subjected to unit step and unit ramp functions. (15M)

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UNIT-III

1. For the three degree of freedom system shown in figure below, obtain the three natural frequencies and the corresponding mode shapes. (15M)
   o= X1 —- X2 X3
   K __f"_] « L
   

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   am e MAN— VWA m
   /777777?77'77‘/;777777777 —J i



OR




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2. Determine the natural frequency of torsional vibrations of a shaft with two circular discs of uniform thickness at the ends. The masses of the discs are M1 = 500 kg and M2 = 1000 kg and their outer diameters are D1 =125 cm and D2 = 190 cm. The length of the shaft is 300 cm and its diameter is 10 cm. Take the Modulus of rigidity for the material of shaft is G = 0.83 x 10¹¹ N/m². (15M)

UNIT-IV

1. Find the lowest natural frequency of transverse vibrations for the system shown in figure below by Rayleigh’s method. Take E=1.96 x 10¹¹ N/m² and I=10^-6 m⁴. (15M)
   40kg
   F' 20kg
   

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   ~ v 4
   C 3
   7
   i = l
   ! 16em ! 8em T Bem !

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OR

2. For the three degree of freedom system shown in figure below find the lowest natural frequency using Stodola’s method. (15M)
   3K
   [am |
   X
   

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   X
   X2
   k
   5

UNIT-V

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1. Calculate the whirling speed of shaft supported by long bearing so as to give zero slope at both ends of the shaft. (15M)

OR

2. Prove that the critical speed of whirling speed for a rotating shaft is same as the frequency of natural transverse vibration. (15M)

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