USN t0nllB72

Seventh Semester B.E. Degree Examination, Dec. 20l3lJan.2Ol4Mechanical Vibrations

Time: 3 hrs. Max. Marks:100N ote : a y w y-!!,(r fu il,

1 u estj on s, s e I yct i n g.

otleast TWO questions from each part.

PART _ APART _ A

I a. With a sketch, explain the beats phenomenon and obtain its resultant motion. (10 Marks)

b. If x(t): uo + Lancosnwt*IU"cosnwt, where x(t) us apefiodic, nonharmonic, obtainn=l n=l

expressions for a6, all and bp. (10 Marks)

(10 Marks)(10 Marks)

oooL

C)(!(.)

Eqz

Jh-boli00.= c{

9dotraO

o2

;::oO

a0<

a6

'l,6

4o'Caoj5

o-E

oj

9Eto6LE

LOJE

>, lib0-c olJ

a=

XoVLo_

U<,r.' C.i

()

o

2 a. What is the effect of mass of a spring on its natural frequency? Derive.b. Find the natural frequencies of Fig. Q2(b).

, Fig. Q2(b)

For an under dar'nped system, derive an expression ofA vibratingrsystem having a mass 3 kg, spring stiffness of 100 N/m and damping coefficientof 3 N - sec/m. Determine damping ratio, damped natural frequency, logarithmic decrement,ratio of two consecutive amplitudei and number of cycles after which the original amplitude

(10 Marks)

(08 Marks)

Discuss the(10 Marks)(10 Marks)

4a.

b.

is reduced to 20Yo. (10 Marks)

Analyse the undertamped system subjected to constant harmonic excitation and show thecomplete solution. (12 Marks)A vibrating system having mass 100 kg is suspended by a spring of stiffness 19600 N/m andis acted upon by a harmonic force of 39.2 N at the undamped natural frequency. Assumingvisious damping with a coefficient of 98 N - sec/m. Determine resonant frequency, phaseangle at resonance, amplitude at resonance, the frequency corresponding to the peakamplitude and damped frequency

PART _ B

5 a. Mention the instruments used to measure displacement and acceleration.relevant frequency response curves.

b. Derive an expression for amplitude of a whirling shafts with air damping.1 r'rf')

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6a.

b.

10ME72

Discuss the effect f mass ratio on frequency ratio of an undamped dynamic vibrationabsorber with derivation. (12 Marks)

Two equal masses are attached to a string having high tension as shown in the Fig. 6(b).

Determine the natural frequencies of the system. (08 Marks)

Fig. Q6(b)

7 a. Determine the influence coefficients of the triple pendulum system as shown in Fig. 7(a).

b.

,, Fig. Q7(a)

Use the Stodo'tra method to determine the lowest natural frequency of four-,1 ,

fieedom spring mass system as shown in Fig. 7(b).

kK

(10 Marks)degrees of

(10 Marks)

Write a short notes on any FOUR :

a. Signal analysisb. Dynamic testing of machines

c. Experimental modal analysisd. Machine condition monitoringe. Orthogonality of principal modes.

{<i<**+

2 of2

Fig. Q7(b)

(20 Marks)

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