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VTU Mechanical Engineering (Semester 7)
Mechanical Vibrations
December 2013
Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

1 (a) With a sketch explain the neats phenomenon and obtain its resultant motion
10 M
1 (b) If x(t)\sim a_{0}\sum_{n\infty1}^{\infty}a_{\eta }\ Cosnwt+\sum_{n\infty 1}^{\infty}b_{\eta } cosnwt, where x(t) us a periodic, non harmonic, obtain expressions for a0, a\infty and b\infity
10 M

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

10 M

3 (a) For an under damped system, derive an expression of response equation
10 M
3 (b) A vibrating system having a mass 3kg. Spring stiffness of 100 N/m and damping coefficient of 3N-sec/m. Determine damping ratio, damped natural frequency, logarithmic decrement, ratio of two consecutive amplitudes and number of cycle after which the original amplitude is reduced to 20%.
10 M

4 (a) Analyse the underamped system subjected to constant harmonic excitation and show the complete solution
12 M
4 (b) A vibrating system having mass 100 kg is suspended by a spring of stiffness 19600 N/m and is acted upon by a harmonic force of 39.2 N at the undamped natural frequency. Assuming vicious damping with a coefficient of 98N-sec/m. Determine resonant frequency: phase angle at response, amplitude at resonance, the frequency corresponding to the peak amplitude and damped frequency
8 M

5 (a) Mention the instruments used to measure displacement and acceleration discuss the relevant frequency response curve
10 M
5 (b) Derive an expression for amplitude of whirling shafts with air damping
10 M

6 (a) Discuss the effect f mass ratio on frequency ratio of an undamped dynamic vibration absorber with derivation
12 M
6 (b) Two equal masses are attached to a string having high tension as shown in the Fig6(b) determine the natural frequencies of the system

8 M

7 (a)

Determine the influence coefficients of the triple pendulum system as shown in fig7(a)

10 M
7 (b) Use the Stodola method to determine the lowest natural frequency of four degrees of freedom spring mass system as shown in fig7(b)

10 M

8 (a) Signal analysis
5 M
8 (b) Dynamic testing of machines.
5 M
8 (c) Experimental modal analysis.
5 M
8 (d) Machine condition monitoring
5 M
8(e) Orthogonality of principle modes
5 M

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