## Mechanical Vibrations - Dec 2013

### Mechanical Engg. (Semester 7)

TOTAL MARKS: 100

TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.

(2) Attempt any **four** from the remaining questions.

(3) Assume data wherever required.

(4) Figures to the right indicate full marks.
**1 (a)** With a sketch explain the neats phenomenon and obtain its resultant motion(10 marks)
**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 a_{0}, a_{\infty} and b_{\infity}(10 marks)
**2 (a)** What is the effect of mass od spring on its natural frequency? Derive(10 marks)
**2 (b)** Find the natural frequencies of Fig.Q2(b)
(10 marks)
**3 (a)** For an under damped system, derive an expression of response equation(10 marks)
**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 marks)
**4 (a)** Analyse the underamped system subjected to constant harmonic excitation and show the complete solution(12 marks)
**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 marks)
**5 (a)** Mention the instruments used to measure displacement and acceleration discuss the relevant frequency response curve(10 marks)
**5 (b)** Derive an expression for amplitude of whirling shafts with air damping(10 marks)
**6 (a)** Discuss the effect f mass ratio on frequency ratio of an undamped dynamic vibration absorber with derivation(12 marks)
**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 marks)
**7 (a)**

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

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