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 a₀, 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)