me010 706 l03 theory of vibration

7/30/2019 ME010 706 L03 Theory of Vibration

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ME010 706 L03

FIRST SERIES EXAMINATION AUGUST 2013BRANCH: MECHANICAL ENGINEERING

ME010 706 L03 Theory of vibration

Time: 2hrs

Max. Marks: 60

PART A (3x3)(Answer All Questions)

1. What do you mean by beat phenomenon?

2. Briefly explain the terms natural frequency and resonance.

3. Determine the degree of freedom needed for the analysis of the mechanical system shown

in figure 1 and specify a set of generalized coordinates that can be used in its analysis.

PART B (5x3)(Answer All Questions)

4. List three differences between the free vibration response of a system

with coulomb damping and the free vibration response of a system with

viscous damping whose free vibrations are under damped.

5. A 500kg vehicle is mounted on springs such that its static deflection is

1.5mm. What is the damping coefficient of a viscous damper to be

added to the system in parallel with spring, such that the system is

critically damped?

6. Obtain the governing equation of motion of a spring mass system by

principle of conservation of energy.

PART C (12x3)

7. Find the natural frequency of oscillation in terms of k and m for the system shown in

figure2

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Figure 1


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ME010 706 L03

Figure 2

Or8. Find the equivalent torsional stiffness for the system shown in figure 3.

Figure 3

AB: Steel shaft with aluminium core (AB=60cm, r1AB=20mm, r2AB=40mm)

BC: Solid steel shaft (BC=80cm, rBC=18mm)DE: Solid aluminium shaft (DE=120cm, rDE=25mm)

Gsteel=80 x 109 N/m2, GAl=40 x 10

9 N/m2

9. An under damped shock absorber is to be designed for an automobile. It is required that

initial amplitude to be reduced to 1/16th in one cycle. The mass of the automobile 200kg

and damped period of vibration in 1 sec. Find necessary stiffness and damping constants

of shock absorber.

Or

10. For the system shown in figure 4 determine (i) undamped natural frequency, (ii) damped

natural frequency, (iii) logarithmic decrement and (iv) if the mass is initially at rest and is

given a velocity of 10 cm/sec, then calculate the amplitude of vibration after 5

oscillations. Given m=20kg, k=10,000 N/m, c=150 N.sec/m.

11. A 200kg machine is placed at the end of 1.8 m long steel(E=210x109N/m2) cantilever

beam. The machine is observed to vibrate with a natural frequency of 21 Hz. What is the

moment of inertia of the beams cross section about its neutral axis?

Or

12. (i) Derive the equation of motion for a simple pendulum and show that its natural

frequency is , where L is length of pendulum and g is acceleration due to gravity.

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Figure 4


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ME010 706 L03

(ii) Assuming that a pendulum is a clock, what will be its length if it has a time period of 1

sec on clock?

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me010 706 l03 theory of vibration

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