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IV B.Tech I Semester Supplementary Examinations, Feb/Mar - 2015

VEHICLE DYNAMICS

(Automobile Engineering)

Time : 3 hours Max. Marks: 75

Answer any FIVE Questions

All Questions carry equal marks

*****

1 a) Compare Ryleigh’s method and energy method in analyzing the vibrations of a

system. [8]

b) A mass of 7 kg is attached to a spring of length 400mm and stiffness 9kN per

meter. Derive the natural frequency of the system. [7]

2 A horizontal spring mass system with coulomb damping has a mass of 5.0 kg

attached to a spring of stiffness 980 N/m. if the co-efficient of friction is 0.025,

calculate

a) The frequency of free oscillations

b) The no of cycles corresponding to the 50% reduction in amplitude if the

initial amplitude is 5.0 cm

c) The time taken to achieve this 50% reduction. [15]

3 An electric motor is supported on a spring & a dashpot. The spring has the

stiffness 6400 N/m & the dashpot offers resistance of 500N at 4.0 m/sec. The

unbalanced mass 0.5 kg rotates at 5 cm radius & the total mass of vibratory

system is 20 kg. The motor runs at 400 rpm. Determine (a) damping factor (b)

amplitude of vibration & phase angle (c) resonant speed & resonant amplitude

& (d) forces exerted by the spring & dashpot on the motor. [15]

4 a) Explain the term whirling or critical speed of a shaft. Prove that the whirling

speed for a rotating shaft is same as that of the frequency of natural transverse

vibration. [5]

b) A rotor of turbo super charger weighing 88.3N is keyed to the center of a

25mm diameter steel shaft 40cm between bearings. determine :

i). the critical speed of shaft.

ii).The amplitude of vibration of the rotor at a speed of 3200 rpm, if the

eccentricity is 0.015mm and

iii). Vibratory force transmitted to the bearings at this speed.

Assume the shaft to be simply supported and that the shaft material has a

density of 8gm/cm3. Take E =2.06x10

11N/m

2.[10]

Code No: R41242 Set No. 1 R10

1 of 2

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5 An automobile weighs 2000kg & has a wheel base of 3.0 meters. Its centre of

gravity is located 1.4 meter behind the front wheel axis & has a radius of

gyration about its C.G as 1.1 meter. The front springs have a combined stiffness

of 6000 kg/cm & rear springs 6500 kg/cm. Find the principle mode of vibration

of the automobile, & locate the nodal points for each mode.

[15]

6 Determine the two natural frequencies & mode shapes for the system shown in

fig. The string is stretched with a large tension T.

3m 2m

l 2l l

[15]

7 a) Discuss various types of troubles in connection with automobile wheels and

tyres.

[8]

b) Briefly explain about tyre construction and physics of tyre traction on dry and

wet

[7]

8 Determine the frequency of the system shown in fig by matrix iteration method.

[15]

2 of 2

Code No: R41242 Set No. 1 R10

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IV B.Tech I Semester Supplementary Examinations, Feb/Mar - 2015

VEHICLE DYNAMICS

(Automobile Engineering)

Time: 3 hours Max. Marks: 75

Answer any FIVE Questions

All Questions carry equal marks

*****

1 a) Describe D’Alembert’s principle in the context of free vibrations [8]

b) A mass of 9 kg is attached to a spring of length 200mm and stiffness 10kN per

meter. derive the natural frequency of the system.

[7]

2 A mass weighing 100 N is supported on springs which deflects 1.8cm under

the weight of the mass. The vibrations of the mass are constrained to be linear

and vertical and are damped by a dash pot which reduces the amplitude to one

quarter of its initial value in two complete oscillations. Find

i) The magnetic of the damping force t unit speed and

ii) The periodic time of damped vibration

[15]

3 A vibrating body is supported by 6 isolators each having stiffness 32000 N/m

& 6 dashpots having damping factor as 400 N-sec/m. the vibrating body is to

be isolated by a rotating device having an amplitude of 0.06 mm at 600 rpm .

take m=30 kg. Determine

a) Amplitude of vibration of the body

b) Dynamic load on each isolator due to vibration.

[15]

4 a) Explain briefly the working principle of vibrometers [5]

b) The motion of a vibratory system is to be recorded by a seismic instrument

having natural frequency 3 rad/sec. what is the reading of the instrument if the

motion is given by the equation Z=2sin2t+3sin3t. Take ᶓ = 0.5

[10]

5 A 1200kg machine is mounted on four identical springs of total spring

constant k and having negligible damping. The machine is subjected to a

harmonic external force of amplitude F0 is 490N and frequency 180rpm.

Determine the amplitude of motion of the machine and the maximum force

transmitted to the foundation because of the unbalanced force when

k=1.96x106N/m.

[15]

Code No: R41242 Set No. 2 R10

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6 A machine part weighing 39N vibrates in a viscous medium. Determine the

damping coefficient when a harmonic exciting force of amplitude 49N results

in resonant amplitude of 1.25cm with a period of 0.2 second. If the system is

excited by a harmonic force of frequency of 4cycles/sec, what will be the

percentage increase in the amplitude of forced vibration when damper is

removed?

[15]

7 Classify tyres from different viewpoints. How does a tubeless tyre differ from a

tubbed tyre in its construction? Compare the merits and demerits of tubeless

tyres.

[15]

8 Determine the natural frequency of the system shown in fig by influence

coefficient method.

m1=100 kg, m 2= 200 kg ,m 2= 300 kg

k 1= 2 k N/m , K 2= 1.5 N/m k 3= 2 k N/m.

[15]

Code No: R41242 Set No. 2 R10

2 of 2

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