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APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY

FIRST SEMESTER M.TECH DEGREE EXAMINATION, DECEMBER 201
7

Mechanical Engineering

(Machine Design)

01ME6101 Advanced Theory of Vibration

Max. Marks : 60 Duration: 3 Hours
Answer any two full questions from each part Limit
answers to the required points.
PART-A
I .a) Show that for finding the natural frequency ofvibration of a spring mass system, the
mass of the spring can be taken into account by adding one third of its mass to the main

mass.
(4 Marks)

b) A homogeneous cylinder of mass 'm' and radius is linked by a spring of stiffness 'k'

N/cm and is resting on an inclined plane as shown in fig. Assume the cylinder rolls without
slipping evaluate the frequency of oscillation for small angle ofoscillation. (5 Marks)

/

Fig. I
2. a) Show that accelerometer is an instrument with high natural frequency and seismograph is an

instrument with low natural frequency. (4 Marks)
b) Determine the normal modes ofvibration of an automobile simulated by the simplified

two DOF system with the following assumed numerical values ?
Total mass : 1500 Kg, C.G Located at 1.8 m from front axle and | .5 m from rear axle.

Equivalent stiffness at front and rear tyre is 380 N/cm and 360 N/cm respectively. Radius

of gyration : 1.2൩ (5 Marks)

3.a) Two equal mass m are attached to light string with tension T. Find the normal mode

frequencies of the system shown in Fig-|
⋅∙−↣⋅⋅⋅⇁⇁↙↮∙∙⋅⋅⋅∙⋅⋅∙⋅⋅⋅∙⋅⋅∘∙

(4 Marks)