Dynamics of Machine Unit III-Transverse Vibration - Short notes and MCQ

1. ME8594 - DYNAMICS OF MACHINES
UNIT-III-FREE VIBRATION
(TRANSVERSE VIBRATION)
By,
Dr.S.SURESH,
Assistant Professor,
Department of Mechanical Engineering
Jayalakshmi Institute of Technology.

2. Different types of vibrations
1. Free vibrations
a) Longitudinal vibration,
b) Transverse vibration, and
c) Torsional vibration.
2. Forced vibrations, and
3. Damped vibration.

3. TRANSVERSE VIBRATION
•Vibration at perpendicular to the axis of the shaft
•Natural Frequency of Free Transverse Vibrations

4. Natural Frequency of Free Transverse Vibrations
•Due to a Point Load Acting Over a Simply Supported Shaft
•Due to a Uniformly distributed Load Acting Over a Simply Supported
Shaft

5. Effect of Inertia of the Constraint in
Transverse Vibration
Considering the effect of inertia of the constraint (Shaft)
Both end fixed = Simply supported =

6. STATIC DEFLECTION (δ)

8.  A shaft supported in ball bearings is assumed
to be simply supported beam.
 A shaft supported in journal bearings is
assumed to be fixed beam.

10. NATURAL FREQUENCY OF FREE TRANSVERSE VIBRATIONS FOR
A SHAFT SUBJECTED TO A NUMBER OF POINT
•Dunkerley’s method

12. Natural Frequency of transverse vibration a shaft
subjected to no. of point loads
1. With considered the mass of the shaft
2. Mass of the shaft is negligence

13. WHIRLING (CRITICAL) SPEED OF A SHAFT
 The speed at which the shaft runs so that the additional
deflection of the shaft from the axis of rotation becomes infinite,
is known as critical or whirling speed.
The critical speed may occur because of
• Eccentric mounting of the rotor
• Non-uniform distribution of rotor material
• Bending of shaft

14. WHIRLING (CRITICAL) SPEED OF A SHAFT
The factor which affects the critical speed of a shaft is
(1) the diameter of the disc
(2) the span of the shaft
(3) eccentricity

15.  Find the displacement in mm of the free longitudinal
vibrations if the Natural frequency is 15 Hz.
 Find the natural frequency in Hz of the free longitudinal
vibrations if the displacement is 2mm.

16.  A vertical spring-mass system has a mass of 0.5 kg and an
initial deflection of 0.2 cm. Find the spring stiffness.
 Calculate logarithmic decrement if damping factor is 0.33.
 Determine logarithmic decrement, if the amplitude of a
vibrating body reduces to 1/6th in two cycles.

17.  Calculate natural frequency of damped vibration, if damping
factor is 0.52 and natural frequency of the system is 30 rad/sec
which consists of machine supported on springs and dashpots.
 Calculate critical damping coefficient in N/m/s from the
following data: mass = 100 Kg and ω = 40rad/s.

18.  A cantilever shaft having 50 mm diameter and a length of 300 mm
has a disc of mass 100 kg at its free end. The Young’s modulus for
the shaft material is 200 GN/m2. Determine the frequency of
transverse vibrations of the shaft. (Ans: 41 Hz)

19. OBJECTIVE TYPE QUESTIONS