Sdof

1. Mechanical Department
COURSE NAME: MECHANICAL VIBRATIONS
Prepared By:
MD ATEEQUE KHAN
(Assistant Professor)
Mechanical Engineering Department
JIT,Barabanki,U.P. INDIA
12/31/2016 1NME-013 MA KHAN

2. Table of Contents
Unit-2
1. Single Degree Freedom: Forced Vibration
2. Harmonic excitation with viscous damping
3. steady state vibrations
4. Forced vibrations with rotating unbalance
5. Forced vibrations with reciprocating unbalance
6. Support excitation
7. Vibration isolation
8. Transmissibility
9. Vibration measuring instruments
10.Displacement measuring instruments
11.Velocity measuring instruments
12.Acceleration measuring instruments
13.Objective Questions
12/31/2016 2NME-013 MA KHAN

3. Unit-2: Mechanical Vibrations
SDoF: Forced Vibration
Undamped forced vibration :
k
m m
0F
0F
xk
..
xm 0
..
Fkxxm 
n
nn
m
F
tCtCx 2
0
21 sincos

 
12/31/2016 3NME-013 MA KHAN

4. Unit-2: Mechanical Vibrations
SDoF: Forced Vibration
Damped forced vibration :
m m
0F
xk
..
xm 0
...
Fxckxxm k
0F
c .
xc
12/31/2016 4NME-013 MA KHAN

5. Unit-2: Mechanical Vibrations
Harmonic excitation with viscous damping
k
tF sin0
c tFxckxxm sin0
...

12/31/2016 5NME-013 MA KHAN

6. Unit-2: Mechanical Vibrations
Forced vibrations with rotating unbalance One may find many rotating systems in industrial
applications. The unbalanced force in such a system can be represented by a mass m with
eccentricity e , which is rotating with angular velocity as shown in below Figure:
2
k
2
kc
m

x
12/31/2016 6NME-013 MA KHAN

7. Unit-2: Mechanical Vibrations
Forced vibrations with reciprocating unbalance
2
2
2
2
2
1
2
tan
21











































n
n
nn
r em
A












12/31/2016 7NME-013 MA KHAN

8. Unit-2: Mechanical Vibrations
Support excitation
Free Body Diagram
Solution of Excitation
12/31/2016 8NME-013 MA KHAN

9. Unit-2: Mechanical Vibrations
Vibration isolation
In various industrial applications, we may find the vibrating machine transmit forces to ground
which in turn vibrate the neighboring machines. So in that case it is necessary to calculate
how much force is transmitted to ground from the machine or from the ground to the machine
otherwise it may cause mechanical damage in the machine.
Vibrating Machine part
12/31/2016 9NME-013 MA KHAN

10. Unit-2: Mechanical Vibrations
Transmissibility
Transmissibility defining the transmissibility TR as the ratio of the force transmitted Force to the disturbing
force one obtains
When damping is negligible
12/31/2016 10NME-013 MA KHAN

11. Unit-2: Mechanical Vibrations
Vibration measuring instruments
12/31/2016 11NME-013 MA KHAN

12. Unit-2: Mechanical Vibrations
Displacement measuring instruments
12/31/2016 12NME-013 MA KHAN

13. Unit-2: Mechanical Vibrations
Acceleration measuring instruments
12/31/2016 13NME-013 MA KHAN