Education

2. Critical Point
Input Energy
Damped Energy
Amplitude
Energy
per
cycle
Time
Amplitud
e
Classifications of Vibrations
 Free Vibration
 Forced Vibration
 Self excited Vibration

4. Equipment Details
01 Piezoelectric accelerometer, DYTRAN: 3145AG
02 Impact hammer, DYTRAN: 5800B4
03 Electro dynamic Shaker, MB dynamics: 50A
04 Data Acquisition System, NI: 9234
05 Data Acquisition System, PHOTON+
03
02
05
04
01
Impact hammer
Accelerometer
specimen
Clamping Mechanism

5. Ref. A Bhattacharyya, Theory of Machine Tools, New Central Book Agency.

6. ζ=0.001
ζ=0.05
ζ=0.1
ζ=0.03
Frequency ratio, r
0.30
0.25
0.20
0.15
0.10
0.50
0.00
0 1 2
Compliance
(displacement
/
force,
mm/N)
Stiffness
Control
Damping
Control
Mass
Control
Ref. Stephenson and Agapiou, Metal cutting Theory and Practice, Taylor and Francis

8. Logarithmic decrement method
20
10
0
-10
-20
0 50 100 150 200
Acceleration,
g
Time ms
0 200 400 600 800 1000
0.8
0.6
0.4
0.2
0
Amplitude,
g
Time ms
0 50 100 150 200
40
20
0
-20
-40
Acceleration,
g
0 200 400 600 800 1000
1.8
1.2
0.6
0
Amplitude,
g
Frequency, Hz
Frequency, Hz
i) Time domain signal
i) Time domain signal
ii) Frequency domain signal ii) Frequency domain signal
680Hz
666Hz
680Hz
678Hz
664Hz
642Hz

10. 200 250 300 350 400
0.0
-1.0
-2.0
-3.0
-4.0
-5.0
A1=4.23, 294 Hz
Frequency, Hz
Imaginary
part
,
m/N
x10
-5
a) Without Excitation current
i) Real part
FRF
m/N
(10
-6
) 12
8
4
0
-4
-8
-12
Frequency Hz
400 500 600 700 800
FRF from shaker excitation test
---- Eqn (3)
---- Eqn (4)
---- Eqn (5)
---- Eqn (6)

12. Modeling of (MDoF) System
k1
m1
k2
m2
k3
X(1) X(2)
FBD(M1)
(1)

13. k1
m1
k2
m2
k3
X(1) X(2)
FBD(M2)
m2
(2)

14. Undamped free vibration

15. To find the roots of the equation, ω1 &ω2, the
determinant of the mass-stiffness is equated to zero.
&

16. Amplitude Ratio
Mode -1 Mode -2

17. Semi Definite Systems
To find the roots of the equation, ω1 & ω2,
the determinant of the mass-stiffness is equated to zero.
m1
k
m2
X(1) X(2)