King Fahd University of Petroleum
and Minerals
College of Engineering Sciences
Mechanical Engineering Department
ME 413: System Dynamics and Control
Term 221
Lab 8: Undamped Vibration Absorber
Student Name: Mohammed Al-Zahrani
ID#: 201755770
Sec.#: 56
Instructor Name: Ahmed Salih
Lab readings:
Table 1. System readings without vibration absorber
Displacement Velocity Acceleration
N ω
amplitude amplitude amplitude
(rpm) (rad/s)
(mm) (mm/s) (mm/s2)
1
Table 2. System readings with vibration absorber
Displacement Velocity Acceleration
N ω
amplitude amplitude amplitude
(rpm) (rad/s)
(mm) (mm/s) (mm/s2)
2
Requirement no. 1:
Complete the two tables presented above.
Table 3. System readings without vibration absorber (Calculated)
Acceleration Velocity amplitude Displacement N
ω (rad/s)
amplitude (mm/s2) (mm/s) amplitude (mm) (rpm)
326.725636 3.9 0.046552821 83.775804 800
612.6105675 6.5 0.068967142 94.24778 900
1151.917306 11 0.105042262 104.71976 1000
1594.358272 14.5 0.131871239 109.95574 1050
2303.834613 20 0.173623574 115.19173 1100
5654.866776 45 0.358098622 125.66371 1200
27227.13633 200 1.469122552 136.13568 1300
98960.16859 700 4.951487118 141.37167 1350
16126.84229 110 0.750301875 146.60766 1400
8639.379797 55 0.350140875 157.07963 1500
6534.512719 39 0.232764104 167.55161 1600
5696.754679 32 0.179751465 178.02358 1700
5654.866776 30 0.159154943 188.49556 1800
5571.090972 28 0.140726476 198.96753 1900
5445.427266 26 0.124140856 209.43951 2000
Table 4. System readings with vibration absorber (Calculated)
Acceleration amplitude Velocity amplitude Displacement N
ω (rad/s)
(mm/s2) (mm/s) amplitude (mm) (rpm)
376.9911184 4.5 0.053714793 83.775804 800
848.2300165 9 0.095492966 94.24778 900
2094.395102 20 0.190985932 104.71976 1000
4398.229715 40 0.363782727 109.95574 1050
51836.27878 450 3.906530421 115.19173 1100
2764.601535 22 0.175070437 125.66371 1200
748.7462491 5.5 0.04040087 136.13568 1300
0 0 0 141.37167 1350
1905.899543 13 0.08867204 146.60766 1400
34557.51919 220 1.400563499 157.07963 1500
7539.822369 45 0.268573966 167.55161 1600
5696.754679 32 0.179751465 178.02358 1700
5277.875658 28 0.148544614 188.49556 1800
4974.188368 25 0.125648639 198.96753 1900
4817.108736 23 0.109816911 209.43951 2000
3
Requirement no. 2:
Using Matlab, plot – on the same graph – the displacement amplitude (in mm) on the
y-axis versus the angular speed (in rad/s) on the x-axis.
clc,clear;
N = [800
900
1000
1050
1100
1200
1300
1350
1400
1500
1600
1700
1800
1900
2000
];
w = (pi/30)*N;
VelAmp = [3.9
6.5
11
14.5
20
45
200
700
110
55
39
32
30
28
26
];
DispAmp = (VelAmp)/w;
VelAmp2 = [4.5
9
20
40
450
22
5.5
0
13
220
45
32
28
25
23
];
DispAmp2 =VelAmp2/w;
plot(w,DispAmp,w,DispAmp2)
4
f = w / 2pi = 141.37167 / (2pi) = 22.5 hz
f = w / 2pi= 115.19173 / (2pi) = 18.33333 hz
f = w / 2pi = 157.07963 / (2pi) = 35.01409 hz
5
Requirement no. 3:
Using Matlab, plot – on the same graph – the velocity amplitude (in mm/s) on the y-
axis versus the angular speed (in rad/s) on the x-axis.
clc,clear;
N = [800
900
1000
1050
1100
1200
1300
1350
1400
1500
1600
1700
1800
1900
2000
];
w = (pi/30)*N;
VelAmp = [3.9
6.5
11
14.5
20
45
200
700
110
55
39
32
30
28
26
];
DispAmp = (VelAmp)/w;
VelAmp2 = [4.5
9
20
40
450
22
5.5
0
13
220
45
32
28
25
23
];
DispAmp2 =VelAmp2/w;
plot(w,VelAmp,w,VelAmp2)
6
7
Requirement no. 4 (Skip this):
Having known that the length l , for which the amplitude of the system vibration is
zero, is measured at 9.0 cm. Compare this measured value of l with the value that can
be calculated by solving Equation (12) given in the lab tutorial document. What is
the percentage difference between the two?. Take the measured value as a
reference for comparison.
Figure 1. The vibration absorber clamped below the motor
1 3
Hint: E=¿ 200 GPa and I = bh
12
Where, b=¿ 22 mm, h=¿ 1.95 mm, and m=¿ 0.45 kg
8
Requirement no. 5:
Discuss your findings and write some conclusions on the effect of the vibration
absorber.
High amplitude is obtained when the system reaches the angular speed
equivalent to its resonance frequency; as a result, significant dynamic
stresses are created, which leads to noise and fatigue issues. The
resonance amplitude is then noticed to have been split into two values
when an absorber is added because the system has now been divided into
a two degree of freedom system. Moreover, all of the absorber's natural
frequencies take place away from the excitation frequency.
