ME3112E Lab 1

Vibration Measurement

by

LIN SHAODUN A0066078X

Group 1A

Date 11-Sept-2012

TABLE OF CONTENTS

OBJECTIVE 1

EXPERIMENT DATA 1

SAMPLE CALCULATION 3

DISCUSSION 4

CONCLUSION 6

1

OBJECTIVES

1. To familiarize with the techniques in measuring dynamic quantities as well as using the

related equipment such as Accelerometer, Shaker, Function generator and Stroboscope.

2. To determine the resonance frequencies and the corresponding mode-shapes of a vibrating

beam with several different techniques.

EXPERIMENT DATA

Table 1a Vibration Measurement

Mode

Theoretical

Natural

Frequency

(Hz)

Experimental Natural Frequency (Hz) Position of Nodes (m)

CRO

(Hz)

Stroboscope Experimental Theoretical

Cycles per min Hz

1 4.53 - - - - -

2 28.41 27.17 1638 27.30 0.375 0.394

3 79.55 76.34 4569 76.15 0.245,0.411 0.238,0.428

4 155.89 152.7 9138 152.3 0.175,0.315,0.435 0.166,0.308,0.442

Table 1b Experimental error comparison

Mode

Theoretical

Natural

Frequency (Hz)

Experimental Natural Frequency (Hz) Position of Nodes (m)

CRO Err (%) Stroboscope Err (%) Experimental Theoretical Err (%)

2 28.41 27.17 4.36% 27.30 3.91% 0.375 0.399 -6.34%

3 79.55 76.34 4.04% 76.15 4.27% 0.245,0.411 0.238,0.427 -1.48%

4 155.89 152.7 2.05% 152.3 2.30% 0.175,0.315,0.435 0.170,0.305,0.441 0.91%

From above table one can see that the experimental result is quite close to theoretical value.

28.41

79.55

155.89

27.17

76.34

152.7

27.3

76.15

152.3

0

50

100

150

200

Mode 2 Mode 3 Mode 4

Fre

qu

ency

(H

z)

Theoretical Natural Frequency

Oscilloscope

Stroboscope

2

Table 2 Mode shape calculation

x x / L

Modes

Mode1 Mode2 Mode3 Mode4

0.0000 0.0 0.00000 0.00000 0.00000 0.00000

0.0475 0.1 0.00749 0.18589 0.45604 0.77008

0.0950 0.2 0.02931 0.60719 1.20804 1.50771

0.1425 0.3 0.06448 1.06951 1.50896 0.86804

0.1900 0.4 0.11201 1.40827 1.04279 -0.62996

0.2375 0.5 0.17094 1.50981 0.01897 -1.41012

0.2850 0.6 0.24028 1.32690 -0.99163 -0.64035

0.3325 0.7 0.29870 0.88332 -1.41012 0.83205

0.3800 0.8 0.37596 0.26515 -0.99732 1.39688

0.4275 0.9 0.45795 -0.40007 0.00215 0.43655

0.4750 1.0 0.54341 -0.97229 1.00141 -1.00041

0.0

0.2

0.4

0.6

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Am

pli

tude

x / L

Mode 1

-2.0

-1.0

0.0

1.0

2.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Am

pli

tude

x / L

Mode 2

-2.0

-1.0

0.0

1.0

2.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Am

pli

tude

x / L

Mode 3

-2.0

-1.0

0.0

1.0

2.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Am

pli

tude

x / L

Mode 4

Experimental Node Position

Experimental Node Position

Experimental Node Position

3

SAMPLE CALCULATION

1. Theoretical Natural Frequency, for Mode 4:

√

√

2. Amplitude of Vibration, for Mode 4 and x/L=0.9:

(

)

( ) ( ) [ ( ) ( )]

3. Node position, for Mode 4:

(

)

4

DISCUSSION

1. Discuss the significance of the resonant frequencies, modes shapes and the effect

of accelerometer's mass on these quantities.

Significance of the resonant frequencies:

Mechanical resonance is the tendency of a mechanical system to absorb more energy when the

frequency of its oscillations matches the system's natural frequency of vibration than it does at

other frequencies. It may cause violent swaying motions and even catastrophic failure in

improperly constructed structures including bridges, buildings, trains, and aircraft. When

designing objects, Engineers must ensure the mechanical resonance frequencies of the component

parts do not match driving vibrational frequencies of motors or other oscillating parts, a

phenomenon known as resonance disaster. (Source: http://en.wikipedia.org/wiki/Resonance)

For industrial application, engineers usually need to design the system structure in higher

resonance frequencies to reduce vibration level. For example, by changing the linear bearing of

an assembly from cross roller to needle bearing, the resonance frequencies of the assembly

significantly improved so does the vibration level.

5

Significance of the mode shape:

For mechanical engineers, mode shapes are useful because they represent the shape that the

structure will vibrate in free motion.

By study the mode shape, it is possible to find out what is the weakest link in the structure so that

engineer knows how to improve the structure to reduce vibration level.

Mode shape predict by FEA software also tells how the structure behaves during vibration.

Below is an example of FEA study of mode shape.

Effect of accelerometer's mass

In the experiment, the accelerometer's mass affects the resonant frequencies of a one-end fixed

beam by 2~4% ( See Page 1). The resonant frequency of a system is described as

√

,

from this equation one can see that the accelerometer only contribute mass to the system without

improve the system stiffness, so the frequency will be reduced. Hence the resonant frequency

measured in experiment is smaller than the theoretical calculation.

As for mode shape, the accelerometer’s mass will reduce the amplitude of vibration as it acting as

a mass damper to dissipate the stored system energy. It may change the position of node and anti-

node as well as the mass distribution of the beam is different from initial assumption.

2. Discuss what is Node and Anti-Node, and the significance of Node and Anti-

Node in industrial application.

A node is a point along a standing wave where the wave has minimal amplitude. The opposite of

a node is an anti-node, a point where the amplitude of the standing wave is a maximum. These

occur midway between the nodes. (Source: http://en.wikipedia.org/wiki/Node_(physics) ).

6

The illustration of node and anti-node is as follow:

The significance of node and anti-node in industrial application :

When install precision equipment which is sensitive to vibration in a building, it is advisable to

study the mode shape of the floor and identify the location of nodes, the equipment should be

installed on the nodes to minimize the effect from vibration.

While in the case the vibration needs to be amplified, for example a musical instrument, the

structure can be modified so that the sound generation component is located near to anti-node.

CONCLUSION

After completed this experiment, I have a better understanding about mechanical system

vibration , resonance frequency and the mode shape.

I also learned how to use accelerometer and stroboscope to measure the resonance frequency of

the beam at different modes, and gained hands on experience on these techniques in measuring

dynamic quantities.