EXPERIMENTAL MODAL ANALYSIS (EMA) STUDY ON MULTI

Journal of Engineering Science and Technology EURECA 2013 Special Issue August (2014) 96 - 116 © School of Engineering, Taylor’s University

96

EXPERIMENTAL MODAL ANALYSIS (EMA) STUDY ON MULTI-BENT COPPER PHOSPHOROUS SUCTION TUBES

PRASHANTH A/L KAMALANATHAN1, MOHAMMAD

HOSSEINI FOULADI1,*

, YAP KIM HAW2

1School of Engineering, Taylor’s University, Taylor's Lakeside Campus,

No. 1 Jalan Taylor's, 47500, Subang Jaya, Selangor DE, Malaysia 2CAE/FEA, Panasonic Appliances Air-Conditioning R & D Malaysia Sdn Bhd

(PAPARADMY 1), 40300, Shah Alam, Selangor DE, Malaysia

*Corresponding Author: [email protected]

Abstract

Modal Analysis provides valuable information about a structure in terms of its

dynamic properties. In this study, an Experimental Modal Analysis (EMA)

procedure was developed for the testing of two different suction tubes under

“free-free” boundary conditions in order to determine its dynamic properties. The results obtained will then act as a benchmark for the dynamic properties

obtained from the Finite Element (FE) Modal Analysis. Preliminary tests were

conducted on a simple plate structure to validate the developed EMA procedure

based on the comparison of the natural frequencies obtained via EMA against

theoretical natural frequencies. An average percentage error of 5% was

observed deeming the developed procedure reliable for testing on copper tubes. The integrated usage of modal parameter estimation algorithms along with

Mode Indicator Functions (MIFs) are evaluated for dynamic properties

extraction from raw Frequency Response Function (FRF) data and was found to

be a reliable method for dynamic property extraction. The outcomes of this

research will be able to assist air-conditioning manufactures in the design

validation process of new copper tube designs in an efficient and cost effective manner without the need for prototype fabrication.

Keywords: Dynamic properties, Modal parameter estimation, Mode indicator

function, Suction tube, Stability diagram.

1. Introduction

Modal Analysis studies on suction tubes are numbered. One of these studies was

on a pipeline structure similar to that of a suction tube while the other was on a

Experimental Modal Analysis (EMA) Study on Multi-Bent Copper Phosphorous �. 97

Journal of Engineering Science and Technology Special Issue 8/2014

suction tube itself. The study done by Loh et al. [1] was on a suction tube that was

attached to the accumulator of the compressor. In this study, the EMA test

procedure was carried out to validate the results obtained from the FE Modal

Analysis. An impact hammer was used to provide the external excitation to the

suction tube and the response of the structure was measured using a single tri-axial

accelerometer. It was found that the results obtained in terms of the natural

frequency of the suction tube compared to the natural frequencies from the EMA

testing procedure has a maximum percentage difference of 8.5% [1]. In the event

where correlation needs to be carried out, the fixed boundary conditions employed

by Loh et al. [1], is not suitable whereas the “free-free” boundary condition which is

used in this study is preferable as it is more reliable [2-3]. The study done by

Haapaniemi et al. [4] was based on a pipeline structure which is almost similar in

shape with a suction tube. EMA was carried out on the pipeline structure using both

an impact hammer and a shaker and it was found that the results obtained from both

testing methods correlated well at lower frequencies. Besides that, it was also

observed that the correlations were better at regions closer to the excitation points.

The author believes that an impact hammer test was more suitable for smaller

structures and in the case where an impact hammer is used to excite a larger

structure, more than one excitation point should be used [4].

The distinguishing factor in this study compared to the previous study is that in

this study, EMA is carried out on a suction tube under “free-free” boundary conditions

as the measurements obtained are very reliable, suitable in cases where correlation is

required and the configuration is easily achieved [2-3]. The suction tube found in the

air-conditioning outdoor unit is attached to the accumulator of the compressor. The

vibrational excitations due to the working conditions of the compressor and the

Nomenclatures

�� Corrected damping

�� Un-corrected damping

�� Natural frequency of a simple plate under “free-free” boundary

conditions

Greek Symbols

�� Lagrange multiplier

ν Poisson’s ratio

� Decay time constant, s

� Natural frequency, Hz

� Un-damped natural frequency, Hz

Abbreviations

CMIF Complex Mode Indicator Function

EMA Experimental Modal Analysis

FFT Fast Fourier Transform

FRF Frequency Response Function

MMIF Multivariate Mode Indicator Function

RFP-Z Rational Fraction Polynomial-Z

SIMO Single Input Multiple Output

SISO Single Input Single Output

98 P. Kamalanathan et al.


excitations present during the transportation of the outdoor unit itself has led to the

fatigue failure of the suction tube due to resonance. The specified frequency range in

which resonance of the suction tube occurs has been identified to be in the range of 0

Hz to 200 Hz. This frequency range is inclusive of the vibration frequencies due to the

operation of the compressor and also due to the vibration frequency contributed by the

vehicle used in the transportation of the air conditioning outdoor unit.

The objective of the current research is to correlate the dynamic properties of

multi-bent copper phosphorous suction tubes attained via FE Modal analysis

against that obtained from the developed EMA testing procedure. This will

provide a greater confidence factor in the results obtained via FE Modal analysis,

resulting in an efficient and inexpensive design validation process of new copper

tubes. In this study, EMA is used to determine the dynamic properties (natural

frequencies, damping ratio, mode shape) of a 2.0 Hp, and a 2.5 Hp suction tube,

hereafter named as Suction Tube 1 and Suction Tube 2 respectively. Both the

suction tubes are shown in Figs. 1(a) and (b). The dynamic properties of the

structure obtained from EMA are used to validate the results obtained from the FE

Modal Analysis method. The reliability of both the Complex Mode Indicator

Function (CMIF) and the Multivariate Mode Indicator Function (MMIF) will be

evaluated in this study in terms of its capability in determining the dynamic

properties of the suction tube while using the Rational Fraction Polynomial-Z

(RFP-Z) algorithm for the modal parameter estimation process. Prior to EMA

testing on the suction tubes, a preliminary study on a simple plate structure was

carried out to validate the developed EMA testing procedure. Theoretical results

in terms of the natural frequencies of the simple plate are calculated and used as a

validation tool for the natural frequencies obtained from the EMA testing

procedure. A low percentage error gives an indication that the EMA testing

procedure that was developed is reliable and can be used to test the suction tubes.

Fig. 1. The Suction Tubes Used in the Study. (a) 2.0 Hp Suction

Tube (Suction Tube 1) and (b) 2.5 Hp Suction Tube (Suction Tube 2).

2. Research Methodology

The frequency span used for both the suction tubes in this study is 200 Hz with a

frequency resolution of 1 Hz, a record length (T) of 1 s, and a sampling time of 0.002

s. The frequency span used for the simple plate was set to 800 Hz with a frequency

resolution of 1 Hz, a record length (T) of 1 s, and a sampling time of 0.0005 s. To

(a

)

(b



conduct the EMA testing procedure, the MTC Hammer software and the PULSE

Reflex software by Brüel & Kjær, a Danish based company were used. In terms of the

hardware used in the study, a 12-channel FFT analyser (Model No: 3053-B-120), a

miniature Impact Hammer (Model No: 8204) and seven single-axial accelerometers

(Model No: 4517) by Brüel & Kjær were used to carry out the EMA testing

procedure. The measurement portion of the EMA testing procedure is carried out on

MTC Hammer. Results from the EMA procedure on MTC Hammer is exported to the

PULSE Reflex software for the extraction of the dynamic properties from the

obtained raw empirical data. Here, various Mode Indicator Functions (MIFs) and

modal parameter estimation algorithms are used to extract the dynamic properties of

the structure from the raw data. The PULSE Reflex software is also equipped with the

capability of using a stability diagram to select the stable poles in order to extract the

dynamic properties of the structure. The overall process is described in Fig. 2.

Fig. 2. The Research Flow Process Used in the Study.

To carry out the FE Modal Analysis procedure, the NX Nastran 8.5 Enterprise

solver by Siemens PLM is used. The NX Nastran 8.5 Enterprise solver does not have

a graphical user interface and it only acts as a solver. To overcome this limitation, the



ANSA software by βETA CAE, a Greek based company is used. The ANSA software

is capable of carrying out high quality and advanced meshing procedures. The ANSA

software is used to carry out the meshing procedure and it is also used to setup the

loadcase for the solving process on the NX Nastran 8.5 Enterprise solver. Since the

NX Nastran 8.5 Enterprise solver does not have a graphical user interface, a platform

is required to observe the mode shapes of the structure. The visualization of the mode

shapes are observed on the µETA software by βETA CAE.

2.1. The finite element (FE) setup

For the FE Modal Analysis in this study, the SOL 103 solver for Normal Modes is

incorporated. The method used in this study for real eigenvalue extraction is the

Lanczos method as it is both reliable and efficient in extracting eigenvalues and

eigenvectors. The eigenvectors are also known as normal modes whereas the

square root of the eigenvalue gives the natural frequency of the structure. In this

study, the ANSA software by βETA CAE is used to set a loadcase parameter

which is required for solving purposes on the NX Nastran 8.5 Enterprise solver.

The Lanczos method uses the EIGRL entry for the loadcase setting.

Shell meshing was used in this study instead of volumetric meshing as it saves

on computational time due to the lower number of elements used and the quality

of the meshing can be easily monitored as compared to a volumetric mesh [5].

The meshing details used in this study for the simple plate and both the suction

tubes are shown in Table 1. Triangular elements were not present in the meshing

and purely quadratic elements were used in the meshing procedure which

indicates the high quality mesh produced. Mapped face meshing was selected for

meshing purposes to produce an even mesh distribution across the surface of the

structure. The mesh used for all three structures can be seen in Figs. 3 to 5.

Table 2 shows the material properties of all three structures used in the study.

Table 1. The Meshing Details of the Different Structures Used in this Study.

Table 2. The Material Properties of the Different Structures used in this Study.

Structure Number of

Elements

Element

Size (m)

Percentage of triangular

elements (%)

Simple Plate 64 000 0.0005 0

Suction Tube

1 (2.0Hp) 142 200 0.0005 0

Suction Tube

2 (2.5Hp) 225 600 0.0005 0

Structure Material

Young’s

Modulus

(E) (GPa)

Mass

Density

(ρ)

(kg/m3)

Poisson’s

Ratio

(ν)

Thickness

(m)

Simple

Plate Steel 212 7850 0.29 0.001

Suction

Tube 1

(2.0 Hp) Copper

Phosphorous 117 8940 0.3

0.0007

Suction

Tube 2

(2.5 Hp)

0.0008



Fig. 3. Mesh of the Simple Plate Strucure.

Fig. 4. Mesh of Suction Tube 1 (2.0 Hp).

Fig. 5. Mesh of Suction Tube 2 (2.5 Hp).

2.2. The experimental modal analysis (EMA) procedure

In this study, a roving hammer test is carried out on all structures. Another testing

method would be the roving accelerometer test, but the roving hammer test is

preferred in this study. The roving accelerometer test is not preferred in this study as it

leads to mass loading problems which can affect the measurements obtained from

EMA [6]. The roving hammer test is regarded as a Single Input Multiple Output

(SIMO) testing condition where the single input refers to a single excitation point for a

particular measurement whereas the multiple output refers to the usage of multiple

accelerometers to measure the response of the structure. A Single Input Single Output

(SISO) testing condition occurs when a roving hammer test is conducted on a

structure with the usage of only one accelerometer to measure the response of the

structure. The SIMO testing procedure is used in this study. The SIMO roving

hammer test is an example of a multiple reference test [7]. In the case of the roving



hammer test, the reference is based on the number of accelerometers used whereas in

the case of a roving accelerometer test, the reference is based on the number of

excitation positions. A multiple reference test is beneficial in the sense that it is

capable of producing redundant data in terms FRFs where in the event that one of the

references are not able to capture a particular mode properly, another reference could

capture the mode hence maintaining the quality of the results obtained [7].

In this study, elastic chords were used to replicate the “free-free” boundary

conditions for EMA testing purposes. These elastic chords have to be attached to

the structure in a manner where it does not constrain the mobility of the structure

that is being tested. By constraining the mobility of the structure, the results

obtained from the testing procedure will be flawed and the dynamic properties of

the structure would not be able to be determined accurately. Besides the elastic

chords, the connection wires from the accelerometer to the FFT analyzer can also

act as a constraining device. The connection wires tend to be tangled up and

messy, hence the wires are at times taped to the test rig which is used to suspend

the structure that is being tested. If the accelerometer’s connection wire is taped is

taped to the test rig in which it limits the movement of the structure, the dynamic

properties extracted from the FRFs data will not be accurate.

This study is conducted in an air-conditioned room where the movement of the air

in the room does result in minor displacement of the structure that is being tested. This

is regarded as noise in the measurement. The presence of noise in this case contributes

to the noise in the output as the slight movement of the structure results in the

detection in terms of the response by the accelerometer. To overcome the presence of

noise in the structure, the FRF estimator H1 is used throughout the study.

3. Results and Discussion

3.1. Preliminary investigation on a simple plate

The theoretical natural frequency is computed based on Eq. (1) which was

developed for a testing procedure under “free-free” boundary conditions [8]. The

equation is capable of computing the first six modes of the simple plate; hence the

results from EMA were limited to the first six modes. This process is carried out

to validate the EMA testing procedure that was developed before proceeding to

the testing of the suction tubes. Theoretical validation for the suction tubes are not

available, hence a preliminary study on a simple plate structure is carried out.

�� = ��

��(��) (1)

where a = length of the plate = 0.2 m, b = width of the plate = 0.08 m

(only used in calculation of the (a/b) ratio), h = height of the plate = 0.001 m,

i = number of half-waves in mode shape along the horizontal axis, j = number of

half-waves in mode shape along the vertical axis, � = mass per unit area of the

plate = 7.85 kg/m2, = Poisson’s ratio of the plate (given value of 0.3),

! = Modulus of elasticity, and � = Lagrange multiplier

This equation is based on the assumption that the Poisson’s ratio of the

material used is equivalent to 0.3. The Lagrange multipliers that are used in the

computation can be seen in Table 3 for a length to width ratio of 2.5. The



correction of damping for the damping ratio obtained from EMA was carried out

and the decay time constant value τa, used in the response weighting is equal to

0.0291 s. The simple plate can be seen in Fig. 6, whereas the AutoMAC plot is

shown in Table 4. On the other hand, the theoretical and experimental results for

the simple plate are shown in Table 5 whereas the comparison between the results

from FE modal analysis against EMA is shown in Table 6.

Fig. 6. The Placement of the Single-Axial Accelerometers on the Simple Plate.

Table 3. The Values for the Lagrange Multiplier for a Length to

Width Ratio of 2.5 for the First 6 Modes of the Simple Plate [8].

Table 4. The AutoMAC Plot Obtained from the

EMA Testing Procedure on the Simple Plate.

Table 5. The Comparison of the Theoretical and Experimental

Results in Terms of the Natural Frequencies for the Simple Plate.

Mode

Theoretical Experimental

(EMA) Percentage

difference

(%) Natural Frequency

�� (Hz) Natural Frequency

� (Hz)

1 135.41 128.64 -5.00

2 206.80 196.87 -4.80

3 376.31 356.14 -5.36

4 447.27 425.54 -4.86

5 735.22 696.26 -5.30

6 747.11 786.99 5.34

"#

�$% 2 for each mode

1 2 3 4 5 6

2.5 21.64 33.05 60.14 71.48 117.5 119.4

- 128.639 196.873 356.144 425.538 696.264 786.993

128.639 1.000 0.003 0.019 0.015 0.033 0.113

196.873 0.003 1.000 0.006 0.010 0.011 0.014

356.144 0.019 0.006 1.000 0.020 0.026 0.110

425.538 0.015 0.010 0.020 1.000 0.019 0.034

696.264 0.033 0.011 0.026 0.019 1.000 0.207

786.993 0.113 0.014 0.110 0.034 0.207 1.000



The AutoMAC plot in Table 4, shows off-diagonal values which are

approximately zero except for Mode 5 and Mode 6 where the off-diagonal value

is equivalent to 0.207. This indicates that Mode 5 and Mode 6 have a slight

degree of similarity. This should not be the case as the mode shapes have to be

different from one mode to another. The value of 0.207 on the AutoMAC plot

indicates that the modal parameters were not extracted properly from the stability

diagram. Based on Table 5, the highest frequency difference between the

theoretical natural frequency and the experimental natural frequency is 5.36%.

The percentage difference observed between the natural frequency obtained from

EMA and the theoretical natural frequency is minimal but not negligible. The

anomalies observed in the frequency difference is due to the assumption made in

the equation that the Poisson’s ratio of the material had to be 0.3, whereas the

plate that was tested using EMA had a Poisson’s ratio of 0.29. Other factors could

also contribute to the percentage difference such as the Young’s Modulus of the

simple plate. In most cases, the material under testing does not always have the

same Young’s Modulus used in the theoretical calculations. It is also observed

that the experimental frequency from Mode 1 to Mode 5 is consistently lower

than the theoretical except for Mode 6 which is the complete opposite. The

simulated mode shapes observed in Figs. 7 and 8 are similar in terms of the

deformation for Mode 1 to Mode 5 except for Mode 6.

The irregularities in the dynamic properties of Mode 6 is observed during the

comparison of the natural frequency from EMA and the theoretical natural

frequency and also during the mode shape comparison between the experimental

mode shapes and the simulated mode shapes. Besides that, the corrected damping

values from Table 6 also showed signs of abnormalities for Mode 6 as it does not

follow the decreasing trend of the damping values. This clearly indicates that the

experimental results in terms of the dynamic properties of Mode 6 are flawed. The

rest of the dynamic properties from Mode 1 to Mode 5 showed good comparisons

particularly between the experimental results and the theoretical results.

The poor results obtained for Mode 6 could be due to the fact that only 4

single-axial accelerometers were used to measure the response of the structure. 5

single-axial accelerometers could improve the results for Mode 6, but it might

reduce the natural frequency of the other modes due the effect of mass loading.

Table 6. The Comparison between Experimental Results and

FE Results in Terms of the Natural Frequencies for the Simple Plate.

Mode

Experimental (EMA) Simulation

(FE) Percentage

Difference

(%)

Natural

Frequency

� ('()

Uncorrected

Damping De

(%)

Corrected

Damping

Dc (%)

Natural

Frequency

� ('()

1 128.64 5.389 5.304 134.18 4.31

2 196.87 4.587 4.531 206.37 4.83

3 356.14 2.063 2.032 372.65 4.64

4 425.54 2.162 2.136 442.58 4.00

5 696.26 1.331 1.315 727.52 4.49

6 786.99 4.646 4.632 738.59 -6.15



Fig. 7. The Comparison of the Experimental Mode Shapes (a) and

Simulated Mode shapes (b) for Mode 1, 2, and 3 for the Simple Plate.

(a) (b)

Mode 1

Mode 3

Mode 2




Simulated Mode shapes (b) for Mode 4, 5, and 6 for the Simple Plate.

(a) (b)

Mode 4

Mode 6

Mode 5



Since the natural frequency is inversely proportional to the mass of a structure,

and increase in the mass due to the addition of an extra accelerometer could

reduce the natural frequency of the structure. In this case, a fifth accelerometer

will add to the mass of the structure and decrease the natural frequencies of the

study which will then lead to a further increase in the percentage difference in the

natural frequency between the theoretical results and the experimental results.

This shows that there is a trade-off where one can either obtain a low percentage

error and fewer modes captured or a high percentage error with a higher number

of modes captured.

Overall, the results show that the EMA testing procedure that was developed

is valid and is reliable in determining the dynamic properties of a structure based

on the low percentage of error observed between the theoretical natural

frequencies and the natural frequencies obtained from EMA. The developed EMA

testing procedure is then used to test both the suction tubes used in the study.

3.2. Integrated study on suction tube 1 (2.0 Hp)

The results obtained from the FE modal analysis is validated against the

experimental results in terms of the dynamic properties obtained. The setup of the

experimental procedure is shown in Fig. 9 and 10. Four single-axial accelerometers

with 34 impact positions are used in this study. The decay time constant, τa, used in

this study is equivalent to 0.0772 s which is used in the computation of the

corrected damping value. The proficiency of carrying out the modal parameter

estimation process is based on the AutoMAC plot which is shown in Table 7. The

stability diagram is shown in Fig. 11, where different shaped and coloured poles

represent different dynamic characteristics of the structure. The aim is to select the

red coloured diamond poles which represent a stable pole in terms of all the

dynamic properties of the structure. Table 8 shows the comparison of the natural

frequencies between the FE modal analysis and the EMA testing procedure while

Fig. 12 shows the comparison between the experimental mode shapes and the mode

shapes obtained from the simulation. The AutoMAC plot in Table 7 shows near

zero off-diagonal values which clearly indicates the proper extraction process of the

modal parameters from the empirical data which are the FRF plots. The favorable

results obtained from the AutoMAC plot shows the quality of the modal parameters

extracted from the raw FRF data which validates the experimental procedure on

Suction Tube 1. Three modes are observed in Suction Tube 1 in the frequency span

of 0 Hz to 200 Hz, from both the FE modal analysis and the EMA. The FE modal

analysis is able to compute the natural frequencies of Suction Tube 1 accurately

based on the small percentage difference that is shown in Table 8. The mode shapes

that can be seen in Fig. 12 shows that the mode shapes obtained from the FE modal

analysis are very similar in terms of the deformation compared to the experimental

mode shapes. The suction tube that is highlighted in blue in Fig. 12 indicates the

mode shape whereas the suction tube which is highlighted purple indicates the un-

deformed state of Suction Tube 1. Overall, the results from the EMA testing

procedure are very satisfactory based on the favourable results the AutoMAC plot.

Besides that, the FE modal analysis clearly indicates that it is able to accurately

compute the mode shapes as the deformation of the mode shape clearly resemble

the experimental mode shapes. The FE modal analysis is also reliable in computing



the natural frequencies of Suction Tube 1 based on the low percentage error

compared to the experimental natural frequencies.

The corrected damping values shows that the third mode at a natural

frequency of 149.71 Hz has the highest possibility of fatigue failure as the

corrected damping percentage of that particular mode is the lowest amongst the

other modes. This conclusion is further strengthened by the high amplitude of the

third CMIF peak that can be seen in the stability diagram in Fig. 11. This

indicates that the third mode of Suction Tube 1 has the highest response compared

to the other modes which results in the highest deformation at the point of

resonance. These arguments indicate that Mode 3 of Suction Tube 1 has the

highest possibility of fatigue failure due to resonance. When Suction Tube 1 is

redesigned to shift its natural frequencies away from the frequency range of 0 Hz

to 200 Hz, more attention should be given to the third mode.

Table 7. The AutoMAC Plot from the EMA Testing of Suction Tube 1.

- 62.844 96.781 149.708

62.844 1.000 0.011 0.108

96.781 0.011 1.000 0.117

149.708 0.108 0.117 1.000

Table 8. The Comparison between Experimental Results

and FE Results in Terms of the Natural Frequencies for Suction Tube 1.

Mode


(FE) Percentage

Difference

(%)

Natural

Frequency

� ('()

Uncorrected

Damping De

(%)

Corrected

Damping

Dc (%)

Natural

Frequency

� ('()

1 62.84 3.547 3.481 64.01 1.86

2 96.78 2.398 2.355 95.22 -1.61

3 149.71 1.623 1.595 151.35 1.10

Fig. 9. The Placement of Accelerometers on Suction Tube 1 under

(a) the “free-free” Boundary Condition and (b) on MTC Hammer.

(a) (b)



Fig. 10. The Impact Locations for Suction Tube 1 on MTC Hammer.

Fig. 11. The Stability Diagram Obtained

from the EMA Testing of Suction Tube 1.

3.3. Integrated study on suction tube 2 (2.5 Hp)

The results obtained in terms of the dynamic properties of Suction Tube 2 form the

FE modal analysis is validated with the results obtained from EMA. This is done by

using 7 single-axial accelerometers to measure the response of the structure and 42

impact locations to provide an excitation force to the structure using a miniature

impact hammer. The setup of the EMA process is shown in Figs. 13 and 14. The

stability diagram is shown in Fig. 15. The AutoMAC plot is used to indicate the

validity of the EMA testing procedure and is shown in Table 9. The comparison of

the simulated mode shapes and the experimental mode shapes are shown in Figs. 16

and 17 whereas the comparison of the natural frequencies between the FE modal

analysis and EMA are shown in Table 10. The decay time constant, τa that is used in

the exponential weighting of the response spectrum is equivalent to 0.043 s which is

required for the computation of the damping correction.



The AutoMAC plot shown in Table 9 indicates that the modal parameters

were not extracted in the best possible manner. Four non-zero off-diagonal values

were observed in the AutoMAC plot which indicates that the dynamic properties

of Suction Tube 2 are not extracted in the best possible manner. This justifies the

fact that the modal parameter stimation process is not done in the best possible

manner. Six modes are obtained from both the EMA test and the FE modal

analysis procedure in the frequency span of 0 Hz to 200 Hz. The interesting

observation in this study is that although the perentage difference in the natural

frequencies between FE modal analysis and the natural frequencies in the EMA

has a maximum value of only 4.67%, the natural frequencies from the FE modal

analysis underpredicts the natural frequencies except for mode 4. This should not

be the case as the natural frequencies from the EMA procedure should be lower

compared to the natural frequencies computed from the FE modal analysis

approach. This is due to the presence of the extra mass from the accelereometers

and since the natural frequency is inversely proportional to mass, the additional

mass results in a lower natural frequency.

Both the results from the simple plate and Suction Tube 1 show that the FE

modal analysis consistently overpredicts the natural frequencies compared to the

experimental natural frequencies which should be the case. The mode shapes that

are observed are only similar for Mode 1 and Mode 2. The rest of the modes

showed a similar deformation pattern, but the direction of the deformation pattern

is the complete opposite. The irregularities observed in the results obtained from

Suction Tube 2 could be due to the positioning of one of the accelerometers and

the impact positions in terms of its axis. When an EMA testing procedure is

carried out, the geometry alignment of the MTC Hammer software must be

similar to the alignment of the structure under actual testing conditions. In the

case of Suction Tube 2, the alignment is positioned in such a way that one of the

accelerometers that is required to be positioned in the X-axis on the MTC

Hammer software could not be achieved under real testing conditions as the plane

of the suction tube is slanted. The slanted portion of Suction Tube 2 also affected

the impact hammer position as excitation to the structure could not be provided to

the correct axis. Biased errors are observed for Suction Tube 2 due the constrains

in terms of the alignment of the axis of the accelerometer and the axis of the

impact locations at the slanted portion of Suction Tube 2. The poor FRF data

contributed to the poor modal parameter extraction process which is jutified based

on the AutoMAC plot in Table 9.

3.4. Study on the degree of the “Free-Free” boundary condition

Table 11 shows the comparison of the natural frequency of the first bending mode

and the natural frequency of the rigid body mode. Based on the results shown in

Table 11, the simple plate and Suction Tube 1 is considered to have a “free-free”

boundary condition as it falls in the range where the rigid body mode has to be in

the frequency range of 10% to 20% of the first bending mode [9]. Suction Tube 2

on the other hand exceeds the 15% range and it is extremely close to the 20%

limit [9, 10]. This is an indication that Suction Tube 2 is not completely “free-

free’ and has a certain degree of constrain to it. This could also be a contributing

factor to the anomalies in the results obtained for Suction Tube 2.




Simulated Mode Shapes (b) for Mode 1, 2, and 3 for Suction Tube 1.

(a) (b)

Mode 1

Mode 2

Mode 3



Fig. 13. The Placement of Accelerometers on Suction Tube 2 under (a) the

“free-free” Boundary Condition and (b) on MTC Hammer.

Fig. 14. The Impact Locations for Suction Tube 2 on MTC Hammer.

Fig. 15. The Stability Diagram Obtained

from the EMA Testing of Suction Tube 2.

(a) (b)





(a) (b)

Mode 1

Mode 2

Mode 3





(a) (b)

Mode 4

Mode 5

Mode 6



Table 9. The AutoMAC Plot from the EMA Testing of Suction Tube 2.

- 38.778 54.017 109.484 144.190 159.870 177.821

38.778 1.000 0.004 0.130 0.008 0.023 0.000

54.017 0.004 1.000 0.004 0.385 0.219 0.200

109.484 0.130 0.004 1.000 0.026 0.321 0.091

144.190 0.008 0.385 0.026 1.000 0.206 0.100

159.870 0.023 0.219 0.321 0.206 1.000 0.176

177.821 0.000 0.200 0.091 0.100 0.176 1.000

Table 10. The Comparison between Experimental Results and FE

Results in Terms of the Natural Frequencies for Suction Tube 2.

Mode


(FE) Percentage

Difference

(%)

Natural

Frequency

� ('()

Uncorrected

Damping De

(%)

Corrected

Damping

Dc (%)

Natural

Frequency

� ('()

1 38.78 9.807 9.617 36.97 -4.67

2 54.02 7.327 7.191 51.60 -4.48

3 109.48 3.043 2.976 104.97 -4.12

4 144.19 2.340 2.289 146.56 1.64

5 159.87 2.436 2.390 155.30 -2.86

6 177.22 2.349 2.307 174.35 -1.62

Table 11. The Evaluation of the “free-free” Boundary Condition

Based on the Rigid Body Mode and the First Bending Mode.

Structure

Rigid

Body

Mode (Hz)

First

Bending

Mode (Hz)

Percentage of the Rigid

Body Mode based on the

First Bending Mode (%)

Simple Plate 10.68 128.64 8.3

Suction Tube 1 3.08 62.84 4.9

Suction Tube 2 7.69 38.78 19.8

4. Conclusion

A complete EMA testing procedure was successfully developed for multi-bent

copper phosphorous tubed based on validated results from a preliminary study on a

simple plate structure. The developed EMA procedure was employed onto Suction

Tube 1 and 2 within a frequency span of 0 Hz to 200 Hz. Successful correlations

between FE modal analysis and EMA in terms of natural frequencies and mode

shapes were observed in Suction Tube 1. However, this was not the case in Suction

Tube. It is postulated that the probable cause of a poor correlation based on Suction

Tube 2 could be attributed to a poor positioning of an accelerometer resulting in

biased errors, thus affecting the raw data obtained. Overall, the developed procedure

to extract the dynamic properties of the multi-bent phosphorous deoxidized copper

tube using the CMIF and the RFP-Z modal parameter estimation algorithm was



capable in determining accurate results except for the biased errors that were

observed in Suction Tube 2.

Acknowledgments

The author would like to thank Mr. Low Lee Leong and Mr. Dimitris Katramados

from βETA CAE Systems for their continuous support and help. The author

would also like to extend his gratitude to the General Manager of PAPARADMY

1, Mr. Cheng Chee Mun for the approval and opportunity to use the software and

equipment available at PAPARADMY1 and to the Deputy Director of

PAPARADMY 1, Mr. Low Seng Chok for the approval of the copper tube

specimens used in the study.

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EXPERIMENTAL MODAL ANALYSIS (EMA) STUDY ON MULTI