Automobile Vibrations and Acoustic Noise Reduction via Modal Analysis Technique

M. A. NASSER Associate Prof:

(Visiting Researcher, Mechanical Engineering Department, The University of Dundee, Dundee, DDI 4HN, Scotland, UK.) Production Engineering & Mechanical Design Dept., Faculty of Engineering, Menoutia University, Shebin El Kom, Egypt.

ABSTRACT: Mechanical vibrations of vehicle exhaust system can cause cabin and environmental noise as well as structural durability concerns. The environmental noise impact due to the high traffic intensity in the urban areas has become a critical concern and considerable amount of calmness are required. Also, the ride comfort is one of the most important objectives of vehicle designers and manufacturers. Automobile noise is complex and has various sources. These sources are engine intake and exhaust noise, drive train, tire noise, and chassis noise. Automobiles are subjected to strict restrictions on intake and exhaust noise based on their displacement and weight, leaving very little options for further noise reduction, In order to develop noise countermeasures under these conditions without resorting to a short-term schedule trial-and-error development, and because noise reduction goals cannot be met by simple extensions of development methods, efforts are now being directed toward new fundamental technologies, The exhaust system is mainly consists of pipes and mufflers. Mufflers as main part of this system are the scope of this paper. Mufflers, which are classified into absorptive and reactive, have many applications; one of them is the vehicle exhaust system. Fibrous and porous materials are used to absorb the noise and vibrations. Noise reduction can be achieved fibrous or porous materials in the absorptive mufflers. While, reactive mufflers are manufactured from conventional materials depends mainly on their geometries. Muffler cylinders with double skin of circular and elliptical shapes were proposed and investigated and compared with the single layer skin cylinders in this study. A method for vibration and vibration-acoustical modelling and evaluation of exhaust systems mufflers boxes was proposed. In this method Finite Element analysis was done to predict the vibration and acoustic noise of muffler systems, and experimental modal analysis was done to measure and extract the natural frequencies, modal damping and mode shapes of the some muffler boxes. Dual channel signal analyzer equipped with computer and modal analysis software. The double skin mufflers with a suitable gape between layers present a good solution for noise vibration and noise reduction. The method provides rigorous framework for exhaust system muffler model creation and verification, as well as analysis and post- processing.

NOMONCLATURE: P : pressure. s : interface surface area. n : normal to the boundary surface of the

LJl M C K mass damping and stiffness matrices. I[ Ye,

+v :

element shape function for pressure.

elemental shape function for displacement.

VI : force vector.

bNH+ . displacement, velocity and acceleration vectors.

i.L> : au pressure load vector for node n

P a,, : air density. sub-script:

As : air/muffler structure coupling.

A : surrounding air.

,I : node.

INTRODUCTION: Automobile noise is a complex and has various sources. There is engine intake and exhaust noise, drive tram and tire noise, even chassis noise. Automobiles are subjected to strict restrictions on intake and exhaust noise based on their displacement and weight, leaving very little room for further noise reduction. In addition, since me engine is exposed, its visual appeal must also be considered when designing it. This means that many of the common- sense techniques are not applicable for cars. In order to develop the noise countermeasures under these conditions without resorting to a short-term schedule trial-and-error development, and because the noise reduction goals cannot be met by simple extensions of development methods, efforts are now being directed toward new fundamental technologies. Since noise reduction usually has an adverse affect on performance it is extremely difficult to achieve without sacrifice. The exhaust silencer provides a perfect example. Simulation is used to determine the silencers internal construction. The muffler designed for low noise sometimes creates increased backpressure and raises temperatures at the piston crown, which can cause engine overheating. For this reason each design element in the silencer is quantitatively investigated to achieve a balance

between low noise and low backpressure. Dynamic structural analysis using fmite element (FE) techniques and experimental modal analysis was conducted as an effective tool in analyzing vibration and acoustical behavior of different types of cylinders to be used in silencers to control the acoustic emission from those parts. For example, with some engines low-frequency engine vibrations are a major noise sources. Adjusting the shape and layout of the silencer reduce resonance and sound level pressures. A major engineering objective is to help developing low- emission, fuel-efficient engines. A high performance engine is needs to be environmental friendly. The designers and manufacturers must tackle such issues, as they strive to develop technology that reduces the cars environmental impact. Mufflers, which are classified into absorptive and reactive, have many applications; one of them is the vehicle exhaust system. Fibrous and porous materials are used to absorb the noise and vibrations. Noise reduction can be achieved fibrous or porous materials in the absorptive mufflers. While, reactive mufflers are manufactured from conventional materials depends mainly on their geometries. Some analytical methods, including: a lumped parameter method, and one, two, and three-dimensional modelling schemes were investigated theoretically and the predictions from the various modelling methods are compared to experimental results for some realistic mufflers. The applicability of different modelling methods is discussed to defme suitability of each method, [l]. Finite-element analysis of a thin muffler element connected with a Helmholtz resonator was conducted. A point impedance method in analogy to the structural point reacceptance method was applied for the manifold frequency calculation. The effects of location of the Helmholtz resonator on the system frequencies and modes are indicated, [Z]. A procedure for the analysis of curved, thin muffler elements, by the application of Hamiltons principle was conducted, which can utilize in compact engines. Analytical results are verified by comparison with the results obtained from a fmite element program. Good agreement was achieved as long as the thickness of the muffler element is sufficiently small compared to the wavelength range of interest Four pole parameters are formulated from the pressure response solutions using the modal series expansion method and orthogonality property, [3]. An object oriented programming methodology was utilized and is implemented using a programming language to investigate the measurement errors in lightly damped structures, A comparative study on two proposed analytical models and experimental test structures are used. The analytical investigation involves a hvo- degree of freedom mass spring damper simulation, while the experimental investigation utilizes an automotive exhaust-muffler system for confvmation of the predicted behaviour, [4]. The structure is divided into several components and the total acoustic characteristics of the machine in terms of acoustic

natural frequencies and mode shapes can be predicted based on those of each component. Muffler component with complex structure, which is difficult to be modelled analytically, is tested an Acoustic Building Block Approach was applied to predict the total acoustic characteristics, [5]. Theoretical method for modellmg of chamber mufflers selecting the transmission loss as muffler characteristics were carried out based on the electrical-acoustic analogy; four-pole electrical ducts represent the muffler elements. The acoustic pressure is analogous to voltage, while the volumetric velocity corresponds to current. Some numerical results are given in the paper for various chamber diameters and lengths. Results were compared to those obtained with other methods, [6]. Analytical solutions for natural frequencies and mode shapes of elliptical cylindrical acoustic cavities were obtained by solving the homogeneous wave equation in elliptical cylindrical co-ordinates. Both hollow cylinder and annular cylinder cases were considered. Natural frequencies and mode shapes were calculated for compressors and small automotive muffler. The results were compared with those of circular cylindrical cavities, which have the same cross-sectional area and volume, [7]. The application of the fmite element and the boundary element methods to problems in acoustics was discussed. Finite Element Analysis of an Industrial Reactive Silencer was enhanced [S]. The problem examined is the acoustical response of a muffler. The ANSYS three-dimensional acoustic elements and the ANSYS axe-symmetric structural elements are used with the structural/acoustical analogy to determine the acoustical response of the muffler. The three sets of numerical results are in good agreement, [9]. An experimental study demonstrates the use of an active muffler attached to an automotive exhaust system to reduce exhaust noise. A controlled experiment for reducing exhaust noise with an active muffler is implemented during run-up on no load was considered. Compared with the conventional method, The presented experimental results showed that the new method is capable of acquiring a reduction of more than 5 dB of exhaust noise in overall sound power level, [lo]. A semi active muffler and active systems as innovative exhaust noise reduction techniques in an exhaust system development were proposed as a solution to the problem of increasing the engine swept volume and engine power without allowing any change in the layout of the exhaust system, which may already be on the borderline from the acoustic point of view. The first solution will change the internal geometry of the muffler system or muffler in accordance with changes of engine conditions during driving. The second one adds antinoise or modulates the pulsating exhaust gas flow in order to smooth the gas pressure pulsation and to get in this way a sound attenuation. The possibilities and limits of both solutions are shown by different measurement results. [ll]. Statistical energy analysis has been used to study

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noise transmission through a commercial motor vehicle and in order to do this various sound and vibration power inputs associated with flanking transmission via the exhaust and engine noise are calculated. A modem commercial motor vehicle that has an exhaust noise sensitivity problem was studied aiming to demonstrate the application of SEA and to study the effects on noise transmission when the exhaust is incorrectly fitted in the case of its misalignment. Airborne and structural paths for sound and vibration transmission to a vehicle saloon were considered. The study showed that for low frequencies, the sound transmission through the vehicle structure is most important. At high frequencies, airborne flanking noise transmission to the floor is important. In this case, exhaust vibration transmission is most important at frequencies between 250 Hz and 1 kHz when the engine is running at 5700 pm, WI. In this paper dynamic structural analysis using FEM techniques and experimental modal analysis was conducted as an effective tool in analyzing vibration and acoustical behavior of different types of cylinders to be used in silencers to control the acoustic emission from those parts. With some engines the low- frequency engine vibrations are a major noise sources. Adjusting the shape and layout of the silencer, reduced resonance and sound level pressures and the resonance changed frequency. Double skin mufflers are proposed to verify the objective for wider frequency range. Muffler boxes have single and double skin of different geometries and dimensions were investigated in this study. A method for vibration and vibration-acoustical modelling and evaluation of exhaust systems mufflers boxes was proposed. In this method finite element analysis was done to predict the vibration and acoustic noise of muffler systems, and experimental modal analysis was done to measure and extract the natural frequencies, modal damping and mode shapes of the some muffler boxes. Dual channel signal analyzer equipped with computer and modal analysis software was used in the modal test. The results indicated that adjusting the shape and layout of the silencer, could reduce resonance and sound level pressures. The method provides rigorous framework for exhaust system muffler model creation and verification, as well as analysis and post-processing.

ANALYSIS: The equation of motion of the muffler steel cylinder of the silencer can be written in the following form:

[M.~.>+[c,~~,,)+[K.~,,~=cf,,) (1 The equation of motion of the system including the air effects may take the following form:

l&f,, IhL I+ [Cl IL I+ k I& >= k >+ if* > (2)

The air pressure load on the steel cylinder surface is obtained from:

k4,t I= pPww s

(3)

The generated force from the structure interface can be written as:

IL >= p%4 w4m s

from the equation (4)

if-A I= IL I& I where,

(5)

(6)

From equation (5) substituting into equation (2)

~,,B.~+~,~~.}+[K,~M1,,}-[R,k,}=~~

From equations (3-6) and combining equations (2) and (7) can be reassembled as the following:

Where

Lb I= PO,, Lt P (9) PLl=-[RI (0) EXPERIMENTAL WORK:

An experimental program was carried out to study the validity of utilizing modal analysis for vibration and noise reduction of muffler systems.

samples: Some widely used commercial muffler boxes were selected for the current study. Cylinders of 10 cm diameter and 40 cm long made of 1.25mm steel plates are used as a single skin muffler box. The double skin layer mufflers have the internal cylinder of the same dimensions, as the single skin one and the gap between the two layers are 0 and 0.5 cm. The elliptical shape cylinder diameters are 14 and 10 cm and 40 cm long made of 1.25 mm steel plates. The gap between the layers was 0 and 5 mm.

instrumentation: The instrumentation that has been used to collect and process model vibration data for the work described later in this section is shown in Fig. (1). The principal components are a PCB model 5353B65 acceler- ometers and PCB 086CO2 impact hammer with their corresponding line-drive supply amplifiers PCB 48OCO2, which allow low-level vibration data to be transmitted to the dynamic signal analyzer. HP 35670A dual channel signal analyser connected by a Pentium PC allows data to be collected easily and transfened directly to ME Scope Modal analysis

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software. MEScope modal Plus, VT520 Vibrant Technology is used for experimental modal analysis.

procedure: The samples were marked for the same mesh used in the finite element analysis as 72 plate elements. The meshing process was made on a turning machine by using a marker pin. Eight axial lines are at 45 for both elliptical and circular shapes. The vibration transducer was fixed on a nodal point at 5 cm from the edge on the inside surface of the single and double skin mufflers as shown in Fig. (1). The excitation was carried out on the 80 points in the radial direction and the 16 comer points were excited in the axial direction also. The input and output signals were passed into the dual channel signal analyser through two signal- conditioning amplifiers. The test models were hanged up to a fixed structure by using soft rubber strings and impacted by using the impact hammer. The vibration signal was measured by the piezoelectric accelerometer. The signals from the impact hammer and the accelerometer were conditioned through the two conditioning amplifiers. The analogue signals of the exciting force and resuking vibration are then passed onto the dual channel signal analyser, which analyses and stores those signals. The processed signals are then passed onto computer equipped with the modal analysis software package.

Fig. (1) Experimental Set-Up.

(a) Outer Surface Meshing.

P IF4

Configuration. :. (2) Model.

RESULTS & DISCUSSION: Dynamic structural analysis using FE techniques and experimental modal analysis was conducted as an effective tool in analyzing vibration and acoustical behavior of different types of cylinders to be used in silencers to control the acoustic emission from those parts. Tables (1) and (2) presents the analytical and experimental natural frequencies and damping of circular and elliptical single and double layer skin muffler cylinders. From the obtained results of natural frequencies it is clear that there is a good agreement between the analytical and experimental results. By inspecting the values of the damping factor of circular cylinders given in table (I) it can be observed that the single skin muffler have limited modes of negative damping namely mode number 16, while modes 9, 11, 12 and 14 of the double skin with 0 mm gap between layers have negative damping values. The phenomenon of negative damping was completely disappeared in the double skin muffler with a gap of 5 mm between the layers. Figures (3)

and (4) present the mode frequencies and damping of circular mufflers which are given in table (1). The inspection of the damping values in table (2) shows the completely disappearance of the negative damping in both single and double skin elliptical mufflers. The values given in table (2) have been plotted in figures (5) and (6). The obtained results motivated the thoroughly inspection of the mode shapes during their animation. Figures (7-9) present the mode shapes of circular single and double skins. The mode shapes were bending breathing and love modes. By comparing the double skin mufflers with the single skin, which is considered the internal layer, some motions in the same location were in phase and others were out of phase. Those motions, which are observed by the animation, deduce the increase of damping values in some cases and the negative damping in other cases in the 0 gap circular cylinder. The negative damping phenomena were completely disappeared in the double skin one with a gap of 5 mm because there is no chance to any contact between the skins. The same thing happened with the elliptical shape mufflers that may be due to the added stifmesses as a result of using elliptical shape. From the models frequency response function, it was observed that there is a great improvement can be obtained by using the double skin mufflers of circular shape with a suitable gap between the layers or elliptical shapes. The reduction of vibration levels was from 5-8 dB. Figures (O-14) present some frequency response functions of the tested models. With some engines the low-frequency engine vibrations are a major noise sources. Adjusting the shape and layout of the silencer, reduced resonance and sound level pressures. Double skin mufflers are proposed to verify the objective for wider frequency range. It is necessary to find method, which permit a fast and economical assessment of noise reduction by using modified FE-models, and measured data, which are applicable in muffler design. This paper reviews current trends and presents some developments in research on the prediction of acoustic behaviour in mufflers, in this particular case of passenger cars exhaust system. A new design of exhaust system is by using double skin mufflers in the silencer. This limits the frequency range of interest to below 8.6 kHz. The method which is developed in this paper can accelerate the design process by indicating and pre-estimating the sound relevant modes of a muffler boxes in an early design stage. The comparison between analytical and experimental modes can be improved careful inspection of both of them. A developed muffler diagnosis indicator ranks the most sensitive degrees of freedom of the muffler box structure in which a negative damping is

appeared. This result can be used for the model validation, and implemented in a cycle for design improvement; it can also be used for the muffler box structural judgement of implemented modifications. The main characteristics of the muffler are insertion loss, dynamic insertion, attenuation, noise reduction and muffler transmission loss. One or more expansion chambers of similar or different geometries are used to reflect and attenuate the incident sound energy in the reactive muffler. The reactive mufflers have widest applications in vehicles because their noise contains discrete tones and those mufflers are narrowband devices. The expansion chambers are inseparably frequency-selective. So, they are not efficient in reducing broadband noise. The chamber length is chosen to cancel very narrowband of frequencies and plays as a notch filter. The actual amount of attenuation is the ratio of cross- sectional area of the expansion chamber to the cross- sectional area of the connecting ducts. In this way good attenuation can be achieved by placing two identical expansion chambers in series. The expansion chamber muffler is a form of both muffler length and wave number (k = 2rt/h = lhf /C ) where k =wave length, f =frequency, and c =sound velocity. The maximum transmission loss is verified when (L = nn/2) or (L = na/4) where L = muffler length, for y1 = 1, 3, 5,. The paper shows how experimental modal analysis and finite element analysis can be combined to provide a tool for a computer aided engineering quiet design and speed up the design cycle in a new methodical way. The employing of modal analysis for such a noise reduction exercise is discussed. By using a test rig for conducting vibration measurements, comparison between prediction and experiment shows good results. The method for the experimental modal analysis of muffler boxes are introduced and verified for circular and elliptical cylinders. This model is used to predict the noise spectra in low, medium and high frequency ranges. The acoustic effects of various items of trim are added to the model as acoustic absorption coefficients to show the significance of trim in reducing low and high frequency boom in car passenger compartments.

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19 / 6002E3 1 5:971E3 1 719.255E-3 1 5633E3 ) 5.615E3 1 784.8OOE-3 I I I 20 / 6 155E3 / 6 144E3 1 946900E-3 1 6.17E3 / 6.192E3 j 898.900E-3 I

Table (1) The Frequencies and Damping of Circular Shapes.

+Circular Single Skin Th. ACircular Double Skin (Gap=O.O) Th. XCircular Double Skin (Gap-OSmm) Th.

q Circular Single Skin Ex. XCircular Double Skin (Gap=O.O) Ex. l Circular Double Skin (Gap=O.Smm) Ex.

4000 mm- *Y

Fig. (3) Frequency of Single and Double Skin Circular Mufflers.

90

5 ..jo 5 z 40 50

.? 30 E 20 d IO

Mode #

Fig. (4) Damping Factors of Single and Double Skin Circular Mufflers.

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Mode #

Single Layer Double Layers

Frequency Damping Frequency Damping ml\ IO,\

_._.. -_ ..__ 1.022E3 1.951

-.._ _._. _-_ , 3.533E3 1.222 1.025 4039E3 4.037E3 1.148 965.315E-3 4.783 4.561E3 1.291

873.200E.3 , 1.433 5.01E3 5.020E3 j 5.530E3 I 1127 5.802E3 5.568E3 893.300E-3 1 6.069E3 1 809 6998-3 6.2lE3 6.040E3 966.4 I 6.547E3 I 455.982E-3 6.582E3

1

L 15 1 7033E3 I 7.029E3 1 825.525E-3 16 1 7.477E3 I 7.578E3 1 556.7348-3 17 1 860E3 I 8.078E3 I 449.7486-3

Ta

~~

ping of Elliptical Shapes. ble (2) The Frequencies and Dam

+Elliptical Single Skin Th. AElliptical Single Skin Ex. XElliptical Double Skin Th. n Elliptical Double Skin Ex.

10000. 9000 8000 7000 6000 5000 4000 3000 2000 1000

0 1 2 3 4 5 6 7 8MoJe#10 11 12 13 14 15 16 17

Fig. (5) Frequency of Elliptical Mufflers.

*Elliptical Single Skin WElliptical Double Skin 60

q

0 1 2 3 4 5 6 7 8 $dJ~ II 12 13 14 15 16 17

Fig. (6) Damping of Elliptical Mufflers.

1198

Fig. (7) Some Mode Shapes of Circular Single Skin Muffler.

1199

j

.i _-- ._. --.-.-- _..---- ----_

: ---__ .__- I _._. - -__. - -- _.^_ ~ _-._ -_ .-

..L _---__ -~-.. -_--- ~----- ---.

,j- _-____ -.--- -..-- -._.__ rye

3

Fig. (8) Some Mode Shapes of Circular Double Skin Muffler (gap=0 mm.).

1200

I

I .^ - A.4 L-- x -2

1 .c_ n.. I I--- I

1

/ ! -m

Fig. (9) Some Mode Shapes of Circular Double Skin Muffler (gap=Smm.).

1201

Fig. (10) Some Frequency Response Functions of Circular Single Layer Skin.

Fig. (11) Some Frequency Response Functions of Circular Double Skin Muffler (gap=Omm.).

4 zmn ,.m* P .sok l=m om Z&d loclX Hr tiL 1.37nl

13 da2 R.-l

P 533m

be3vn

Pwta

Fig. (12) Some Frequency Response Functions of Circular Double Skin Muffler (gap=5mm.).

1202

672.m

519m

Red

36&n

21.4iu

6,1&a

tK3 FI.q l=Xm C2ZilP NW6

0.00 SMk (Sl.Zm@ 6.432t4 HZ

lO.Ok

Fig. (13) Some Frequency Response Functions of Elliptical Single Skin Mulller.

453,

Rsmk

33zm

Io.lra

I

SMlk nr

R.rl

3a.4m

6s.Irn

FL*rl

.%.sb

t I r - 1

SBOk IO.Ok 473%

1 6Wm o.ixl S.o#k kO.Ok liz

5Mk u-

Fig. (14) Some Frequency Response Functions of Elliptical Double Skin Mulller.

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CONCLUSIONS: 1. Adjusting the shape and layout of the silencer by

using double skin mufflers, can reduce resonance and sound level pressures.

2,Finite element methods and experimental modal analysis are used successfully to analyse a reactive muffler for vehicle exhaust system.

3. A developed muffler diagnosis indicator ranks the most sensitive degrees of freedom of the muffler box structure in which a negative damping is appeared. This result can be used for the model validation, and implemented in a cycle for design improvement; it can also be used for the muffler box structural judgement of implemented modifications.

4. The method can be applied to determine the acoustic modes and to study the interaction of the structural modes of the muffler boxes.

5.Noise source survey technology has advanced significantly, allowing accurate and efficient proximate measurement of once difficult-to-specify noise sources, low-frequency noise sources and noises with multiple source components.

6.Noise sources in the over 2khz range which were previously difficult to survey can now be surveyed by using experimental modal analysis methods.

7,Mufflers are widely used in industry for noise reduction in vehicles or exhaust pulsation attenuation in machinery. Various modeling schemes have been employed in the past for the analysis of muffler acoustical performance. However, it is often encountered in practical applications that a suitable modeling method must be chosen for each specific case because all modeling methods have different advantages and limitations.

REFERENCES: [l]. Peter C. C., Evaluation of Several Analytical

Methods on Muffler Acoustic Modeling, Noise Control Engineering J., Vol. 46, No. 3, May- Jun., 1998, PP 109-l 19.

[Z]. Lai Peter C. C. & Soedel Werner, Free Gas Pulsation of a Helmholtz Resonator Attached to a Thin Mufler Element, Noise and Vibration Research (SAE) Special Publications, Vol. 1363, Feb 1998, SAE, Warrendale, PA, USA, PP 49- 58.

[3]. Lai P. C. C. & Soedel W., Two-Dimensional Analysis of Thin Shell- or Plate-Like Mufler Elements of Non-Uniform Thickness, J. of Sound & Vibration, Vol. 195, No. 3, Aug 22, 1996, PP 445-475.

[4]. Phillips Allyn W., Simulation Environment for the Investigation of Measurement Errors in Lightly Damped Structures, Froc. of the Ilfi Int. Modal Analysis Conf.. Part 1, Kissimmee, FL, USA, Feb. l-4, 1993, PP 340-349.

IS]. Okubo N. & Takeuchi K. Development of Acoustic Building Block Approach and its Application, Proc. of the 11 Int. Modal Analysis Conf., Kissimmee, FL, USA, Feb.l-4, 1993, PP 13751379

161. Petronijevic Z. & Kojic A., ModelZing of Chamber Mufflers by Four-Pole Electrical Ducts, Int. .I. of Vehicle Design, Vol. 17, No. 1, 1996, PP 92-104.

[7]. Hong K. & Kim J., Natural Mode Analysis of Hollow and Annular Elliptical Cylindrical Cavities, .I. of Sound & Vibration, Vol. 183, No. 2, June 1, 1995, p 327-351.

IS]. Cazzolato B. S., Howard C.Q. & Hansen C. H., Finite Element Analysis of an Industrial Reactive Silencer, Proc. of 5 Int. Comgress of Sound & Vibration, 1997, PP 1659-1668.

(91. Seybert A. F., McMains T. H. & Rouch K. E., Acoustical Analysis Using Finite Elements and Bounday Elements, 4 Int-ANSYS Conf. & Exhib. 1989, Part 2, PA, USA. PP 7.26-7.41, Pittsburgh, PA, USA. May l-5,1989.

[lo]. Kim Heung Seob, Hong Jin-Seok & Oh Jae Eung A. F., Active Noise Control with the Active Muffler in Automotive Exhaust Systems, JSME Int. J., Series-C, Vol.41, No. 2, Jun 1998, PP 178-183.

[Ill. Krause P. Weltens H & Hutchins S. M., Advanced Design of Automotive Exhaust Silencer Systems, Worldwide Passenger Car Conference and Exposition. Dearborn, MI, USA, Sep. 28-act. 1,1992, SAE Technical Paper Series, SAE, Warrendale, PA, USA, 9220, 88., PP l-11.

[12]. Steel J. A., Farser G. & Sendall P., A Study of Exhaust system Noise, Proc. of the Instn. of Mechanical Engineers Part D, J. of Automobile Engineering, V. 214: (Dl), 2000, PP 75-83.

ACKNOWLEDGEMENTS: The author would like to thank the support of M&ERI, NWRC, Egyptian Ministry of Irrigation and Water Resources for the experimental facilities they have offered me to conduct this work, in particular to Prof. H&l and Dr. Abdel Rahman. Also the author would like to thank the support of the Mechanical Engineering Department, the University of Dundee, in particular to Prof. Jim Hewit the Professor of Mechanical Engineering for the computing and other facilities he has offered me to conduct this paper.

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