the effect of perforation on the dynamics of a flexible panel

8/10/2019 The effect of perforation on the dynamics of a flexible panel

1/18


2/18

Advances in Acoustics and Vibration

Patil et al. [] also used a curve tting technique todevelop an effective resonant requency ormula rom simu-lation data or ve perorated plates using FEM. Te ormulawas a unction o the so-called mass remnant ratio (MR),that is, the ratio o surace area o a perorated plate to thato the solid plate or the same dimension. Te ormula was

then expressedas a seventh order polynomial unction o MR.However, the ormula was applicable only or the rst threemodes o vibration.

Recently, Mali and Singru [] proposed a technique usingconcentrated negative mass in the Galerkin method to modelthe natural requency o a perorated plate. It is shown thatthe analytical results are in good agreement with those roma FEM model, but only or small size o holes.

As previous works were concerned with only the dynamicproperties o the peroration, this paper investigates thechange o vibration level due to the introduction o holes intoa solid panel. As no established analytical model is available

to calculate the mobility o the peroration, the numeri-cal model is thereore implemented using Finite ElementMethod (FEM). Te numerical calculation o mobility o theperoration is then compared against that o the solid plate inone-third octave band requency.

2. Mobility

.. Teoretical Model. Mobility is dened as the ratiobetween the vibration velocity Vand the excitation orcegiven as a unction o requency,() = V()/(). For anite rectangular plate with dimensions , the mobility atan arbitrary point

(,)subjected to a point orce

at

(

,

)is given by []

()= =1

, ,21 + 2 , ()

where is theth mass-normalized mode shape o thestructure, is theth natural requency, and is thedamping loss actor. A case ofen considered is that o arectangular plate with simply supported boundary conditionsas this system provides a simple analytical solution. For asimply supported rectangular plate, the mode shape can berepresented by sine unctions. Tis and the natural requency

or mode(, )are, respectively, , = 2sin

sin

,

=

2 + 2 ,

()

whereis the total mass o the plate,is the mass per unitarea, and = 3/12(1 V2)is the plate bending stiffnessor is Youngs modulus, is the plate thickness, and isPoissons ratio. Te next section discusses the FE model usedto calculate the mobility o the perorated plate.

x

y

z

a = 0.3 m

Xb =0.2 m

(0,0)

X = excitation and

response point

F : Schematic diagram o the panel and the excitation point.

.. Finite Element (FE) Model

... Validation with Teory. Te model o the peroratedpanel is developed here using PARAN and NASRANsofware programs. In order to ensure the FE model used is

valid in terms o the element size and setting o the boundarycondition, the result is validated against the theoreticalmobility as in ().

A FE model o a solid panel having dimensions o.. m and thickness mm is developed with simplysupported condition along all the edges. Te panels are madeo aluminium having Youngs modulus o GPa, density o

kgm3, and Poissons ratio o .. Te D shell elementsare used to model plate structures where a shell structure car-ries loads in all directions and thereore undergoes bendingand twisting, as well as in-plane deormation [].

Te mesh element type used in the FE model is the basictwo-dimensional triangular element (ria shape and Paver).Te element size is set to be much smaller than hal o thestructural wavelength corresponding to the maximum re-quency o analysis to give accurate results at high requencies.Te global edge length o each element is set to be . mwhich is sufficient to provide accurate result up to kHz.Te plate was set to be an ideal simply supported boundarycondition, where the displacement is restrained at the plateedges, but the rotation is set to be ree. Te location othe excitation orce and the response are the same or allsimulated plates or consistency o plate mobility analysis.

An excitation orce o N is applied slightly away romthe centroid o the panel at coordinates (., .) where the(,) is at the bottom lef corner o the plate as illustrated inFigure . Tis is to generate optimum numbers o vibration

modes particularly at low requencies. Te damping lossactor is set to be . which is a typically small value ormost engineering structures. Te vibration level o the panelis analyzed in the requency range o Hz to kHz. From theFE calculation, by extracting the vibration velocity rom theresponse point and as a unit orce was used, this result givesthe mobility. Te result is postprocessed using MALAB.For the theory, the calculation was also perormed usingMALAB or modes ( = 20, = 20) up to kHzwith the same location o excitation orce and response aswell as the value o the damping actor. Te comparisono the results is shown inFigure (a)with good agreementparticularly below kHz. Above kHz, small discrepancies


3/18


Mo

bility

(m

/Ns)

FE model

Teory

Frequency (Hz)

101 102 103

101

100

101

102

103

(a)

Frequency (Hz)

FE model

Teory

100

90

80

70

60

50

40

30

20

10

0

101 102 103 104

Mo

bility

(dbre

1m/Ns)

(b)

F : Comparison o mobility o a solid panel rom FE model and rom analytical calculation: (a) narrow band and (b) one-third octaveband.

(a) (b)

F : Examples o the Finite Element model o the perorations with different mesh size represented by the global edge length (GEL): (a)GEL = mm and (b) GEL = mm.

can be observed, but the average level is almost the same asseen in one-third octave band requencies inFigure (b).

In order to ensure the right meshing is used in this study,the effect o the size o the mesh is also investigated bysimulating the mobility o a perorated panel with different

global edge length (GEL) o the mesh. Figure shows twoexamples o the FE model with different meshing size.Figure plots the mobility or our different GELs. It can beobserved that the results or perorated plates with GEL = mm and mm havethe same results which collapsetogetheror the corresponding requency range. For larger GEL, thatis, GEL = mm and GEL = mm, the mobility shifs tohigher requency. Tus, or the rest o the simulation, GEL= mm is used in this study.

... FE Model for Perforated Panels. Te simulated sam-ples o perorated panels are determined by varying theperoration ratio with xed diameter or number o holes

: Parameters o theperoratedpanelwith xed hole diameterand different number o holes and peroration ratio.

Name Number o holes Diameter

(mm)Peroration ratio

(%)

P-- P--

P--

and also by varying the diameter and number o holes withxed peroration ratio. For comprehensive study, this alsoincludes the arrangement o holes in the plate, which can bea triangular pattern (usually reerred to as diagonal pattern)or a square array as well as the hole distributions in theplate, that is, those concentrated on the middle or along theplate edges. Te choice o these parameters is summarizedin ables , , , , and. For convenience o reerring o


4/18


Frequency (Hz)

101 102 103 104

101

100

101

102

103

= 21%, GEL= 0.003 m

= 21%, GEL= 0.005 m

= 21%, GEL= 0.010 m

= 21%, GEL= 0.020 m

Mo

bility

(dbre1m/Ns)

F : Mobility o a solid plate with different global edge length o the mesh.

: Parameters o the perorated panel with different holediameter and number o holes and xed peroration ratios.



(%)

P--

P--

P--

P--

P-- P--

P--

P--

P--

: Parameters o the perorated panel with xed number oholes and different hole diameter and peroration ratio.



(%)

P-- P--

P--

P--

the plate, each perorated plate is named according to itsparameter, where the rst part o the numbers indicates thenumber o holes,the secondpart is the diameter, andthe thirdpart is the peroration ratio. Te plate parameters are chosento represent any possibilities o peroration conguration inpractice.Figure shows examples o the Finite Element (FE)

: Parameters o the perorated panel with different holedistributions.

Name Number o

holesDiameter


(%)

P--

P---edge

P---center

P--

P---edge P---center

: Parameters o the perorated panel with different holearrays.

Name Number o

holesDiameter


(%)

P--

P---tria

P--

P---tria

model o perorated panels rom PARAN sofware with themesh condition as described inSection ...

... Validation with Experiment. A modal test is carriedout to validate the FE result. Te experimental setup ormeasuring the mobility is shown in Figure . o realisethe ree-ree boundary conditions, the plate was hung ver-tically using light-rope. At the same location where theKistler instrumented hammer stroked, a DYRAN tear-drop accelerometer was attached to the plate to measure


5/18


(a) (b)

(c) (d)

(e) ()

(g) (h)

F : Examples o the Finite Element model o the perorations. Fixed hole diameter: (a) P-- and (b) P--; xed perorationratio: (c) P-- and (d) P--; different hole arrangement: (e) P-- and ( ) P--; different hole distribution: (g) P---edge and (h) P---center.

Accelerometer

Hammer

Analyser

Computer

F : Experimental setup or mobility measurement using impact hammer.


6/18


FE model, solid

Experiment, solid

Frequency (Hz)

101 102 103

101

102

100

101

102

103

104

Mo

bility

(1m/Ns)

(a)

Frequency (Hz)

101 102 103

101

102

100

101

102

103

104

Mo

bility(1m/Ns)

Experiment,N = 40,d = 14mm, = 10%FE model,N = 40,d = 14mm, = 10%

(b)

Frequency (Hz)

101 102 103

101

102

100

101

102

103

104

Mo

bility

(1m/Ns)

FE model,N = 20, d = 28 mm, = 21%Experiment,N = 20, d = 28 mm, = 21%

(c)

Frequency (Hz)

101 102 103

101

102

100

101

102

103

104

Mo

bility

(1m/Ns)

FE model,N = 20, d = 28 mm, = 21%Experiment,N = 20, d = 28 mm, = 21%

(d)

F : Comparison o the mobility or solid and perorated panels rom FE model and experiment: (a) solid and (b)-(c) perorated panelsat different peroration ratio. (d) ranser mobility or xed peroration ratio o %.

the plate acceleration. Te signal was recorded and processed

using Data Physics signal analyzer.Figure shows the resultsrom the FE models and the experiment where satisactoryagreement is achieved. Small discrepancies occur whichmight be due to the nonuniormity o the panel in theexperiment which is different rom the ideal plate dened inthe FE model.

3. Simulation Results and Discussion

Te numerical results rom the FE model are presented inone-third octave bands to observe the average level omobility in a requency band rather than to deal with detailso discrepancies in the narrow band. Also or convenience

o analysis, it is o interest to observe the amount o mobil-

ity level which increases due to peroration. Tis can beexpressed with the effect o peroration in dB unit by

= 20 log10 , ()

where is the mobility o the perorated plate and is orthe solid plate. Te results are presented or both mobilityYand effect o perorationXpositioned side-by-side.

.. Effect of Hole Diameter and Number of Holes at FixedPerforation Ratio. In Figure , it is shown that, by comparingthe solid and the perorated plates, introduction o pero-ration increases the mobility rom low to high requency.


7/18


N = 40,d = 14mm, = 10%

N = 80, d = 10 mm, = 10%N = 20, d = 20 mm, = 10%

Solid plate

100

80

60

40

20

20

0

Mo

bility(d

bre1m/Ns)

Frequency (Hz)

101 102 103 104

(a)

20

10

70

60

50

40

30

20

10

0

N = 40,d = 14 mm, = 10%

N = 80, d = 10 mm, = 10%N = 20, d = 20 mm, = 10%

X

(dBre

f1m/Ns)

Frequency (Hz)

101 102 103 104

(b)

N = 20, d = 28 mm, = 21%

N = 30,d = 23 mm, = 21%

N = 40,d = 20 mm, = 21%

100

80

60

40

20

20

0

Mo

bility(dbre1m/Ns)

Frequency (Hz)

101 102 103 104

Solid plate

(c)

N = 20, d = 28 mm, = 21%

N = 30,d = 23mm, = 21%

N = 40,d = 20 mm, = 21%

20

10

70

60

50

40

30

20

10

0X

(dBre

f1m/Ns)

Frequency (Hz)

101 102 103 104

(d)

N = 20, d = 34 mm, = 30%

N = 30, d = 28 mm, = 30%

N = 58, d = 20 mm, = 30%

100

80

60

40

20

20

0

Mob

ility(dbre1m/Ns)

Frequency (Hz)

101 102 103 104

Solid plate

(e)

N = 20, d = 34 mm, = 30%

N = 30,d = 28 mm, = 30%

N = 58,d = 20 mm, = 30%

20

10

70

60

50

40

30

20

10

0X

(dBre

f1m/Ns)

Frequency (Hz)

101 102 103 104

()

F : Mobility ((a), (c), and (e)) and effect o peroration ((b), (d), ()) o the perorated panels with different hole diameters and numbero holes at xed peroration ratio.


8/18


Frequency (Hz)

101 102 103 104100

80

60

40

20

20

0

Mo

bility(dbre

1m/Ns)

N = 40, d = 10mm, = 5%

N = 80, d = 10 mm, = 10%

N = 160, d = 10 mm, = 21%

Solid plate

(a)

Frequency (Hz)

101 102 103 104

20

10

70

60

50

40

30

20

10

0

X

(dBre

f1m

/Ns)

N = 40, d = 10mm, = 5%N = 80, d = 10 mm, = 10%

N = 160, d = 10 mm, = 21%

(b)

Frequency (Hz)

101 102 103 104100

80

60

40

20

20

0

Mo

bility(dbre1m/Ns)

N = 40,d = 10mm, = 5%

N = 40,d = 15 mm, = 12%

N = 40,d = 20 mm, = 21%

Solid plate

(c)

Frequency (Hz)

101 102 103 104

20

10

70

60

50

40

30

20

10

0

X

(dBre

f1m/Ns)

N = 40,d = 10 mm, = 5%N = 40,d = 15 mm, = 12%

N = 40,d = 20 mm, = 21%

(d)

F : Mobility ((a), (c)) and effect o peroration ((b), (d)) o the perorated panels with xed hole diameter and xed number o holes.

Te level o increment becomes greater as the perorationratio increases. However, among the perorated plates withxed peroration ratio, varying the hole diameter as well asthe number o holes does not have signicant change onthe mobility except at high requencies (above kHz). Tiscan also be seen in the effect o peroration results. Te

variation o mobility or different hole diameters (with xedperoration ratio) can be clearly observed as the perorationratio is increased. Te largest hole diameter gives the highestmobility at high requencies. Tis indicates that, at highrequencies, the mobility o the perorations depends on thehole density in the panel where large hole density (manyholes, but smaller) is preerred to reduce vibration. Larger

hole density hasalso beenshownto produce the greatestnoisereduction effect [,].

It should be noted here that the high peaks shownin the effect o peroration at low requencies below kHz, or example, at the undamental requency o the plate,that is, Hz, are the effects due to the natural requencyshif because o peroration [], although the level at theundamental requency as seen in Figure (e) is alsoincreased by roughly dB compared to the level at theundamental requency o the solid plate.

.. Effect of Perforation Ratio at Fixed Hole Diameter or FixedNumber of Holes. Te effect o increasing the peroration


9/18


Frequency (Hz)

101 102 103 104100

80

60

40

20

20

0

Mo

bility(dbre1m/Ns)

Square,N = 40,d = 14mm, = 10%

riangular,N = 41,d = 14 mm, = 10%

Solid plate

(a)

Frequency (Hz)

101 102 103 104

20

10

70

60

50

40

30

20

10

0

X

(dBre

f1m/Ns)

Square,N = 40,d = 14mm, = 10%

riangular,N = 41,d = 14 mm, = 10%

(b)

Frequency (Hz)

101 102 103 104100

80

60

40

20

20

0

Mo

bility(dbre1m/Ns)

Square,N = 40,d = 20 mm, = 21%

riangular,N = 41, d = 20 mm, = 21%

Solid plate

(c)

Frequency (Hz)

101 102 103 104

20

10

70

60

50

40

30

20

10

0

X

(dBre

f1m/Ns)

Square,N = 40,d = 20 mm, = 21%

riangular,N = 41, d = 20 mm, = 21%

(d)

F : Mobility ((a), (c)) and effect o peroration ((b), (d)) o the perorated panels with different hole arrays and at xed perorationratio.

ratio, by maintaining the hole diameter and by increasingthe number o holes, is plotted inFigure where, as alreadydiscussed, the mobility increases as the peroration ratioincreases.Figure (b)shows that, or % peroration ratio,the mobility can increase to almost dB.

.. Effect of Hole Arrays at Fixed Perforation Ratio. Fordifferent peroration arrays, that is, square and triangular, atxed peroration ratio inFigure , both peroration arraysalso show less signicant effect on theplatemobilitywith eachother. Te mobility again increases as the peroration ratio is

increased (c. Figures(b)and (d)). Tis again conrmsthat it is the number o holes per unit area (hole density)which affects the plate mobility, not the hole arrays.

.. Effect of Holes Arrangement at Fixed Perforation Ratio.For different arrangement o holes, that is, uniorm acrossthe plate surace, at the edges o the plate and at the centero plate, the result gives different mobility level or xedperoration.Figure shows that the panel with centralizedarrangement o holes shows the highestincrement o mobilitylevel, ollowed by the uniormly distributed holes across the


10/18


Frequency (Hz)

101 102 103 104100

80

60

40

20

20

40

0

Mo

bility(dbre

1m/Ns)

Solid plate

N = 40, d = 14mm, = 10%uniform

N = 40,d = 14 mm, = 10%edge

N = 40,d = 14 mm, = 10%center

(a)

Frequency (Hz)

101 102 103 104

20

20

40

60

80

0

X

(dBre

f1m/N

s)

N = 40, d = 14 mm, = 10%uniform

N = 40,d = 14 mm, = 10%edge

N = 40,d = 14 mm, = 10%center

(b)

Frequency (Hz)

101 102 103 104100

80

60

40

20

20

40

0

M

obility(dbre1m/Ns)

Solid plate

N = 20, d = 28 mm, = 21%uniform

N = 20, d = 28 mm, = 21%edge

N = 20, d = 28 mm, = 21%center

(c)

Frequency (Hz)

101 102 103 104

20

20

40

60

80

0

X

(dBre

f1m/Ns)

N = 20, d = 28 mm, = 21%uniform

N = 20, d = 28 mm, = 21%edge

N = 20, d = 28 mm, = 21%center

(d)

F : Mobility ((a), (c)) and effect o peroration ((b), (d)) o the perorated panels with different hole arrangement.

plate and the holes at the edges o the plate. Te holes at theplate edges can be a useul design or a noise control measurewhere noise can be reduced at a particular requency range,that is, at the edge mode region [].

Te mobility can be signicantly increased orhigher per-oration ratio or the centralized holes which can obviouslybe seen in the effect o peroration in Figures(b)and(d). Te stiffness o the plate reduces signicantly when theconcentration o the holes is moved towards the center o the

panel, but no effect is obvious rom the mobility result whenthe holes are spread away rom the center and concentratedto the plate edges.

.. Effect of Boundary Condition. It is also interesting toobserve the effect o the boundary conditions to ensure thegenerality o the conclusion drawn rom the study. Anothertwo sets o perorated panels rom FE models with ree-reeand clamped-clamped boundary conditions are developed


11/18


12/18


Frequency (Hz)

101 102 103 104100

80

60

40

20

20

0

Mo

bility(dbre

1m/Ns)

N = 40, d = 10mm, = 5%

N = 80, d = 10 mm, = 10%

N = 160, d = 10 mm, = 21%

Solid plate

(a)

Frequency (Hz)

101 102 103 104

20

10

70

60

50

40

30

20

10

0

X

(dBre

f1m

/Ns)

N = 40, d = 10 mm, = 5%

N = 80, d = 10 mm, = 10%

N = 160, d = 10 mm, = 21%

(b)

Frequency (Hz)

101 102 103 104100

80

60

40

20

20

40

0

Mo

bility(dbre1m/Ns)

Solid plateN = 20, d = 28 mm, = 21%uniform

N = 20, d = 28 mm, = 21%edge

N = 20, d = 28 mm, = 21%center

(c)

Frequency (Hz)

101 102 103 104

20

40

100

60

80

40

20

0X

(dBre

f1m/Ns)

N = 20, d = 28 mm, = 21%uniform

N = 20, d = 28 mm, = 21%edge

N = 20, d = 28 mm, = 21%center

(d)

F : Mobility ((a), (c)) and effect o peroration ((b), (d)) o the perorated panels or ree-ree edges or (a)-(b) xed hole diameterwith increasing peroration ratio and (c)-(d) different arrangement o holes at xed peroration ratio.

separation between holes is large (Figures (a)and (b)).Tis is because the local stiffness around the hole is lowercompared to the one away rom the hole and thus increasesthe mobility. As the hole separation becomes smaller, theprevious localized stiffness reduction now becomes moreglobal across the plate. Hence, or larger peroration ratios,the change o the mobility due to the change o the responselocation is not too obvious as seen in Figures(c)-(d)and(e)-().

Figure shows the contour o stress distribution cal-culated rom PASRAN and NASRAN which can beassociated with the phenomena o stiffness reduction. It canbe observed that the highest stress level is concentratedonly around the excitation point close to the hole or smallperoration ratio as seen in Figure (a). Te concentrationo the stress distributes to more holes as the holes arecloser together (high peroration ratio) as in Figure (b).As the holes become more closer as shown in Figure (c),


13/18


Solid plate

Frequency (Hz)

101 102 103 104100

80

60

40

20

20

40

60

0

Mo

bility(dbre1m/Ns)

N = 20, d = 28 mm, = 21%

N = 30,d = 23mm, = 21%N = 40,d = 20mm, = 21%

(a)

Frequency (Hz)

101 102 103 104

20

10

70

60

50

40

30

20

10

0

X

(dBre

f1

m/Ns)

N = 20, d = 28 mm, = 21%N = 30,d = 23 mm, = 21%

N = 40,d = 20 mm, = 21%

(b)

Solid plate

Frequency (Hz)

101 102 103 104100

80

60

40

20

20

0

Mo

bility(dbre1m/Ns)

riangular,N = 41, d = 20 mm, = 21%

N = 40, d = 20mm, = 21%Square,

(c)

Frequency (Hz)

101 102 103 104

20

10

70

60

50

40

30

20

10

0

X

(dBre

f1m/Ns)

riangular,N = 41,d = 20 mm, = 21%

N = 40, d = 20mm, = 21%Square,

(d)

F : Mobility ((a), (c)) and effect o peroration ((b), (d)) o the perorated panels or clamped-clamped edges or (a)-(b) xedperoration ratio and (c)-(d) different arrays o holes at xed peroration ratio.

the level o stress increases and almost all holes have highconcentration o stress.

4. Conclusion

Te mobility o perorated plates with varying holes geome-tries and peroration patterns has been investigated by usingFinite Element Method. It is ound that the mobility increasesas the peroration ratio increases. For a xed perorationratio, however, the small hole density (small number, butlargediameter holes) gives the most effect to increase vibration

at high requency. Te effect can also be seen or holesconcentrated in the center o the panel, where vibrationcan be signicantly increased compared to those distributeduniormly or arranged around the plate edges at a xedperoration ratio. Te peroration arrays (either triangularor square) were shown to have insignicant effect on theplate mobility or the same peroration ratio. Te samephenomenon is also ound or different boundary conditions,that is, ree-ree and clamped-clamped edges, where theresults show a similar trend o the effect o perorationwith that rom the simply supported edges. Te orcing and


14/18


Frequency (Hz)

101 102 103 104100

80

60

40

20

20

40

60

0

Mo

bility(dbre

1m/Ns)

N = 40, d = 10mm, = 5%

N = 80, d = 10 mm, = 10%

N = 160, d = 10 mm, = 21%

Solid plate

(a)

Frequency (Hz)

101 102 103 104

20

10

70

60

50

40

3020

10

0

X

(dBre

f1m

/Ns)

N = 40, d = 10mm, = 5%

N = 80, d = 10 mm, = 10%

N = 160, d = 10 mm, = 21%

(b)

Frequency (Hz)

101 102 103 104100

80

60

40

20

20

40

60

0

Mo

bility(dbre1m/Ns)

Solid plate

N = 20, d = 28 mm, = 21%uniform

N = 20, d = 28 mm, = 21%edge

N = 20, d = 28 mm, = 21%center

(c)

Frequency (Hz)

101 102 103 104

20

80

60

40

20

0

X

(dBre

f1m/Ns)

N = 20, d = 28 mm, = 21%uniform

N = 20, d = 28 mm, = 21%edge

N = 20, d = 28 mm, = 21%center

(d)

F : Mobility ((a), (c)) and effect o peroration ((b), (d)) o the perorated panels or clamped-clamped edges or (a)-(b) xed holediameter with increasing peroration ratio and (c)-(d) different arrangement o holes at xed peroration ratio.

response location at the plate can also give different results.For low peroration ratio or low density (low number oholes per unit area), the mobility is more sensitive aroundthe vicinity o the hole and thereore response locationaround this area gives higher mobility. As the perorationratio increases, where the holes become much closer together(higher hole density), the location o the response becomesinsensitive to the mobility result. Tis is due to the globalstiffness reduction throughout the individual area o the

holes and thus throughout the surace o the plate. All thesendings can be used as the general guidance in designing

vibrating structures with perorated plates.

Conflict of Interests

Te authors declare that no nancial relation exists eitherdirectly or indirectly between the authors andthe commercialentities mentioned in the paper.


15/18


Frequency (Hz)

101 102 103 104100

80

60

40

20

20

0

Mo

bility(dbr

e1m/Ns)

N = 40, d = 10mm, = 5%, point 1

N = 40,d = 10 mm, = 5%, point 2

(a) (b)

Frequency (Hz)

101 102 103 104100

80

60

40

20

20

0

Mo

bility(dbre1m/Ns)

N = 40,d = 14mm, = 10%, point 1

N = 40,d = 14mm, = 10%, point 2

(c) (d)

Frequency (Hz)

101 102 103 104100

80

60

40

20

20

0

Mobility(dbre1m/Ns)

N = 40,d = 20 mm, = 21%, point 1

N = 40,d = 20 mm, = 21%, point 2

(e) ()

F : Mobility ((a), (c), and (e)) and different response location ((b), (d), and ()) at perorated panels.


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X

Y

Max3.52 + 007 @Nd 261Min1.77 + 006 @Nd 374

3.52 + 0073.30 + 0073.07 + 0072.85 + 0072.63 + 007

2.41 + 0072.18 + 0071.96 + 0071.74 + 0071.51 + 0071.29 + 0071.07 + 0078.45 + 0066.22 + 0063.99 + 0061.77 + 006

Default fringe:

(a)

X

Y

4.23 + 0073.96 + 0073.68 + 0073.41 + 0073.13 + 0072.86 + 0072.58 + 0072.31 + 0072.03 + 0071.76 + 0071.48 + 0071.20 + 0079.29 + 0066.54 + 0063.78 + 0061.03 + 006

Max4.23 + 007 @Nd 517Min1.03 + 006 @Nd 32

Default fringe:

(b)

X

Y

4.55 + 0074.26 + 0073.96 + 0073.67 + 0073.37 + 0073.08 + 0072.78 + 0072.49 + 0072.19 + 0071.90 + 0071.61 + 0071.31 + 007

1.02 + 0077.23 + 0064.29 + 0061.34 + 006

Max4.55 + 007 @Nd 461Min1.34 + 006 @Nd 32

Default fringe:

(c)

F : Stress contour o the perorated panels with different hole densities: (a) small hole density, (b) large hole density, and (c) holeconcentrated at the center.


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Acknowledgment

Te nancial support or this project is provided by theUniversiti eknikal Malaysia Melaka under the Short ermResearch Grant no. PJP//FKM (C)/S.

References[] A. Putra andD. J. Tompson, Sound radiation rom perorated

plates, Journal of Sound and Vibration, vol. , no. , pp., .

[] A. Putra andD. J. Tompson, Radiation efficiency o unbaffledand perorated plates near a rigid reecting surace,Journal ofSound and Vibration, vol. , no. , pp. , .

[] R. Bailey and R. Hicks, Behavior o perorated plates underplane stress,Journal of Mechanical Engineering Science, vol. ,pp. , .

[] W. J. ODonnel and B. F. Langer, Design o perorated plates,Journal of Manufacturing Science and Engineering, vol., no. ,pp. , .

[] A. I. Soler and W. S. Hill, Effective bending properties orstress analysis o rectangular tube sheets,Journal Engineeringfor Power, vol. , no. , pp. , .

[] M. Forskitt, J. R. Moon, and P. A. Brook, Elastic properties oplates perorated by cusp-shaped holes,Applied MathematicalModelling, vol. , no. , pp. , .

[] K. A. Burgemeister and C. H. Hansen, Calculating resonancerequencies o perorated panels,Journal of Sound and Vibra-tion, vol. , no. , pp. , .

[] D. C. Patil, S. S. Gawade, and K. D. Mali, Dynamic responseanalysis o rectangular perorated plates with varying sizes ocircular peroration holes, inProceedings of the Interna-tional Congress on Sound and Vibration, Cairns, Australia, July.

[] K. D.Mali andP. M. Singru, Determination o theundamentalrequency o perorated rectangular plates: concentrated nega-tive mass approach or the peroration,Advances in Acousticsand Vibration, Article ID , .

[] P. Gardonio and M. J. Brennan, Mobility and impedancemethods in structural dynamics, inAdvanced Applications inAcoustics, Noise and Vibration, F. J. Fahy and J. G. Walker, Eds.,chapter , CRC Press, .

[] S. S. Quek and G. R. Liu, Finite Element Method: A PracticalCourse, vol. , .

[] F. J. Fahy and P. Gardonio, Sound and Structural Vibration:Radiation, ransmission and Response, Academic Press, Oxord,UK, .


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