96 free-field microphone type 40AE and ½ inch CCP
preamplifier type 26CA to record the incident sound and the reflected sound from the sample.
3. RESULTS AND DISCUSSION 3.1 Effect of thickness of fiber
Figure 3 shows the sound absorption coefficient of kenaf fiber for different thicknesses. The result shows
that sample with thickness of 10 mm has absorption coefficient greater than 0.5 above 3500 Hz. Whereas,
for the 30 mm sample, the absorption coefficient is greater than 0.5 above 1000 Hz and approaches unity at
around 2000 Hz. The increment of the thickness can be seen to significantly improve the absorption coefficient.
3.2 Effect of air gap
Figure 4 shows the sound absorption measured on a 20 mm thick kenaf fiber, with different air gap
thicknesses.
The results show that the peak shifts to lower frequency as the air gap increases, but in consequences,
the absorption at high frequencies are reduced. Figure 5 plots the sound absorption coefficient of fiber with
thickness of 10 mm, measured with rigid backing, and 10 mm of air gap. This also compared with 20 mm fiber.
Comparing the 10 mm without and with air gap backing, the latter has greater absorption coefficient as
already shown in Figure 4. However, with identical total thickness, i.e. for 20 mm fiber and 20 mm fiber-air, the
performance of air gapped fiber is lower than that from the sample with more fibers.
4. CONCLUSIONS
Measurement on the sound absorption of kenaf fiber shows that kenaf fiber has a potential to be
employed as an alternative acoustic material. The experimental results show that for 30 mm thick sample,
the performance can closely reach unity above 1.5 kHz. Additional air gap for thinner sample of 20 mm thick is
also shown to improve the absorption coefficient close to unity.
5. REFERENCES [1] F. Asdrubali, “Survey on the Acoustical Properties
of New Sustainable Materials for Noise Control,” in Euronoise 2006, 30, 2006.
[2] L. P. Bastos, G. D. S. V. de Melo, and N. S. Soeiro, “Panels Manufactured from Vegetable Fibers: An
Alternative Approach for Controlling Noises in Indoor Environments,” Advances in Acoustics and
Vibration, vol 2012, 2012. [3] A. Putra, Y. Abdullah, H. Efendy, W. M. Farid, M.
R. Ayob and M. S. Py, “Utilizing Sugarcane Wasted Fibers As a Sustainable Acoustic
Absorber,” in Procedia Engineering, 53, 2013. [4] A. Putra, Y. Abdullah, H. Efendy, W. M. F. W.
Mohamad, and N. L. Salleh, “Biomass from Paddy Waste Fibers as Sustainable Acoustic Material,”
Advances in Acoustics and Vibration, vol 2013, 2013.
[5] F. D’Alessandro, and G. Pispola, “Sound Absorption Properties of Sustainable Fibrous
Materials in an Enhanced Reverberation Room,” in The 2005 Congress and Exposition on Noise
Control Engineering, 2005. [6] A. M. Mohd Edeerozey, H. M. Akil, A. B. Azhar,
and M. I. Zainal Ariffin, “Chemical Modification of Kenaf Fibers,” Materials Letters, 6110, 2023-
2025, 2007. Figure 3 Sound absorption coefficient of Kenaf fiber
with thickness of, 10 mm ─, 20 mm ---, 30 mm ∙∙∙.
Figure 4 Sound absorption coefficient of 20 mm thick Kenaf fiber with air gap thickness of,
10 mm ─, 20 mm ---, 30 mm ∙∙∙. Figure 5 Sound absorption coefficient of kenaf fiber
with thickness of 10 mm backed with rigid backing ─, 10 mm with air gap of
10 mm ---, and 20 mm with rigid backing ∙∙∙.
__________ © Centre for Advanced Research on Energy
Mobility of rectangular plate with constraint and unconstraint edges
K.H. Lim
1
, A. Putra
1,2,
, R. Ramlan
1,2 1
Faculty of Mechanical Engineering, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, 76100 Durian Tunggal, Melaka, Malaysia.
2
Centre for Advanced Research on Energy, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, 76100 Durian Tunggal, Melaka, Malaysia.
Corresponding e-mail: azma.putrautem.edu.my
Keywords: Mobility; vibration; plate ABSTRACT – Several theories have been established in
calculating the mobility of rectangular plate. However, there is still a lacking of discussion on the mobility of
plate with various boundary conditions. In this paper, modal summation approach is used to present the
mobility of rectangular plates with various constraint and unconstraint edges to discuss their effect on the level of
vibration across the frequency range. It is found that at very low frequency 1-20 Hz that the more constraint the
edges the lower the mobility.
1. INTRODUCTION
Concepts of mobility and impedance have been commonly used to investigate the responses of forced
structures and power radiated or transmitted by the structures. Over the years, many technique and different
approaches have been used to find the mobility of plates with various boundary conditions. The exact solutions
available are for plate with simply supported, at least one pair of opposite edges. Extensive study has been carried
out by Leissa [1] and presented the mode shape of the plates with various boundary conditions in monograph.
Later, Warburton [2] produced a set of approximate frequency formulas derived from Rayleigh method in
calculating mobility of the plates with various boundary conditions. The assumption is that the mode shape of the
plate is the multiplication of vibrating beam eigenfunctions. The objective of this paper is to calculate
and to present the mobility across the frequency of excitation with various boundary conditions using modal
summation approach.
2. METHODOLOGY
Consider a plate with dimension
x
l and
y
l as shown in Figure 1. The reference point is located at the corner
of the plate, O .
Figure 1 Rectangular plate with dimension � and �
�
and thickness
h
. According to Soedel [3], mobilities of finite plates
can be written in terms of a modal summation. The mobility of the plate can be calculated by [3]
1 1 2
2 1
1 2
2
] 1
[ ,
,
m n mn
y x
mn mn
z z
j l
hl y
x y
x j
F v
Y
1 where
z
v
is the velocity of the plate in z-direction,
z
F
is the force excitation,
,
2 2
y x
mn
is the ,
n m
th bending natural mode and
mn
is the ,
n m
th natural frequency and
is the loss factor and is harmonic circular frequency with implicit time dependence
t j
e
. Mode shape of the plate
,
2 2
y x
mn
is the product of the characteristic function of beam in x-direction and
y-direction which is ,
y x
y x
mn
2 The characteristic function of the beam can be
found in [3]. Natural frequencies for rectangular plates with various boundary conditions given by [2]
mn x
mn
q l
v Eh
2 2
2
1 12
3
where
2
2 2
4 4
b a
a n
G m
G q
y x
mn
with
y x
l l
a
and 1
n J
m J
v n
H m
vH b
y x
y x
for v is Poisson ratio, E is Young modulus,
h
is thickness of the plate, and
is density of the plate. The coefficient
x
G ,
y
G ,
x
J ,
y
J ,
x
H and
y
H for different boundary conditions correspond to the number of mode
, n
m th
can be found in [2].
3. RESULTS AND DISCUSSION
Results presented in the paper are calculated for aluminum plate with dimensions of
003 .
6 .
5 .
m
3
, Young modulus of
10
10 1
. 7
Nm
2
, Poisson ratio of 0.3,
