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RESPONSE VARIATION OF CHLADNI PATTERNS ON VIBRATING
ELASTIC PLATE UNDER ELECTRO-MECHANICAL OSCILLATION
A. E. Ikpe1,*, A. E. Ndon2 and E. M. Etuk3 1, DEPT OF MECHANICAL ENGINEERING, UNIVERSITY OF BENIN, P.M.B. 1154, BENIN, EDO STATE, NIGERIA 2, DEPT OF CIVIL ENGINEERING, AKWA IBOM STATE UNIVERSITY, MKPAT ENIN, AKWA IBOM STATE, NIGERIA 3, DEPT OF PRODUCTION ENGINEERING, UNIVERSITY OF BENIN, P.M.B. 1154, BENIN, EDO STATE, NIGERIA
Figure 4: Modal Frequency at 7s Figure 5: Modal Frequency at 14s
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RESPONSE VARIATION OF CHLADNI PATTERNS ON VIBRATING ELASTIC PLATE UNDER ELECTRO-MECHANICAL OSCILLATION, A. E. Ikpe, et. al
Nigerian Journal of Technology, Vol. 38, No. 3, July 2019 545
Figure 6: Modal Frequency at 21s Figure 7: Modal Frequency at 28s
Figure 8: Modal Frequency at 35s Figure 9: Modal Frequency at 42s
Figure 10: Modal Frequency at 49s Figure 11: Modal Frequency at 56s
Figure 12: Chladni Patterns Obtain from the Experimental Procedure
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RESPONSE VARIATION OF CHLADNI PATTERNS ON VIBRATING ELASTIC PLATE UNDER ELECTRO-MECHANICAL OSCILLATION, A. E. Ikpe, et. al
Nigerian Journal of Technology, Vol. 38, No. 3, July 2019 546
Figure 13: Chladni Patterns Obtain from HYPERMESH Solver
Figure 14: Chladni Patterns Obtain from ANSYS R15.0 Solver
Figure 15: Chladni Patterns Obtain from CATIA Solver
Finite Element Method (FEM) is a useful tool that has
become relevant in numerical, statistical and in most
complex problems that human capacity would barely
unravel. For example, the application of three finite
element solvers in this study (CATIA 2017 version,
ANSYS R15.0 2017 version and HYPERMESH 2016
version) have helped unravel the complexities
surrounding the theory of Chladni patterns. From the
graphical representation (see Figure 4-11) of modal
frequencies obtained from experimentally and
through the use of FEM, frequency values obtained
from HYPERMESH solver is observed to be the closest
RESPONSE VARIATION OF CHLADNI PATTERNS ON VIBRATING ELASTIC PLATE UNDER ELECTRO-MECHANICAL OSCILLATION, A. E. Ikpe, et. al
Nigerian Journal of Technology, Vol. 38, No. 3, July 2019 547
to the modal frequencies obtained experimentally.
This agrees with the investigation carried out by
Owunna et al. [7] on experimental modal analysis of
a flat plate subjected to vibration. The experimental
investigation in this study was designed to show the
influence of a plate geometry on the modal shapes
(the shapes characterized by line patterns appear as
the frequencies resonate with the thin plate) formed
when the plate is subjected to vibration (the overlap
of the waves results an interference pattern of
nodes). Therefore, a thin sheet of metal excited at
resonance is divided into various patterns vibrating in
opposite directions bounded by lines of vibration
referred to as nodal lines. The visibility of these nodal
lines was achieved by sprinkling sugar on the surface
of the excited thin plate under vibration. The various
positions on the surface of the plate where the sugar
particles bunched up and appeared to halt in motion
are known as the nodes. In other words, as the
frequency varies, the position of the nodes adjust
gradually until they stagnate at a point where fine
imaginary lines patterns are formed [17]. By so
doing, the sugar particles skitter from one end of the
plate to the other and bunches up at a point,
transforming itself into a more complex geometric
shapes. In the experimental process, it was observed
that as the frequency varied, the position of the
nodes adjusted across the top plane of the plate. It
was also observed that the longer the excitation time,
the higher the modal frequencies and the more
complex the shapes and patterns formed on the plate
surface as shown in Tables 1-4 and Figures 12-15. In
this case, higher frequencies imply more peaks in the
sound wave, and thus increasing nodes in the
resulting interference pattern. Therefore, as the
sound waves resonate through the thin metal sheet,
there is a backward reflection of the sound towards
the source, producing a sound that irritates the ear.
In recent times, loud speaker and electronic signal
generator such as the electromagnetic single axis
systems have been employed to control the
frequency of the sound as it increases. It should be
noted that the line patterns, mode shapes as well as
the frequencies obtained in this study is only for
square plate, as the use of circular, triangular and
rectangular plates will provide great variety of
patterns different from those presented in this study.
Figure 16a represent the forces experienced by
particles with high damping coefficients while Figure
16b represent the forces experienced by particles
with low damping coefficients.
The resulting velocity of a grain particle bouncing on
the surface of a vibrating plate depends upon the
velocity of the plate upon impact, particle velocity
before collision, and the viscous damping coefficient.
Rise in the viscous damping coefficient proportionally
decreases the resulting particle velocity by absorbing
more of the force applied on the vibrating plate.
However, in cases where the damping force is
sufficient enough such that the breakoff force
exceeds the applied force, then the particle will not
bounce at all, and will rather stick to the plate surface
in a short period of time until the force exerted by the
plate exceeds the breakoff force including the effect
of viscous damping. This agrees with the
investigation carried out by Shridhar [9], and plays a
vital role in any successful experiment on acoustically
excited plate.
a b
Figure 16: Effect of Particle Damping on the Force Exerted on a Bouncing Particle on a Vibrating Plate
RESPONSE VARIATION OF CHLADNI PATTERNS ON VIBRATING ELASTIC PLATE UNDER ELECTRO-MECHANICAL OSCILLATION, A. E. Ikpe, et. al
Nigerian Journal of Technology, Vol. 38, No. 3, July 2019 548
4. CONCLUSION
Finite Element Method has been successfully
employed in this study to emulate the modal
frequencies and patterns in thin plates under acoustic
excitation, and the results obtained correlates with
the experimental values. This can serve as alternative
to the numerical and experimental methods,
considering the proximity between the experimental
values and FEM values. For further investigation in
engineering field, FEM can be adopted to check the
effects of acoustic excitations on displacement,
deformation and stress profiles of thin plates. This
could unravel the challenges surrounding the stress
build-ups in mechanical and structural components in
relation to their failure mechanisms.
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