Relaxation stage for resonance simulation of bamboo-like tree or system

1. International Conference of
Mathematics and Natural Sciences
3-4 November 2016, Bandung, Indonesia 1
Resonance condition of bamboo-like
trees based on granular particle-spring
model: Relaxation stage
S. Viridi1
, S. N. Khotimah2
, R. Kurniadi3
,
Novitrian4
, K. Basar5
, A. Purqon6
Physics Department, Institut Teknologi Bandung
Jalan Ganesha 10, Bandung 40132, Indonesia
1
dudung@fi.itb.ac.id, 2
nurul@fi.itb.ac.id, 3
rijalkl@fi.itb.ac.id,
4
novit@fi.itb.ac.id, 5
khbasa@fi.itb.ac.id, 6
acep@fi.itb.ac.id

2. International Conference of
Mathematics and Natural Sciences
3-4 November 2016, Bandung, Indonesia 2
Outline
• Introduction
• Model
• Results and discussion
• Summary

3. International Conference of
Mathematics and Natural Sciences
3-4 November 2016, Bandung, Indonesia 3
Introduction

4. Previous results 1
• It considered linear and bending springs as
model of interaction between particles
International Conference of
Mathematics and Natural Sciences
3-4 November 2016, Bandung, Indonesia 4
ISBS 2015, Medan

5. Previous results 1 (cont.)
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3-4 November 2016, Bandung, Indonesia 5

6. Previous results 1 (cont.)
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3-4 November 2016, Bandung, Indonesia 6

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Previous results (cont.)
• Unstable configuration: N = 9, λijk = 0.1164

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3-4 November 2016, Bandung, Indonesia 8
Previous results 1 (cont.)
• Stable configuration: N = 9, λijk = 0.0873

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Mathematics and Natural Sciences
3-4 November 2016, Bandung, Indonesia 9
Previous results 1 (cont.)

10. Previous results 2
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3-4 November 2016, Bandung, Indonesia 10
SNI 2016, Denpasar

11. Previous results 2 (cont.)
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3-4 November 2016, Bandung, Indonesia 11

12. Previous results 2 (cont.)
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Mathematics and Natural Sciences
3-4 November 2016, Bandung, Indonesia 12

13. Previous results 2 (cont.)
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Mathematics and Natural Sciences
3-4 November 2016, Bandung, Indonesia 13

14. Previous results 2 (cont.)
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Mathematics and Natural Sciences
3-4 November 2016, Bandung, Indonesia 14

15. Previous results 2 (cont.)
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Mathematics and Natural Sciences
3-4 November 2016, Bandung, Indonesia 15

16. International Conference of
Mathematics and Natural Sciences
3-4 November 2016, Bandung, Indonesia 16
Model

17. Model
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Mathematics and Natural Sciences
3-4 November 2016, Bandung, Indonesia 17
More simple
model is proposed

18. Model (cont.)
• Forces
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Mathematics and Natural Sciences
3-4 November 2016, Bandung, Indonesia 18
gmF G
i

=
( ) ijijijL
L
ij rlrkF ˆ−−=

( )wi
D
i vvDF

−−= πη3

19. Model (cont.)
• Numerical method
International Conference of
Mathematics and Natural Sciences
3-4 November 2016, Bandung, Indonesia 19
( ) ( )
( ) ( )[ ] ( ){ }∑ ∑
+
−= =
−
∆−−−−−−
−−=
2
2
2
1
,
2
2
ˆ111
1
3
i
ij k
ijijLkjik
wi
i
rlrkNjuju
m
vv
m
D
g
dt
trd
δ
πη 

( ) ( ) ( )
1,0,1
1
=∆+=
∆+
+
+
n
dt
trd
t
dt
trd
dt
ttrd
n
i
n
n
i
n
n
i
n 

20. Model (cont.)
• Stages:
– relaxation: without wind
– resonance: wind is "turned on and off"
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3-4 November 2016, Bandung, Indonesia 20

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3-4 November 2016, Bandung, Indonesia 21
Results and discussion

22. Results and discussion
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3-4 November 2016, Bandung, Indonesia 22

23. Results and discussion (cont.)
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Mathematics and Natural Sciences
3-4 November 2016, Bandung, Indonesia 23

24. Results and discussion (cont.)
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Mathematics and Natural Sciences
3-4 November 2016, Bandung, Indonesia 24
0
5
10
15
20
25
30
0
0.5
1
1.5
0 0.5 1 1.5 2 2.5 3
yT
t

25. Results and discussion (cont.)
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Mathematics and Natural Sciences
3-4 November 2016, Bandung, Indonesia 25
more stable final
states?

26. International Conference of
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3-4 November 2016, Bandung, Indonesia 26
Summary

27. Summary
• Another model of bamboo-tree like model has
been tested for relaxation stage
• Even it is more simple than previous one, it
hardly achieves final stable state with current
parameters value
• Tortuosity and vertical position of particle at
free edge tends to decrease as expected
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Mathematics and Natural Sciences
3-4 November 2016, Bandung, Indonesia 27
.

28. Acknowledgements
• Part of this work is supported by RIK ITB with
contract number 006q/I1.C01/PL/2016
• This presentation is supported by ICMNS 2016
Committee and Faculty of Mathematics and
Natural Sciences, Institut Teknologi Bandung
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3-4 November 2016, Bandung, Indonesia 28

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Thank you