Resonance condition of bamboo-like trees based on granular particle-spring model: Relaxation stage

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 BandungJalan Ganesha 10, Bandung 40132, [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]


Outline

• Introduction• Model• Results and discussion• Summary


Introduction

Previous results 1

• It considered linear and bending springs as model of interaction between particles


ISBS 2015, Medan

Previous results 1 (cont.)





Previous results (cont.)

• Unstable configuration: N = 9, λijk = 0.1164



• Stable configuration: N = 9, λijk = 0.0873



Previous results 2


SNI 2016, Denpasar












Model

Model


More simple model is proposed

Model (cont.)

• Forces


gmF Gi

ijijijLLij rlrkF ˆ

wiDi vvDF

3

Model (cont.)

• Numerical method


2

2

2

1,

2

2

ˆ1111

3

i

ij kijijLkjik

wii

rlrkNjujum

vvmDg

dttrd

1,0,1

1

ndt

trdt

dttrd

dtttrd

ni

n

ni

n

ni

n

Model (cont.)

• Stages:– relaxation: without wind– resonance: wind is "turned on and off"



Results and discussion

Results and discussion


Results and discussion (cont.)




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



more stable final states?


Summary

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


.

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



Thank you