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In Searching of Trees Natural Vibration Frequency Based on Granular Particles

Interactions and Vibration

S. Viridi1,*, P. Patana2, S.A. Subrata3, H. Hertiasa1, M. Abdullah1

1Institut Teknologi Bandung, Jl. Ganesha 10, Bandung 40132, Indonesia2University of Sumatera Utara, Jl. Biotechnologi 1, Medan 20155, Indonesia

3Gadjah Mada University, Jl. Agro 1, Bulaksumur, Yogyakarta 55281, Indonesia*dudung@gmail.com

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Outline

• Introduction• Model• Molecular dynamics method• Nomenclature of tree model• Simulation parameters• Results and discussion• Summaries

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Introduction

• A tree is an interesting entity from physics point of view

• Morphology of a tree is influenced by factors that is inducing stresses on tree diameter variation (Dassot et al., 2015)

• Even in details, angle of individual leaf inclination is under influence of its weight and wind (Tadrist et al., 2014)

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Introduction (cont.)

• These factors also induce the density and strength of the wood (Fournier et al., 2013)

• Various branch diameters of a tree are response to winds from its surrounding and also other factors such as rains, snows, fruits, and upper parts of the tree, since a branch must support the stress induced by this loads (Eloy, 2011)

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Introduction (cont.)

• Tree damage after a storm can be used to predict the wind velocity (Frelich and Ostuno, 2012)

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Model

• Two dimension model

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Model (cont.)

• Push-pull spring force

ijijijSij rlrcS ˆ

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Model (cont.)

• Bending spring force

ijkijkBijk c

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Model (cont.)

• Gravitation force

• Wind force

gmG ii

wiFi vvDcF

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Model (cont.)

• Neighbor particles interaction

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Molecular dynamics method

• Newton’s second law of motion

trtrtrB

trtrS

tvtvDcm

gta

kjiijk

ikijjiij

wiFi

i

,,

,

1

,

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Molecular dynamics .. (cont.)

• Euler algorithm

ttatvttv iii

tttvtrttr iii

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Nomenclature of tree model

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Simulation parameters

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Simulation parameters (cont.)

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Results and discussion

• Unstable configuration: N = 9, λijk = 0.1164

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Results and discussion (cont.)

• Stable configuration: N = 9, λijk = 0.0873

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Results and discussion (cont.)

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Results and discussion (cont.)

• Introducing wind v = 1 on N = 9 (stable)

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Results and discussion (cont.)

• Introducing wind v = 16 on N = 9 (unstable)

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Results and discussion (cont.)

• Introducing wind v = 64 on N = 9 (stable)

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Results and discussion (cont.)

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Summaries

• A tree model based on granular particle has been constructed

• Relaxation process small value of λijk in order to give stable tree configuration

• There is certain value of wind velocity that turn the stable configuration into unstable one resonance frequency

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Acknowledgements

• DAAD and Committee of ISBS 2015 is supporting dissemination part of this work

• Riset Unggulan Perguruan Tinggi - Desentralisasi Dikti in year 2015 with contract number 310i/I1.C01/PL/2015 is supporting calculation part of this work

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Thank you