2015-10-17 ISBS 2015, Medan, Indonesia 1 In Searching of Trees Natural Vibration Frequency Based on Granular Particles Interactions and Vibration S. Viridi 1,* , P. Patana 2 , S.A. Subrata 3 , H. Hertiasa 1 , M. Abdullah 1 1 Institut Teknologi Bandung, Jl. Ganesha 10, Bandung 40132, Indonesia 2 University of Sumatera Utara, Jl. Biotechnologi 1, Medan 20155, Indonesia 3 Gadjah Mada University, Jl. Agro 1, Bulaksumur, Yogyakarta 55281, Indonesia *[email protected]
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In Searching of Trees Natural Vibration Frequency Based on Granular Particles Interactions and Vibration
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2015-10-17 ISBS 2015, Medan, Indonesia 1
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
• 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