䊐䉳䉺ᛛⴚ⎇ⓥႎ๔㩷╙ 㪋㪍 ภ㩷 㩷 㪉㪇㪈㪇 ᐕ㩷㩷 㐳ᄢ఺㔡᭴ㅧ‛䈱䊏䉾䊃ጀ᷷ᐲ䈫఺㔡ⵝ⟎䈮↢䈛䉎⋧ኻᄌ૏䈱㑐ଥ䈮䈧䈇䈩䈱⠨ኤታ᷹䈫⸃ᨆ⚿ᨐᲧセਛ ጊ ᣽ ዏ᭎ⷐ㐳ᄢ఺㔡ᑪ‛䈱఺㔡ⵝ⟎䈱᷷ᐲિ❗䈮䉋䉍↢䈛䉎⋧ኻᄌ૏䈫఺㔡䊏䉾䊃ጀ䈱᷷ᐲ䉕 1 ᐕᒝ䈮ᷰ䈦䈩⸘᷹䈚䈢䇯ᑪደ䇮䊏䉾䊃ጀ䇮ၮ␆䉴䊤䊑䇮࿾⋚♽䉕 1 ᰴర䊝䊂䊦ൻ䈚䇮ᄖ᳇᷷䊂䊷䉺䉕౉ജ䈫䈚䈩䇮FEM(Finite ElementMethod)ᚻᴺ䈮䉋䉎᷷ᐲ⸃ᨆ䉕䈍䈖䈭䈦䈢䇯᷹ⷰ䈘䉏䈢఺㔡䊏䉾䊃ጀ䈱᷷ᐲ䈮䈾䈿৻⥌䈜䉎⚿ᨐ䉕ᓧ䈢䇯䈖䈱⸘▚䈘䉏䈢਄ደ䈫ၮ␆䉴䊤䊑䈱᷷ᐲ䈱ᤨ㑆ᄌൻ䈫䇮ၮ␆䉴䊤䊑ਅ䈮ㆡಾ䈭೰ᕈ䉕ᜬ䈧᳓ᐔ࿾⋚෻ജ䊋䊈䉕⠨䈋䉎䈖䈫䈮䉋䉍䇮᷹ⷰ䈘䉏䈢఺㔡ⵝ⟎䈱⋧ኻᄌ૏䉕䈾䈿⺑᣿䈜䉎䈖䈫䈏䈪䈐䈢䇯▚ቯ䈘䉏䈢᳓ᐔ࿾⋚෻ജ䊋䊈ቯᢙ䈲 x䍂yᣇะ䈪Ꮕ䈏⷗䉌䉏䈢䈏䇮↢䈛䈩䈇䉎⋧ኻᄌ૏䈱ၮᧄ⊛䈭ᯏ᭴䈲ᛠ䈋䉎䈖䈫䈏䈪䈐䈢䈫䈇䈋䉎䇯A Study on Relative displacements of Rubber Bearings on a Very-longspan Base-isolated Structure Caused by Atmospheric Temperature--- Comparison of Field Measurement and Analysis --Abstract
Relative horizontal displacements of rubber bearing on a very long spanbase-isolation building were measured for more than one year. Over the same
period, the ambient temperature around the rubber bearings (that is, atmospherictemperature in the pit space for rubber bearings) was measured. Observed
temperatures are well explained by the one-dimensional thermal EFM (FiniteElement Method) model, which consists of floor slab, air layer, foundation slab
and soil layers. The structure was then modeled as a system of floor slab andfoundation slab with uniformly distributed ground reaction force linear spring.
Based on this structural model and the results of thermal analysis, the stiffnessof ground reaction force spring is inversely evaluated to produce relative
displacement results consistent with observed ones. The values of reduced
stiffness of ground reaction force spring for two horizontal directions (x and y)
are a little different, but it can be said that we could get to the root of themechanism of occurrence of relative rubber bearing displacements caused byatmospheric temperature.
䉨䊷䊪䊷䊄䋺㩷 ఺㔡᭴ㅧ‛㩷 ᷷ᐲિ❗㩷 ᳓ᐔ࿾⋚෻ജଥᢙ㩷 ታ᷹㩷 ᷷ᐲ⸃ᨆ㩷䋭㪈㪊䋭䊐䉳䉺ᛛⴚ⎇ⓥႎ๔㩷 ╙ 㪋㪍 ภ䊏䉾䊃ጀ᷷ᐲᄌൻ䈲ᄖ᳇᷷ᄌൻ䈮ኻ䈚䈩 0.88 ୚䈱ᄌൻ§䋱䋮䈲䈛䉄䈮䈪⋧㑐ଥᢙ䈲 0.94 䈫㜞䈇୯䉕␜䈚䈩䉎䇯࿑ 2.6 䈲 ux,uy╩⠪䈲㐳ᄢ఺㔡䊒䊧䉴䊃䊧䉴䊃᭴ㅧ‛(ୖᐶ↪ㅜ)䈱᪞䈫ᄖ᳇᷷㑐ଥ䉕␜䈜䇯ᄖ᳇᷷䈫䈱⋧㑐ᕈ䈲 ux 䈏 0.83䇮䈱ゲᣇะ䉪䊥䊷䊒⃻⽎䉕ᛒ䈇䇮ᄐ౻ᢙ࿁䈱᷹㊂⚿ᨐ䈎䉌䇮uy 䈏 0.92 䈫㜞䈇䇯⴫ 2.1 䈮⸘᷹⚿ᨐ䉕䉁䈫䉄䈢䇯ᮮᵿ䈱⃻⽎䈫䈚䈩䇮᭎䈰਄ደ䈏ᣣᐔဋᄖ᳇᷷ᄌൻ䈱⚂ 1/2 䈮ኻᐕ㑆ᄖ᳇᷷ᄌൻ䈲 26.7㷄䇮਄ደゎ૕䈱✢⤘ᒛ₸㱓䉕䈚䈩⥄↱િ❗䈚䈩䈇䉎䈫⷗䉌䉏䉎䈖䈫䉕ႎ๔䈚䈢䇯1)2)㩷 䈖䈱

1.0䊶10-5/㷄䇮਄ደ䈱ઍ⴫⊛᷷ᐲᄌൻ䈏ᄖ᳇᷷ᄌൻ䈱⚂㩷

1/2 䈱ᗧ๧䈲⚻㛎⊛䈭੐ታ䈫䈚䈩ฃ䈔ᱛ䉄䇮ᒰᤨ䇮䈠䉏

䋱/2 䈫䈜䉎䈫䇮ux 䈱ᐕ㑆ᄌൻ䈲એ਄ㅊ᳞䈚䈭䈎䈦䈢䇯ᧄႎ๔䈪䈲䇮หᑪ‛䈱㓈ㇱ䈱఺㔡

18.7mm=26.7/2 䊶 1E-0.5 䊶 140000 䈫 䈭 䉍 䇮 ⷰ ᷹ 䈘 䉏 䈢ⵝ⟎਄ਅ䈱⋧ኻᄌ૏䇮఺㔡䊏䉾䊃ጀ䋨એਅ䊏䉾䊃ጀ䋩ౝ᳇

19.4mm 䈮ㄭ䈇䇯䈧䉁䉍䇮ᣢႎ 1)2)䈱⚿ᨐ䈏ⵣઃ䈔䉌䉏䈢䇯᷷䉕 1 ᐕ䈅䉁䉍䈮䉒䈢䈦䈩⸘᷹䈚䈢⚿ᨐ䉕ಽᨆ䈚䇮਄⸥䈱䊏䉾䊃ጀ᷷ᐲ䉅ᄖ᳇᷷䈮䈾䈿ห⒟ᐲ䈮ㅪേ䈚䈩䈇䉎䈱䈪⃻⽎䉕 1 ᰴర᷷ᐲ⸃ᨆ䇮◲න䈭䊙䉪䊨䊝䊂䊦䈮ၮ䈨䈇䈩䈖䈱⚂ 1/2 䈱ᗧ๧䉕એਅ䈪⠨ኤ䈜䉎䇯᭎䈰⸃㉼䈪䈐䉎䈖䈫䉕ႎ๔䈜䉎䇯㩷 ⷐὐ䈲䇮਄ደゎ૕䇮఺㔡ⵝ⟎ਅ䈱ၮ␆䉴䊤䊑䈲᭎⇛ᣣᐔဋᄖ᳇᷷䈮ᓥ䈦䈩િ❗䈜䉎䈏ၮ␆䉴䊤䊑䈲᧮ၮ␆䈱᳓ᐔ࿾⋚෻ജଥᢙ䈮䉋䉎᜔᧤䉕ฃ䈔䈠䈱Ꮕಽ䈏᷹ⷰ䈘䉏䈩䈇䉎䈫⸃㉼䈜䉎䉅䈱䈪䈅䉎䇯㩷 䈭䈍䇮ᢥ₂ 3)䉅ห䈛໧㗴䉕ᛒ䈦䈩䈇䉎䇯ᧄႎ䈪䈲䇮㩷
1 ᰴర᷷ᐲ⸃ᨆ䊝䊂䊦䈮䈍䈇䈩䇮䊏䉾䊃ጀ䈮⴫㕙ᾲવ㆐⋧ኻᄌ૏ⷐ⚛䇮឵᳇ⷐ⚛䇮ユ኿ⷐ⚛䉕↪䈇䈢䉋䉍⥄ὼ䈭䊝䊂䊦䉕↪䈇䈩䈇䉎ὐ䈮㆑䈇䈏䈅䉍䇮䉁䈢⚿ᨐ䉕⹦⚦䈮␜䈚䈩䈇䉎䇯఺㔡ⵝ⟎§䋲䋮㩷 ⸘᷹䈍䉋䈶⚿ᨐ᭎ⷐ
㪉㪅㪈㩷 ⸘᷹᭎ⷐ㩷࿑ 2.1㩷 ᑪ‛᭎ⷐ䈫䊏䉾䊃ጀ⸘᷹૏⟎㩷

࿑ 2.1 䈮ኻ⽎ᑪ‛䈱ᄖᒻ⁁䋨280䊶103䊶26.4m(H)䇮4㪊㪌㓏ᑪ䇮᧮ၮ␆䋩᷹ቯ૏⟎䉕␜䈜䇯䊏䉾䊃ጀ䈱㜞䈘䈲 1.9m䇮

㪊㪇㪉㪌㷄

⚂ 5cm 䈱䉩䊞䉾䊒䉕ㅢ䈛䈩ⓨ᳇䈱಴౉䉍䈏䈅䉎䇯఺㔡ⵝ⟎䈱਄ਅ䈱⋧ኻᄌ૏䈲䊧䊷䉱䊷ᄌ૏⸘䈪䇮䊏䉾䊃ጀ᳇᷷㪉㪇㪈㪌䈲ᾲ㔚ኻ䈪 2 ▎ᚲ 10 ಽ㑆㓒䈪⸘᷹䈚䈢䇯⸘᷹ᦼ㑆䈲䊏䉾䊃ౝ䇭ᣣᦨᄢ䊏䉾䊃ౝ䇭ᣣᦨዊᮮᵿ䇭ᣣᐔဋ㩷㪈㪇㪌2008 ᐕ 6 ᦬ 12 ᣣ䌾2009 ᐕ 7 ᦬ 14 ᣣ䉁䈪 398 ᣣ㑆䈪㪇䈅䉎䇯䊏䉾䊃ጀౝ᷷ᐲ䈱૏⟎䈮䉋䉎㆑䈇䈲ዊ䈘䈒䇮䉁䈢䇮᷷㪇㪊㪇㪍㪇ᐲ䇮⋧ኻᄌ૏䈱 1 ᣣ䈱ਛ䈪䈱ᄌൻ䈲ዊ䈘䈇䈱䈪䇮㓈ⷺㇱ㪐㪇 㪈㪉㪇 㪈㪌㪇 㪈㪏㪇 㪉㪈㪇 㪉㪋㪇 㪉㪎㪇 㪊㪇㪇 㪊㪊㪇 㪊㪍㪇 㪊㪐㪇ᣣ䇭䇭㪈㪆㪈䈎䉌䈮ਗ䈼ᦧ䈋䇭㩷㩷㪉㪇㪇㪏㪆㪇㪍㪆㪈㪉㪄㪉㪇㪇㪐㪆㪇㪎㪆㪈㪋䈪䈱 Data 䈮䈧䈇䈩䇮ᣣᐔဋ䈫ᣣᦨᄢᦨዊ୯䈮㓸⚂䈚䈩

࿑ 2.2 ࡇ࠶࠻ጀ᷷ᐲᄌൻ ⸘᷹⚿ᨐಽᨆ䈜䉎䈖䈫䈮䈚䈢䇯એਅ䇮․䈮ᢿ䉌䈭䈇㒢䉍ᣣᐔဋ䈮䈧䈇䈩䈱㊂䈪䈅䉎䇯㪈㪌㪉㪅㪉 ⸘᷹⚿ᨐ᭎ⷐ㩷 㩷㪈㪇㪬㫏㪄ᐕᐔဋ㩷㩷㫄㫄࿑ 2.2 䈮䊏䉾䊃ጀ䈱᷷ᐲᄌൻ䉕䇮࿑ 2.3 ࿑ 2.4 䈮⋧ኻᄌ૏ ux䍂uy 䈱ᣣᄌൻ䉕␜䈜䇯ᓟ䈱⸃ᨆ୯䈫䈱Ყセ䉕ኈᤃ䈮䈜䉎䈢䉄䇮2009 ᐕ 1 ᦬ 1 ᣣ䈎䉌 7 ᦬ 14 ᣣ䇮2008 ᐕ 7
᦬ 15 䈎䉌 12 ᦬ 31 ᣣ䈱㗅䈮 Data 䉕❬䈕䈩⴫␜䈚䈩䈇㪌㪇㪄㪌ᣣᐔဋ㫌㫏㪄ᐕᐔဋᣣᦨᄢ㫌㫏㪄ᐕᐔဋᣣᦨዊ㫌㫏㪄ᐕᐔဋ㪄㪈㪇㪄㪈㪌㪇䉎䇯ᮮᵿ䈱᳇᷷ᖱႎ䈲หᦼ㑆䈱 AMeDAS 䈱 Data 䈮䉋㪊㪇㪍㪇㪐㪇 㪈㪉㪇 㪈㪌㪇 㪈㪏㪇 㪉㪈㪇 㪉㪋㪇 㪉㪎㪇 㪊㪇㪇 㪊㪊㪇 㪊㪍㪇 㪊㪐㪇ᣣ䇭䇭㪈㪆㪈䈎䉌䈮ਗ䈼ᦧ䈋䇭㪉㪇㪇㪏㪆㪇㪍㪆㪈㪉㪄㪉㪇㪇㪐㪆㪇㪎㪆㪈㪋䉎䇯㵰䊏䉾䊃ጀ䈱᷷ᐲᄌൻ䈲䇮ᄖ᳇᷷ᄌൻ䈮Ყ䈼䈩⋧ᒰዊ䈘䈇䈪䈅䉐䈉㵱䈫䈱੍ᗐ䈮෻䈚䈩หᦼ㑆䈱ᮮᵿ䈱᷷ᐲ䈫䈾

࿑ 2.3 ⋧ኻᄌ૏ ux ߩᄌൻ ᐕᐔဋ߆ࠄߩ஍Ꮕ䈿ห䈛ᄌൻ䉕䈚䈩䈇䉎䇯ux,uy 䈱ᐕ㑆ᄌേ䈲 ux 䈱᭎䈰  ⸘᷹⚿ᨐ

1/2 䈪䈅䉍䇮ux 䉋䉍䉅⍴๟ᦼ䈱ᄌേ䈏⋡┙䈧䉋䈉䈮⷗䈋䉎䇯
࿑ 2.5 䈮䈲䊏䉾䊃ጀ᷷ᐲ䈫ᮮᵿ䈱ᄖ᳇᷷䈫䈱㑐ଥ䉕␜䈜䇯䋭㪈㪋䋭㐳ᄢ఺㔡᭴ㅧ‛ߩࡇ࠶࠻ጀ᷷ᐲߣ఺㔡ⵝ⟎ߦ↢ߓࠆ⋧ኻᄌ૏ߩ㑐ଥߦߟ޿ߡߩ⠨ኤ ታ᷹ߣ⸃ᨆ⚿ᨐᲧセ§䋳䋮㩷  ᰴర᷷ᐲ⸃ᨆ㪈㪌㪈㪇㪬㫏㪄ᐕᐔဋ㩷㫄㫄㪌㪊㪅㪈㩷 ⸃ᨆኻ⽎䊝䊂䊦㩷㪇㪄㪌ᣣᐔဋ㫌㫐㪄ᐕᐔဋᣣᦨᄢ㫌㫐㪄ᐕᐔဋᣣᦨዊ㫌㫐㪄ᐕᐔဋ㪄㪈㪇਄ደ䈎䉌࿾⋚䉁䈪䉕 1 ᰴర䊝䊂䊦䈫䈚䈩ᐕ㑆䈱᷷ᐲ⸃ᨆ䉕ⴕ䈭䈉䇯⸃ᨆ⋡⊛䈲䇮᷹ⷰ䈘䉏䈢䊏䉾䊃ጀ᷷ᐲ䉕⺑᣿㪄㪈㪌㪇㪊㪇㪍㪇㪐㪇 㪈㪉㪇 㪈㪌㪇 㪈㪏㪇 㪉㪈㪇 㪉㪋㪇 㪉㪎㪇 㪊㪇㪇 㪊㪊㪇 㪊㪍㪇 㪊㪐㪇䈜䉎䈖䈫䇮䈠䈱⚿ᨐ䈮ၮ䈨䈇䈩਄ደ䇮ၮ␆䉴䊤䊑ㇱಽ䈱ઍᣣ䇭䇭㪈㪆㪈䈎䉌䈮ਗ䈼ᦧ䈋䇭㪉㪇㪇㪏㪆㪇㪍㪆㪈㪉㪄㪉㪇㪇㪐㪆㪇㪎㪆㪈㪋⴫᷷ᐲ䈱ᣣᄌൻ䉕▚ቯ䈚䇮᷹ⷰ䈘䉏䈢఺㔡ⵝ⟎䈱⋧ኻᄌ૏䈱⸃㉼䉕ⴕ䈭䈉䈖䈫䈮䈅䉎䇯੹࿁䈱䊝䊂䊦䈲䇮䊏䉾䊃ጀ

࿑ 2.4㩷 ⋧ኻᄌ૏ uy ߩᄌൻ ⸘᷹⚿ᨐ䈍䉍ᣢႎ 3)䉋䉍䉅⥄ὼ䈭䊝䊂䊦䈮䈭䈦䈩䈇䉎䇯㪉㪇㪇㪏㪆㪇㪍㪆㪈㪉㪄㪉㪇㪇㪐㪆㪇㪎㪆㪈㪋㪊㪌䊏䉾䊃ౝ䇭ᣣᐔဋ᷷ᐲ䇭㷄䈮⴫㕙ᾲવ㆐ⷐ⚛䇮ユ኿વ㆐ⷐ⚛䇮឵᳇ⷐ⚛䉕↪䈇䈩㪊㪇⸃ᨆ䊝䊂䊦䉕࿑ 3.1 䈮␜䈜䇯1 ᰴర䊝䊂䊦ൻ䈮䈅䈢䈦࿁Ꮻ䈎䉌䈱஍Ꮕ㪪㪫㪛㪔㪈㪅㪋㪎㷄䈩䈱೨ឭ䈲ᰴ䈫䈚䈢䇯㪉㪌㪉㪇㫐㩷㪔㩷㪇㪅㪏㪎㪏㪏㫏㩷㪂㩷㪉㪅㪐㪍㪌㪊㽲 ਄ደ䈱᷷ᐲ䈲 1 㓏ᐥ䉴䊤䊑䉮䊮䉪䊥䊷䊃䈪ઍ⴫䈜䉎䇯㪈㪌㪩 㩷㪔㩷㪇㪅㪐㪋㪉㪋㽳㩷 Ყセ⊛㐿᡼⊛䈭ᑪ‛䈫䈚䇮1 㓏ᐥ䉴䊤䊑䈲ቶౝ䈱ઍ㪉㪈㪇⴫⊛⴫㕙ᾲવ㆐ଥᢙ㱍i 䈪ᄖ᳇᷷ᐲ䈮ᦑ䈘䉏䉎䇯㱍i=䊏䉾䊃ౝ䇭ᣣᐔဋ✢ᒻ㩷㩿䊏䉾䊃ౝ䇭ᣣᐔဋ㪀㪌

33480. J /(m^2Hour㷄㪇㪇㪌㪈㪇㪈㪌㪉㪇㽴 䍩䍽䍍䍢ጀ䈱ⓨ᳇䈲឵᳇࿁ᢙ Nv ࿁/Hour 䉕ฃ䈔䉎䇯㪉㪌㪊㪇㪊㪌ᮮᵿ䇭ᣣᐔဋ᷷ᐲ㩷㷄㽵㩷 䊏䉾䊃ጀ䈱ⓨ᳇䈫䇮1 㓏ᐥ䉴䊤䊑䇮ၮ␆䉴䊤䊑㑆䈲ቶౝ䈱ᮡḰ⊛䈭⴫㕙ᾲવ㆐ଥᢙ䈪ᾲ䈱᝼ฃ䈏䈅䉎䇯

࿑ 2.5 ࡇ࠶࠻ጀ᷷ᐲߣᄖ᳇᷷ߩኻᔕ ⸘᷹⚿ᨐ㪈㪌ฃ䈏䈅䉎䋨288K 䈪䈱䉮䊮䉪䊥䊷䊃ო㕙ห჻㑆䈱୯䈪㫐㩷㪔㩷㪇㪅㪎㪎㪏㪊㫏㩷㪄㩷㪇㪅㪇㪇㪎㪉㪩㪉 㩷㪔㩷㪇㪅㪏㪊㪋㪊㪈㪇㫌㫏㪄ᐕᐔဋ㩷㩷㫄㫄㽶 䋱㓏ᐥ䉴䊤䊑䇮ၮ␆䉴䊤䊑㑆䈮䈲ユ኿䉕ㅢ䈛䈢ᾲ䈱᝼㱍rad=17280. J /(m^2Hour㷄䇮)࿁Ꮻ䈎䉌䈱஍Ꮕ㪪㪫㪛㪔㪉㪅㪋㪌㷄㪌䈭䈍䇮࿾⋚ᦨਅጀ䈮䈲⴫㕙ᾲવ㆐ଥᢙ㱍o = 83700.

㪇J /(m^2Hour㷄)䉕↪䈇䈢䇯ਥⷐㇱಽ䈱ᾲ․ᕈ䉕⴫ 3.1

㪄㪌䈮␜䈜䇯࿯ㇱಽ䈮䈧䈇䈩䈲ᢥ₂ 4)䈱୯䉕ណ↪䈚䈩䈇䉎䇯㪄㪈㪇ᄖ᳇ ᷷᷷ ᐲ 䈱ᤨೞ ᱧ 䈲 ᜛ᒛ AMeDAS ᳇⽎ ᮡḰ㫌㫏䇭ᐕᐔဋ䈎䉌䈱Ꮕಽ㩷✢ᒻ㩷㩿㫌㫏䇭ᐕᐔဋ䈎䉌䈱Ꮕಽ㩷㪀㪄㪈㪌㪄㪈㪌㪄㪈㪇㪄㪌㪇㪌㪈㪇

Data(ᮮᵿ䇮1 ᤨ㑆㑆㓒)䉕↪䈇䈢䇯⸘▚䈲 1 ᤨ㑆㑆㓒䈪㪈㪌

2 ᐕ㑆ಽⴕ䈭䈇䇮ೋᦼ᷷ᐲᓇ㗀䈏ᶖ䈋䈢⸃䉕ᓧ䈢䇯⸘᷹ᣣᐔဋᄖ᳇᷷㪄ᐕᐔဋ䇭㷄࿑ 2.6

Data 䈫ห᭽䈮ᣣᐔဋ䇮ᣣᦨᄢ䇮ᦨዊ୯䈮ᄌ឵䈚䈢䇯ᄙ䈒䈱䊌䊤䊜䊷䉺䊷䈏㑐ଥ䈜䉎䈱䈪ᰴ䈱Ბ㓏䉕〯䉖䈪䊌䊤䊜ux ߣᄖ᳇᷷ߩኻᔕ ⸘᷹⚿ᨐ䊷䉺䊷䉕⛉䉍ㄟ䉖䈪ⴕ䈦䈢䇯㪍㫐㩷㪔㩷㪇㪅㪊㪇㪊㪎㫏㩷㪄㩷㪇㪅㪇㪇㪉㪐㪩㪉 㩷㪔㩷㪇㪅㪐㪉㪇㪏㫌䌹㪄㫌䌹㪸㫍㪼㩷㫄㫄㪋䉁䈝䇮࿯䈱ᾲ․ᕈᓇ㗀䉕ᬌ⸛䈚䈢䇯࿯䈱ᾲ․ᕈ䈲฽᳓₸䈱⇣䈭䉎 3 ⒳㘃(ḨẢ䇮ੇ῎䇮ਛ㑆ᐲ)䉕 Nv=1 䈱႐ว࿁Ꮻ䈎䉌䈱஍Ꮕ㪪㪫㪛㪔㪇㪅㪍㪉㪏㷄㪉䈮䈧䈇䈩ᬌ⸛䈚䈢䇯࿯ጀㇱಽ䈮䈲᷷ᐲಽᏓ䈮Ꮕ䈏⷗䉌䉏䉎䈏䇮䈠䉏䉋䉍਄䈱ㇱಽ䈮䈲䈾䈫䉖䈬Ꮕ䈏⃻䉒䉏䈩䈖䈭䈇㪇㪄㪉䈖䈫䉕⏕⹺䈚䈢䇯䈠䉏᡿䇮એ㒠䈱⸃ᨆ䈪䈲䇮࿯䈱ᾲ․ᕈ䈲㫌䌹䇭ᐕᐔဋ䈎䉌䈱Ꮕಽ㩷㪄㪋ḨẢ࿯䈮㒢ቯ䈚䈢䇯✢ᒻ㩷㩿㫌䌹䇭ᐕᐔဋ䈎䉌䈱Ꮕಽ㪄㪍㪄㪈㪌㪄㪈㪇㪄㪌㪇⛯䈇䈩䊏䉾䊃ጀ䈱឵᳇࿁ᢙ Nv 䉕 2䌾0.05 䈮ᄌൻ䈘䈞䈩ᓇ㗀䉕ᬌ⸛䈚䈢䇯࿑ 3.3 䈮࿑ 3.1 䈱 Node4,5 䈱ᤨ㑆ᄌ㪌㪈㪇㪈㪌ᣣᐔဋᄖ᳇᷷㪄ᐕᐔဋ䇭㷄ൻ䉕␜䈜䇯឵᳇࿁ᢙ䈲 Node4 䈮䈲䈾䈫䉖䈬ᓇ㗀䈞䈝䇮

࿑ 2.7 uy ߣᄖ᳇᷷ߩኻᔕ ⸘᷹⚿ᨐ

Node5 䈮⴫䉏䇮឵᳇࿁ᢙ䈏ዊ䈘䈇䈾䈬ᄖ᳇᷷䈱⍴๟ᦼ

⴫ 2.1 ⸘᷹⚿ᨐ߹ߣ߼ᣣᐔဋ䈱ᐕᐔဋᣣᐔဋ䈱ᐕᦨᄢᣣᐔဋ䈱ᐕᦨዊᣣᐔဋ䈱㩿ᦨᄢ䋭ᦨዊ㪀䊏䉾䊃ౝ᷷ᐲ
㷄

㪈㪎㪅㪌㪊
㪉㪎㪅㪐㪇
㪍㪅㪌㪇㪉㪈㪅㪋㪇㩷ᮮᵿ㩷㩷㷄㪈㪍㪅㪌㪏㪊㪇㪅㪇㪇㪊㪅㪊㪇㪉㪍㪅㪎㪇㫌㫏㩷㫄㫄㪄㪉㪅㪐㪋㪎㪅㪋㪇㪄㪈㪉㪅㪇㪇㪈㪐㪅㪋㪇ᚑಽ䈏ᶖ䈋䉎௑ะ䈏䉂䉌䉏䉎䇯䊏䉾䊃ጀ᳇᷷䈱᷹ⷰ૏⟎䈲 Node4 䈮ㄭ䈒䇮䈠䈱ᗧ๧䈪䈲឵᳇࿁ᢙ䈱ᓇ㗀䈲䉂䉌㩷㫌㫐㩷㫄㫄㪄㪈㪅㪌㪍
㪊㪅㪇㪈
㪄㪍㪅㪊㪈
㪐㪅㪊㪉䉏䈭䈇䈖䈫䈮䈭䉎䇯䈠䉏᡿䇮એਅ䈪䈲 Nv=1 䈱႐ว䉕ઍ⴫୯䈫䈚䈩ᛒ䈉䈖䈫䈮䈚䈢䇯࿑ 3.4 䈮䈲᷹ⷰ୯䋨࿑ 2.2䋩䈫Ყセ䋭㪈㪌䋭䊐䉳䉺ᛛⴚ⎇ⓥႎ๔㩷 ╙ 㪋㪍 ภ㪊㪌࿑ 3.5 䈮䈲䇮᷹ⷰ୯䋨࿑ 2.5䋩䈫Ყセ䈜䈼䈐䊏䉾䊃ጀ᷷ᐲ䈫㪊㪇ᄖ᳇᷷㑐ଥ䉕␜䈜䇯᷹ⷰ୯䈫⸘▚୯䈱䊧䊮䉳䈲⦟䈒৻⥌㪉㪌䈚䈩䈇䉎䈏⸃ᨆ䈱ᣇ䈏⋧㑐ᕈ䈏㜞䈒䇮࿁Ꮻ✢䈎䉌䈱஍Ꮕ㪉㪇㷄䈜䈼䈐 Node4 䈱ᣣᐔဋ䇮ᣣᦨᄢᦨዊ䈱ᤨ㑆ᄌൻ䉕␜䈜䇯䈱ᮡḰ஍Ꮕ(STD)䈏䉇䉇ᄢ䈐䉄䈪䈅䉎䇯࿑ 3.6 䈮䈲ᐥ䉴㪈㪌㪈㪇䊤䊑䇮ၮ␆䉴䊤䊑䇮ਔ⠪䈱᷷ᐲᏅ䈱ᤨ㑆ᄌൻ䉕␜䈜䇯㪌ᐥ䉴䊤䊑䇮ၮ␆䉴䊤䊑㑆䈱᷷ᐲᏅᄌൻ䈲ᄖ᳇᷷ᄌൻ䉋㪇㪇䉍䉅⋧ᒰዊ䈘䈒䇮න⚐䈮䉴䊤䊑䇮ၮ␆䉴䊤䊑䈱᷷ᐲᄌൻ䈮䉋䉎⥄↱િ❗䈪䈲⸘᷹⚿ᨐ䉕⺑᣿䈪䈐䈭䈇䈖䈫䈮䈭䉎䇯㪌䋴䋸 䋹䋶ᐥ䉴䊤䊑 ⓨ᳇ጀ㪇㪅㪈㪏㫄 㪈㪅㪐㫄࿾⋚㩷㪈㪈ಽഀၮ␆䉴䊤䊑㪇㪅㪊㫄㪉㪌ᐕᐔဋ᷷ᐲ㪫㪸㫍㪼㩷㱍㫆㪈㪉㪇 㪈㪌㪇 㪈㪏㪇 㪉㪈㪇 㪉㪋㪇 㪉㪎㪇 㪊㪇㪇 㪊㪊㪇 㪊㪍㪇 㪊㪐㪇ᣣ࿾⋚ෘ䈘㪈㪇㪅㪉㫄㪈㪇㪇㪌㪈㪇㪈㪌㪉㪇㪉㪌㪊㪇ᣣᐔဋᄖ᳇᷷䇭㷄㪊㪌

࿑ 3.5㩷 䊏䉾䊃ጀ᷷ᐲ䈫ᄖ᳇᷷䈱ኻᔕ㩷 ⸃ᨆ⚿ᨐ㪊㪌㪊㪇㪉㪌㪉㪇㪈㪌㪈㪇㪌㪇㪄㪌㪄㪈㪇ᄖ᳇᷷䉴䊤 䊑 㪄ၮ␆䉴䊤 䊑 ᷷ᐲᏅᣣᐔဋ᷷ᐲ㩷㷄ၮ␆䉴䊤 䊑䉴䊤 䊑㩿䍛䍵䊑ၮ␆䉴䊤䊑᷷ᐲᏅ䋩㪇㪉㪇㫐㩷㪔㩷㪇㪅㪏㪌㪏㩷㫏㩷㪂㩷㪉㪅㪉㪉㪏㪉㪩 㩷㪔㩷㪇㪅㪐㪍㪊㪇㩷 ⓨ᳇ጀ䈱឵᳇࿁ᢙ䋺㩷 Nv=2䌾0.05 ࿁/Hour㪉㪌㪥㫆㪻㪼㪋㩷ᣣᐔဋ✢ᒻ㩷㩿㪥㫆㪻㪼㪋㩷ᣣᐔဋ㪀㪈㪌㪌ᾲવ⛔₸䇭㱗 ⾰㊂Ყᾲኒᐲ䇭㱝㪡㪆㩿㫄㪟㫆㫌㫉㷄䋩 㪚㩷㩷㪡㪆㩿㪢㪾㷄䋩 㪢㪾㪆㫄㪵㪊䉮䊮䉪䊥䊷䊃㪌㪏㪍㪏㪏㪎㪐㪉㪊㪇㪇ⓨ᳇㪏㪍㪅㪏㪈㪇㪇㪍㪈㪅㪉㪌࿯㩷ḨẢ㪉㪎㪋㪊㪊㪈㪎㪇㪈㪉㪊㪍࿯㩷ੇ῎㪍㪍㪍㪇㪈㪊㪍㪇㪉㪈㪊㪎࿯㩷ਛ㑆㪋㪌㪊㪍㪉㪈㪈㪇㪈㪍㪊㪐⸃ᨆ㩷㪥㫆㪻㪼㪋㩷㩷⸘᷹૏⟎ㄭற࿁Ꮻ䈎䉌䈱஍Ꮕ㪪㪫㪛㪔㪈㪅㪉㪊㷄㪉㪇⴫ 3.1㩷 ↪䈇䈢ᾲ․ᕈ৻ⷩ

ᣣᐔဋ᷷ᐲ㩷㷄㪐㪇㪊㪇࿑ 3.1 㪈 ᰴరᾲ⸃ᨆ䊝䊂䊦㪊㪇㪍㪇

࿑ 3.4 䊏䉾䊃ጀ(Node4)᷷ᐲ䈱ᤨ㑆ᄌൻ㩷 㩷 ⸃ᨆ⚿ᨐ䋷㱍㫀㱍㫀឵᳇࿁ᢙ㪥㫍ᄖ᳇㪫㫆㩷㱍㫀㪊㪇䋲䋰ᣣᐔဋ᷷ᐲ㩷㷄䋱 䋲 䋳ᄖ᳇᷷㪥㫆㪻㪼㪋㩷ᣣᐔဋ㪥㫆㪻㪼㪋㩷ᣣᦨ㜞㪥㫆㪻㪼㪋㩷ᣣᦨૐ㪥㫍㪔㪉㪥㫍㪔㪈㪥㫍㪔㪇㪅㪉㪥㫍㪔㪇㪅㪇㪌㪊㪇㪍㪇㪐㪇㪈㪉㪇 㪈㪌㪇 㪈㪏㪇 㪉㪈㪇 㪉㪋㪇 㪉㪎㪇 㪊㪇㪇 㪊㪊㪇 㪊㪍㪇 㪊㪐㪇ᣣ㩷 ࿑ 3.6㩷 ᐥ䉴䊤䊑䇮ၮ␆䉴䊤䊑䇮ਔ⠪䈱᷷ᐲᏅ䈱ᤨ㑆ᄌൻ㩷 ⸃ᨆ⚿ᨐ㪈㪌㪈㪇㪌§䋴䋮◲࿾⋚෻ജଥᢙផቯ㪇㪇㩷㪊㪇 㪍㪇 㪐㪇 㪈㪉㪇 㪈㪌㪇 㪈㪏㪇 㪉㪈㪇 㪉㪋㪇 㪉㪎㪇 㪊㪇㪇 㪊㪊㪇 㪊㪍㪇 㪊㪐㪇ᣣ⋧ኻᄌ૏ 㫌㫏㪃㫌㫐 䈱ᤨ㑆ᄌൻ䈱ᯏ᭴䉕⠨䈋䉎䇯ᐥ䉴䊤䊑䈫䉕࿑ 3.2㩷 Node5 䈱᷷ᐲ䈻䈱឵᳇࿁ᢙ Nv ᓇ㗀㩷 ⸃ᨆ⚿ᨐᡰ䈋䉎఺㔡ⵝ⟎䈱᳓ᐔ೰ᕈ䈲ᐥ䉴䊤䊑䇮ၮ␆䉴䊤䊑䈱ゲ⸃ᨆ㩷㪥㫆㪻㪼㪌㩷㪥㫆㪻㪼㪌㩷㩷䊏䉾䊃ጀਛᄩ೰ᕈ䈮Ყ䈼䈩ήⷞ䈪䈐䉎䈾䈬චಽዊ䈘䈇䈱䈪䇮ᐥ䉴䊤䊑㪊㪌ᣣᐔဋ᷷ᐲ㩷㷄㪊㪇㪉㪌㪉㪇㪥㪭䋽㪉㪥㫍䋽㪈㪥䌶䋽㪇㪅㪉㪥㫍䋽㪇㪅㪇㪌䈲᷷ᐲᄌൻ䈮ኻ䈚䈩⥄↱િ❗䈜䉎䈏䇮ၮ␆䉴䊤䊑䈱િ❗
䈲࿑ 4.1 䈱᭽䈭᧮࿾⋚♽䈱࿾⋚෻ജଥᢙ䈱ሽ࿷䈮䉋䉍⥄↱િ❗䈏ᛥ೙䈘䉏䈩䈇䉎䈫⠨䈋䉎䇯㪈㪌㪈㪇㪌ၮ␆䉴䊤䊑㪇㪇㪊㪇 㪍㪇 㪐㪇 㪈㪉㪇 㪈㪌㪇 㪈㪏㪇 㪉㪈㪇 㪉㪋㪇 㪉㪎㪇 㪊㪇㪇 㪊㪊㪇 㪊㪍㪇 㪊㪐㪇࿾⋚ᣣuKEAಽᏓ䈞䉖ᢿ䍨䍼䍦 k h ave  bL
࿑ 3.3㩷 Node䋵䈱᷷ᐲ䈻䈱឵᳇࿁ᢙ Nv ᓇ㗀㩷 ⸃ᨆ⚿ᨐ

࿑ 4.1 ၮ␆ࠬ࡜ࡉߩ᷷ᐲિ❗ᬌࡕ࠺࡞㩷䋭㪈㪍䋭㐳ᄢ఺㔡᭴ㅧ‛ߩࡇ࠶࠻ጀ᷷ᐲߣ఺㔡ⵝ⟎ߦ↢ߓࠆ⋧ኻᄌ૏ߩ㑐ଥߦߟ޿ߡߩ⠨ኤ ታ᷹ߣ⸃ᨆ⚿ᨐᲧセ䈜䇯࿑ 2.3 ࿑ 2.4 䈱⸘᷹⚿ᨐ䈮Ყ䈼䉎䈫⍴๟ᦼᚑಽ䈏ᄙ䈖䈱䊝䊂䊦䈪 㫏 ૏⟎䈱᳓ᐔᄌ૏䈲ᰴ䈪䈅䉎䇯㩷u ( x)

P  'T  Lsinh( E䈇䈏ో૕⊛䈭௑ะ䈲⦟䈒ᝒ䈋䈩䈇䉎䇯ᰴ䈮䇮੹࿁ᓧ䉌䉏x)
L (1)䈢᳓ᐔ࿾⋚෻ജଥᢙ䈱୯䈱䉥䊷䉻䊷䉕ᬌ⸛䈜䉎䇯ᢥ₂ 5)䈮䉋䉎න᧮䈱 ࿾⋚෻ജଥ ᢙ䈲䇮ᄌ૏ଐ ሽᕈ䈏䈅䉎䈎

E cosh E䉌䇮㩷 㵱ᄌ૏䈲ၮ␆䉴䊤䊑ਛᔃ䈎䉌䈱〒㔌䈮Ყ଀䈜䉎㵱䈫઒~~㱎䋺࿾⋚䊋䊈㪆ゲ೰ᕈᲧ㪃 k 㩷 䋺৻ቯ䈫䈚䈢࿾⋚෻ജଥᢙ㩷ቯ䈚䈢ᐔဋ⊛䈭࿾⋚෻ജଥᢙ䉕䇮䈖䈖䈪ㅒ▚ቯ䈘䉏䈢 k㪙䋺ၮ␆䉴䊤䊑᏷䋨⋥੤ᣇะ䈱䉴䊤䊑᏷㪆䋲䋩㪃 EA 㩷 䋺ၮ␆䉴ߣᲧセߔࠆ‫ޕ‬ᢥ₂ 5)䈮䉋䉎ᐔဋ⊛䈭࿾⋚෻ജଥᢙ䈱⴫䊤䊑䈱ゲ೰ᕈ㩷~k B  L2EAE⃻䈲 Appendix 䈮␜䈚䈩䈅䉎䇯Ყセ䈱⚿ᨐ䉕࿑ 4.7 䈮␜䈜䇯ᦨᄢ 1 䋙⒟ᐲ䈱ᄌ૏䉕⠨䈋䈢႐ว䇮x ᣇะ䈪ᜰ㊎䈎(2)㩷

䉌▚ቯ䈘䉏䉎୯䈱⚂ 1/4 ⒟ᐲ䈪䈅䉎䈖䈫䈏䉒䈎䉎䇯㐳ᤨ㑆タ⩄䈱⁁ᘒ䈏ᗐቯ䈘䉏䉎䈱䈪⚂ 1/4 ⒟ᐲ䈫䈇䈉୯䈮䈲ᅷᒰᕈ䈏䈅䉎䈫⠨䈋䉎䇯㩷ᦨᄖ✼ 㫏㪔㪣 䈪䈲㩷 ᰴ䈱䉋䈉䈮ᦠ䈔䉎䇯㩷u K  'T  L  I (3) 㩷 Itanh( E )E㩷 㩷 㩷 (4)㩷㱂㱢䋺ᦨᄖ✼ᄌ૏㪆⥄↱િ䈶䈮䉋䉎ᦨᄖ✼ᄌ૏䋨࿑ 㪋㪅㪉 ෳᾖ䋩㩷 㩷 ࿾⋚䊶ၮ␆䉴䊤䊑♽䈱㱂䉕઒ቯ䈜䉎䈫 㫏㪔㪣 䈮䈍䈇䈩䈲㩷 ᐥ䉴䊤䊑䈫ၮ␆䉴䊤䊑䈱⋧ኻᄌ૏䈲ᰴ䈱᭽䈮⴫⃻䈪䈐䉎䇯㩷 㩷㪈㪅㪈
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㱂䋽㫋㪸㫅㪿㩿㱎㪀㪆㱎㪇u (t ) K (T2 (t )  Te ) L  K (T8 (t )  Te ) L  I  (5)㪇㪅㪌㪈㪈㪅㪌㪉㪉㪅㪌㱎㪊࿑ 4.2  ǪߣǾ㑐ଥ (4)ᑼT2 㨮 T8 㧦ᐥࠬ࡜ࡉ‫ޔ‬ၮ␆ࠬ࡜ࡉߩ᷷ᐲ‫ ޔ‬Te 㧦ᐕᐔဋ㪈㪌㫐㩷㪔㩷㪇㪅㪎㪎㪇㪈㫏㩷㪄㩷㪉㪜㪄㪈㪋㪩㪉 㩷㪔㩷㪇㪅㪐㪏㪈㪋㪈㪇t㧦ᤨ㑆ߎߎߢߪ‫⸃ޔ‬ᨆߦࠃࠆᐥࠬ࡜ࡉ‫ޔ‬ၮ␆ࠬ࡜ࡉ᷷ᐲ
ࠍ↪޿ߡ(4)ᑼߦᓥ޿‫ޔ‬᷹ቯߐࠇߚᄖ᳇᷷ߣ ux,uy 㑐ଥ㧔࿑ 2.6‫ޔ‬࿑ 2.7㧕ߦㄭ޿㑐ଥࠍᓧࠄࠇࠆࠃ߁ߦ x㨮㫌㫏㩷㪄ᐕᐔဋ㩷㩷㫄㫄

᳇᷷ K㧦✢⤘ᒛଥᢙ㧔10-5/͠㧕㪇㪄㪌㫌㫏㪄ᐕᐔဋ✢ᒻ㩷㩿㫌㫏㪄ᐕᐔဋ㪀㪄㪈㪇y ᣇะߩǾࠍቯ߼ࠆߎߣ߇ߢ߈‫ޔ‬ᰴߩ᭽ߦ࿾⋚෻ജଥ

㪄㪈㪌~㪄㪈㪌ᢙ k ࠍㅒ▚⊛ߦ᳞߼ࠆߎߣ߇ߢ߈ࠆ‫ౕߩߘޕ‬૕⊛ߥᚻ⛯߈ߪᰴߢ޽ࠆ‫ޕ‬࿁Ꮻ䈎䉌䈱஍Ꮕ㪪㪫㪛㪔㪇㪅㪎㪐㫄㫄

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㪈㪌ᣣᐔဋᄖ᳇᷷㪄ᐕᐔဋ䇭㷄࿑ 4.3 ux ߣᄖ᳇᷷ߩኻᔕ Ǿ=0.50 ⸃ᨆ⚿ᨐdu㽲㩷䈱࿁Ꮻଥᢙ䇮 u max  u min 㩷 䈏⸘᷹୯䈮䈾䈿৻dTe~⥌䈜䉎䇯㽳㩿㪋㪀ᑼ䉋䉍ኻᔕ䈜䉎㱎䉕᳞䉄㩷 㽴㩿㪉㪀ᑼ䉋䉍 k 㩷 䉕㪍㫌䌹㪄ᐕᐔဋ㩷㫄㫄㪋᳿ቯ䈜䉎䇯ㆡಾ䈭㱢䉕ዉ౉䈜䉎䈖䈫䈮䉋䉍䇮⋧ኻᄌ૏䈫ᄖ᳇᷷䈫䈱⋧㑐ᕈ䈏䈏഍⊛䈮ᡷༀ䈘䉏䇮⸘᷹⚿ᨐ䈮䈾䈿ㄭ䈇⚿ᨐ䉕ᓧ䉎䈖䈫䈏䈪䈐䉎䇯㩷㫐㩷㪔㩷㪇㪅㪊㪇㪈㫏㩷㪄㩷㪎㪜㪄㪈㪌㪩㪉 㩷㪔㩷㪇㪅㪐㪏㪊㪋࿁Ꮻ䈎䉌䈱஍Ꮕ㪪㪫㪛㪔㪇㪅㪉㪐㪈㫄㫄㪉㪇㪄㪉㫌䌹㪄ᐕᐔဋ㪄㪋㩷 䈖 䈉 䈚 䈩 䇮 ᳓ ᐔ ࿾ ⋚ ෻ ജ ଥ ᢙ 䈫 䈚 䈩 1.44 䊶 10-04✢ᒻ㩷㩿㫌䌹㪄ᐕᐔဋ㪀㪄㪍tonf/(cm3) (x ᣇะ)䇮1.35䊶10-05tonf/(cm3)䈱୯䉕ᓧ䈢䇯䌹㪄㪈㪌ᣇะ䈱୯䈏 x ᣇะ䉋䉍⚂ 1 ᩴዊ䈘䈇⚿ᨐ䈫䈭䈦䈢䇯㩷 䈖䉏䈾䈬䈱Ꮕ䈏䈅䉎䈱䈲᣿䉌䈎䈮⍦⋫䈪䈅䉎䈏䇮੹࿁⠨䈋䈢㪄㪈㪇㪄㪌㪇㪌㪈㪇㪈㪌ᣣᐔဋᄖ᳇᷷㪄ᐕᐔဋ䇭㷄࿑ 4.4 uy ߣᄖ᳇᷷ߩኻᔕ Ǿ=0.45 ⸃ᨆ⚿ᨐᯏ᭴䈏ᄢ䈐䈒䈲ᄖ䉏䈩䈇䈭䈇䉅䈱䈫⠨䈋䈩䈇䉎䇯㩷㩷㩷 䈖䈉䈚䈩᳞䉁䈦䈢 ux,uy 䈱ᤨೞᱧ䉕࿑ 4.5䇮࿑ 4.6 䈮␜䋭㪈㪎䋭䊐䉳䉺ᛛⴚ⎇ⓥႎ๔㩷 ╙ 㪋㪍 ภ㫌㫏㩷㪄ᐕᐔဋ㩷㩷㫄㫄㪈㪌ᨆ䊶⸘᷹⚿ᨐᲧセ㪃䊐䉳䉺ᛛⴚ⎇ⓥႎ๔ 㪋㪋 ภ㪃㪉㪇㪇㪏㩷 㪊㪀㩷㩷㱂㪔㪇㪅㪌㪈㪇ਛጊ䇮㐳ᄢ఺㔡᭴ㅧ‛䈱᷷ᐲિ❗⸘᷹䈫⸃㉼㪃ᣣᧄᑪ▽㪌ቇળᄢળ᪪᭎㓸㩿ർ㒽㪀㪃㪥㫆㪉㪇㪈㪈㪏㪃㪉㪇㪈㪇㪃㩷 㪋㪀㪀દ⮮ඳᄦ㪃⫾㪇ᾲጀ䉕᦭䈜䉎࿾ਅゎ૕䈱᷷ᐲಽᏓᕈ⁁䈮㑐䈜䉎⎇ⓥ㪃᭴ㅧ♽⺰ᢥ㓸㪃╙ 㪋㪎㪈 ภ㪃㪈㪐㪄㪉㪏㪃㪈㪐㪐㪌 ᐕ 㪌 ᦬㪃㩷㪌㪀ᣣᧄᑪ▽ቇ㪄㪌㪄㪈㪇ળ㩷 ᑪ▽ၮ␆᭴ㅧ⸳⸘ᜰ㊎㩷 㪈㪐㪏㪏㩿㫇㫇㪉㪌㪊㪄㪉㪌㪋㪀㩷㫌㫏㪄ᐕᐔဋ㪄㪈㪌㪇㪊㪇㪍㪇㪐㪇㪘㫇㫇㪼㫅㪻㫀㫏㩷 㩷 㩷㪈㪉㪇 㪈㪌㪇 㪈㪏㪇 㪉㪈㪇 㪉㪋㪇 㪉㪎㪇 㪊㪇㪇 㪊㪊㪇 㪊㪍㪇 㪊㪐㪇ᣣ㩷㪈㪆㪈⿠ὐᜰ㊎䈱᳓ᐔ࿾⋚෻ജଥᢙ 㪢㪿 䈱⴫⃻䈲ᄌ૏ଐሽᕈ䈏䈅䉍䇮ᰴ䈱ᒻ䉕䈚䈩䈇䉎䇯㩷࿑ 4.5 ux ߩᤨ㑆ᄌൻ ⸃ᨆ⚿ᨐA  K h0 㩷㩷 㩷 㩷 㩷 A 3.16 㧦 㫌㪓㪇㪅㪈㪺㫄㩷 㩷 㩷 㩷 㩷 㩷 㩷 㩷 㩷 㩷 㩷 㩷 㩿㪸㪈㪀㩷㩷 㩷 㩷 㩷 㩷 A 1 / u 㩷 䋺㫌㪕㪇㪅㪈㪺㫄㩷K h 0 D  [  E 0 B 3 / 4 㩷 㩷 㪢㪥㪆㫄㪊㩷㩷 㩷 Kh㩷㱂䋽㪇㪅㪋㪌㪈㪌㫌㫏㩷㪄㫌㫏㪸㫍㪼㩷㩷㫄㫄㪈㪇㪌㪇㩷 㪙䋺᧮ᓘ㩿㪺㫄㪀㪆㪈㪺㫄㩷 ήᰴర㩷㪄㪌㪜㪇䋺ᄌᒻଥᢙ㩷 㪢㪥㪆㫄㪉㻍㪎㪇㪇䍃㪥㪸㫍㪼㩷㫌䌹㪄ᐕᐔဋ㪄㪈㪇㪥㪸㫍㪼䋺ᐔဋ 㪥 ୯㩷 㩷 㱚䋺න᧮䈱ᤨ䋱㩷㪄㪈㪌㪇㪊㪇㪍㪇㪐㪇㱍䋺㻍㪎㪇㪇䍃㪥㪸㫍㪼 䈪▚ቯ䈚䈢ᤨ㩷 ੹࿁䈲 㪍㪇㩷㪈㪉㪇 㪈㪌㪇 㪈㪏㪇 㪉㪈㪇 㪉㪋㪇 㪉㪎㪇 㪊㪇㪇 㪊㪊㪇 㪊㪍㪇 㪊㪐㪇ᣣ㩷㩷㪈㪆㪈⿠ὐ੹࿁㩷 㪙㪔㪈㪈㪇䇮㱚㪔㪈㩷 㱍㪔㪍㪇 䉋䉍ᰴ䉕ᓧ䉎䇯㩷㩷 㪢㪿㪇㪔㪊㪎㪇㪋㪅㪢㪥㪆㫄㪊㪔㪊㪅㪎㪜㪄㪇㪋㪫㫆㫅㪽㪆㪺㫄㪊㩷࿑ 4.6 uy ߩᤨ㑆ᄌൻ ⸃ᨆ⚿ᨐ㵱ᄌ૏䈲ၮ␆䉴䊤䊑ਛᔃ䈎䉌䈱〒㔌䈮Ყ଀䈜䉎㵱䈫䈚䈩㪈㪅㪋㪜㪄㪇㪊ᐔဋ࿾⋚᳓ᐔ෻ജଥᢙ㩷㫂㪿㪸㫍㪼㩷㫋㫆㫅㪽㪆㪺㫄㪊᧚䈮ᷰ䈦䈩䈱ᐔဋ୯㩿ᦨᄖ✼ᄌ૏䈱㑐ᢙ䈫䈭䉎㪀䉕᳞䉄䈫㪈㪅㪉㪜㪄㪇㪊kh㪈㪅㪇㪜㪄㪇㪊ᰴ䈱᭽䈮䈭䉎䇯㫌䋺ᦨᄖ✼ᄌ૏㩿㪺㫄㪀䉕⁛┙ᄌᢙ䈫䈚䈩䇮ήk h aveᰴరൻ䈘䉏䈢ᐔဋ᳓ᐔ࿾⋚ଥᢙ䋺㩷 㪢㪿㪸㫍㪼㪆㪢㪿㪇㩷㪏㪅㪇㪜㪄㪇㪋ᐔဋ࿾⋚෻ജଥᢙ㪍㪅㪇㪜㪄㪇㪋䈱⴫⃻䈲ᰴ䈫䈭䉎䇯㩷⸘᷹䈎䉌䌸ᣇะ⸘᷹䈎䉌䌹ᣇะ㪋㪅㪇㪜㪄㪇㪋⸘᷹䈎䉌㫏㫐ᐔဋªºL« L9 1»1dx » / L« ³ 3.016dx  ³x »L9 1 u «0(a2)㩷
«¬L »¼㪉㪅㪇㪜㪄㪇㪋㪇㪅㪇㪜㪂㪇㪇㪇㪇㪅㪉㪇㪅㪋㪇㪅㪍㪇㪅㪏㪈㪈㪅㪉㪈㪅㪋㪈㪅㪍㪈㪅㪏

K have / K h 0㪉ၮ␆䉴䊤䊑㩷┵ㇱᄌ૏㩷㫌㩷㪺㫄࿑ 4.7 ᐔဋ᳓ᐔ࿾⋚෻ജଥᢙ ⸘᷹߆ࠄߩផቯ୯ߣ㩷ᜰ㊎୯߆ࠄߩ⸘▚୯ߩኻᔕ3.16] 1 §䋵䋮䉁䈫䉄2  2 ]1uߚߛߒ ] 1 { 0.1 / u㩷㪈 ᐕᒝ䈮䉒䈢䉎䊏䉾䊃ጀ䈱᳇᷷䇮఺㔡ⵝ⟎਄ਅ䈱⋧ኻᄌ(a3)㩷
㩷૏⸘᷹⚿ᨐ䉕ႎ๔䈚䈢䇯䉁䈢䇮㪈 ᰴర᷷ᐲ⸃ᨆ䇮◲න䈭䊙䈵 䈫 䈖 䈫 㩷䉪䊨䊝䊂䊦䈮ၮ䈨䈇䈩䇮᷹ⷰ䈘䉏䈢఺㔡ⵝ⟎਄ਅ䈱⋧ኻ㩷 ⠨䈋䈩䉂䉏䈳ᒰ䈢䉍೨䈱ᯏ᭴䈪䈚ᄌ૏䈲䇮਄ደゎ૕䇮ၮ␆䉴䊤䊑䈲᭎⇛ᣣᐔဋᄖ᳇᷷䈮ᓥ䈦䈩િ❗䈜䉎䈏ၮ␆䉴䊤䊑䈲᧮ၮ␆䈱᳓ᐔ࿾⋚෻ജଥ䈢䈏䇮⚻㛎⍮䈫䈚䈩৻ᣤฃ䈔౉䉏䈢ᢙ䈮䉋䉎᜔᧤䉕ฃ䈔䈠䈱Ꮕಽ䈏᷹ⷰ䈘䉏䈩䈇䈢䈫⸃㉼䈪੐ታ䈱⺑᣿䈏䈧䈇䈩䉴䉾䉨䊥䈚䉁䈚䈐䉎䈖䈫䉕␜䈚䈢䇯䉁䈢䇮䈠䈱ᤨ䈱᳓ᐔ࿾⋚෻ജଥᢙ䈱୯䈢䇯㩷䈏⍮䉏䈢䇯㩷ਛጊ㩷 ᣽ዏ㩷ෳ ⠨ ᢥ ₂㩷㩷㪈㪀㩷 ਛጊ᣽ዏ㪃㐳ᄢ఺㔡䊒䊧䉴䊃䊧䉴䊃᭴ㅧ‛䈱䉪䊥䊷䊒⸃㩷ᨆ㪃ᣣᧄᑪ▽ቇળᄢળ᪪᭎㓸㩿ਛ࿖㪀㪃㪥㫆㪉㪊㪋㪈㪏㪃㪉㪇㪇㪏㩷 㪉㪀ਛጊ᣽ዏ㪃㩷 ᐔ㕙᭴ㅧ‛䈱䉪䊥䊷䊒⸃ᨆ㩷 ⸃ᨆᴺ䈫㐳ᄢ఺㔡䊒䊧䉴䊃䊧䉴䊃䊒䊧䉨䊞䉴䊃䉮䊮䉪䊥䊷䊃᭴ㅧ‛䈮䈧䈇䈩䈱⸃䋭㪈㪏䋭