(2.8) ߎߩᑼ߆ࠄ㧘ᑼ(2.5)ߩ▵ὐᄌ૏ܷሺݔǡ ߱ሻߪᰴߩࠃ߁ߦߥࠆ㧚 ܷሺݔǡ ߱ሻ ൌ ܽଵ݁ି௜௞ಽ௫൅ ܽଶ݁ା௜௞ಽ௫ൌ ࢋሺݔǡ ߱ሻࢇ (2.9) ߚߛߒ㧘 ࢋሺݔǡ ߱ሻ ൌ ሾ݁ି௜௞ಽ௫ ݁ା௜௞ಽ௫ሿ (2.10

(1)

ࠬࡍࠢ࠻࡞ⷐ⚛ᴺߦၮߠߊ㜞ᝄേᢙ⿠ᝄߦࠃࠆ᭴ㅧ‛ߩ៊்หቯߦߟ޿ߡ

Damage Identification Technique using High-Frequency Excitation based on the Spectral Element Method

ฎᎹᗲሶ*㧘᧻የථᒎ**㧘⷏Ꮉᤩม**

Aiko Furukawa, Takuya Matsuo, Koji Nishikawa

*੩ㇺᄢቇᄢቇ㒮ಎᢎ᝼, Ꮏቇ⎇ⓥ⑼㧔ޥ615-8540੩ㇺᏒ⷏੩඙੩ㇺᄢቇ᩵㧕

**੩ㇺᄢቇᄢቇ㒮ୃ჻⺖⒟, Ꮏቇ⎇ⓥ⑼㧔ޥ615-8540੩ㇺᏒ⷏੩඙੩ㇺᄢቇ᩵㧕

This paper presents a damage identification technique using high-frequency excitation based on the spectral element method for the structural health monitoring. Considering a drawback of the low-frequency-based damage identification technique, this study proposes a damage identification technique using kHz-level frequency that can detect smaller damage efficiently. It is assumed that the structure is excited with a harmonic force by a piezoelectric actuator and that the method focuses on the difference of the frequency response function (FRF) by damage. Moreover, it uses the spectral element method that is suitable for analyzing structural responses at high frequency domain. The effectiveness of the proposed method was verified by numerical simulations.

Key Words: damage identification, spectral element method, high-frequency, FRF

ࠠ࡯ࡢ࡯࠼㧦៊்หቯ㧘ࠬࡍࠢ࠻࡞ⷐ⚛ᴺ㧘㜞ᝄേᢙ㧘๟ᵄᢙᔕ╵㑐ᢙ

ߪߓ߼ߦ

⃻࿷ࠊ߇࿖ߢߪ㧘㜞ᐲ⚻ᷣᚑ㐳ᦼߦ᨞⸳ߐࠇߚᯅ᪞ߩ

⠧᧎ൻ߇␠ળ໧㗴ߣߥߞߡ߅ࠅ㧘࿾㔡ᄙ⊒࿖ߢ޽ࠆࠊ߇

࿖ߦ߅޿ߡ㧘⠧᧎ൻߒߚᯅ᪞ߪᏱߦ࿾㔡ߦࠃࠆෂᯏߦᦑ ߐࠇߡ޿ࠆߣ޿߃ࠆ㧚ߎߩࠃ߁ߥ⠧᧎ൻߒߚᯅ᪞ࠍ᠗෰

ߒᣂߚߦ᨞⸳ߔࠆߩߪ⩨ᄢߥࠦࠬ࠻߇߆߆ࠆߚ߼㧘ᑪ⸳

ᛩ⾗߇ᷫዋ௑ะߦ޽ࠆᤓ੹ߢߪ㧘ᣢ⸳ᯅ᪞ߩᣂⷙᦝᣂߪ

࿎㔍ߢ޽ࠆ㧚ߒߚ߇ߞߡ㧘ᯅ᪞ߩㆡಾߥ⛽ᜬ࡮▤ℂߣߘ ߩࠦࠬ࠻೥ᷫ߇ᔅ㗇ߩ⺖㗴ߢ޽ࠆ㧚

ߎߩࠃ߁ߥਛ㧘ฦ࿖ߢᯅ᪞ߩ㊀ᄢ៊்੐᡿߇ᄙ⊒ߒߡ ߅ࠅ㧘ࠊ߇࿖ߦ߅޿ߡ߽2007ᐕߦᧁᦥᎹᄢᯅ߿ᧄ⨿ᄢᯅ ߩᢳ᧚⎕ᢿ੐᡿߇⊒↢ߒߚ㧚޿ߕࠇ߽㜞ᐲ⚻ᷣᚑ㐳ᦼߦ ᑪ⸳ߐࠇ㧘ଏ↪ᓟ40㨪45ᐕ߇⚻ㆊߒߚ㍑࠻࡜ࠬᯅߩ੐᡿

ߢ޽ࠆ ¹⁾㧚ߎߩࠃ߁ߥ㊀ᄢ੐᡿߇⊒↢ߔࠆ೨ߦ㧘੐೨ߦ

៊்ࠍ⊒⷗ߔࠆߩ߇㊀ⷐߢ޽ࠆ㧚

ᯅ᪞ߩ⛽ᜬ࡮▤ℂߦ߅޿ߡ៊்ࠍ⊒⷗ߔࠆᣇᴺߩਛᔃ ߣߥߞߡ޿ࠆߩߪ⋡ⷞὐᬌߢ޽ࠆ㧚⋡ⷞὐᬌߪ㧘ᄙߊߩ ഭജߣᤨ㑆߇߆߆ࠅ㧘ߐࠄߦ್ቯ⚿ᨐߦ߽߫ࠄߟ߈߇↢

ߓࠆน⢻ᕈ߇޽ࠅ㧘ߘߩା㗬ᕈߩ໧㗴߇ᜰ៰ߐࠇߡ޿ࠆ㧚

៊்߇⷗߃ࠆ▸࿐ߦ߅޿ߡߪ㧘⋡ⷞߪ᦭ലߥᚻᲑߢ޽ࠆ

ߣ޿߃ࠆ߇㧘⷗߃ߥ޿㧘⷗ߦⴕߌߥ޿႐ᚲߩ៊்ࠍᬌ಴

ߔࠆߎߣߪߢ߈ߕ㧘߹ߚ㧘ᄖოߢⷒࠊࠇߡ޿ࠆౝㇱߩ៊

்ࠍ⊒⷗ߔࠆߦߪ㧘ᄖოࠍขࠅ㒰߆ߥߌࠇ߫ߥࠄߕ㧘⤘

ᄢߥࠦࠬ࠻ߣᤨ㑆߇߆߆ࠆߣ޿߁໧㗴߽޽ࠆ²⁾㧚 ߎߩࠃ߁ߥ໧㗴ࠍ⸃᳿ߔࠆߚ߼㧘⋡ⷞὐᬌߦઍࠊࠆ៊

்ߦࠃࠆᝄേ․ᕈߩᄌൻࠍ೑↪ߒߚ៊்ᬌ಴ᚻᴺߢ޽ࠆ

᭴ㅧࡋ࡞ࠬࡕ࠾࠲࡝ࡦࠣߩ⎇ⓥ߇ㅴ߼ࠄࠇߡ޿ࠆ㧚ᧄ⺰

ᢥߢߪ㧘ᓥ᧪ߩ⎇ⓥߩ໧㗴ὐࠍ〯߹߃㧘៊்ᬌ಴ᚻᴺߩ

৻ߟࠍឭ᩺ߒ㧘ߘߩఝ૏ᕈࠍᬌ⸽ߔࠆߎߣ߇⋡⊛ߢ޽ࠆ㧚 ᝄേ․ᕈߩᄌൻࠍ೑↪ߒߡ᭴ㅧ‛ߩ៊்ࠍᬌ಴ߔࠆߚ

߼ߩ᭽ޘߥᚻᴺ ^3)~5)߇ឭ᩺ߐࠇߡ޿ࠆ㧚ᓸേ⸘᷹ߥߤߩ Hz࡟ࡌ࡞ߩૐᝄേᢙ㗔ၞߩᝄേ․ᕈࠍ೑↪ߔࠆ߽ߩߪ㧘 ዊߐߥ៊்ߩᬌ಴ߦߪㆡߒߡ߅ࠄߕ㧘᭴ㅧ‛ో૕߇ᝄേ

ߔࠆߚ߼ᯅ᪞ో૕ߦ࠮ࡦࠨࠍ⸳⟎ߒߥߌࠇ߫ߥࠄߥ޿ߣ

޿߁໧㗴߇޽ࠆ㧚⿥㖸ᵄᬌᩏߥߤߩ MHz࡟ࡌ࡞ߩ㜞ᝄ

േᢙ㗔ၞߩᝄേ․ᕈࠍ೑↪ߔࠆ߽ߩߪ㧘৻ᐲߦᬌᩏߢ߈ ࠆ▸࿐߇㕖Ᏹߦ⁜ߊ᭴ㅧ‛ో૕ࠍᬌᩏߔࠆߩߦ㕖Ᏹߦᤨ

㑆߇߆߆ࠆߣ޿߁໧㗴߇޽ࠆ㧚ߘߎߢᧄ⎇ⓥߢߪ㧘ዊߐ ߥ៊்ࠍല₸ࠃߊᬌ಴ߢ߈ࠆkHz࡟ࡌ࡞ߩ㜞ᝄേᢙ㗔ၞ

ߩᝄേ․ᕈࠍ೑↪ߒߚ៊்หቯᚻᴺࠍឭ᩺ߔࠆ㧚࿶㔚ဳ

ࠕࠢ࠴ࡘࠛ࡯࠲ߢߩ⺞๺ᄖജߩ⿠ᝄࠍᗐቯߒ㧘៊்ߦ઻

(2)

߁๟ᵄᢙᔕ╵㑐ᢙߩᄌൻߦ⌕⋡ߔࠆ㧚หቯߦ㜞ᝄേᢙ㗔

ၞߩ⸃ᨆߦㆡߒߚࠬࡍࠢ࠻࡞ⷐ⚛ᴺ ⁶⁾ࠍ↪޿ࠆߩ߇․ᓽ ߢ޽ࠆ㧚ᢙ୯ࠪࡒࡘ࡟࡯࡚ࠪࡦߦࠃߞߡឭ᩺ᚻᴺߩ᦭↪

ᕈࠍᬌ⸽ߔࠆ㧚

ࠬࡍࠢ࠻࡞ⷐ⚛ᴺ

ࠬࡍࠢ࠻࡞ⷐ⚛ᴺߦߟ޿ߡߘߩ᭎ⷐࠍ⺑᣿ߔࠆߣߣ߽

ߦ㧘᦭㒢ⷐ⚛ᴺߣߩ⸃ᨆ⚿ᨐߩᲧセࠍⴕ߁㧚

᦭㒢ⷐ⚛ᴺ㧔FEM㧕߿ࠬࡍࠢ࠻࡞ⷐ⚛ᴺ㧔SEM㧕ߢߪ㧘

᭴ㅧ‛ࠍ᦭㒢୘ߩⷐ⚛ߩ㓸ว૕ߣߒߡᝒ߃㧘ฦⷐ⚛߇ⷐ

⚛਄ߩ▵ὐߢㅪ⚿ߐࠇߡ޿ࠆ߽ߩߣߒߡ⠨߃ࠆ㧚ⷐ⚛ౝ

ߩᄌ૏ࠍ▵ὐᄌ૏ߢ⵬㑆ߔࠆ㓙㧘FEMߢߪᄙ㗄ᑼߢ⵬㑆 ߔࠆߩߦኻߒ㧘SEMߢߪᝄേᢙߩ㑐ᢙߢ⵬㑆ߔࠆ㧚හߜ SEM ߪ▵ὐᄌ૏ߣ▵ὐജߩ㑐ଥࠍ⴫ߔേ೰ᕈⴕ೉ࠍᝄ

േᢙᲤߦ᭴▽ߔࠆ๟ᵄᢙ㗔ၞߩ⸃ᴺߢ޽ࠆ㧚

ቯᑼൻ

ࠝࠗ࡜࡯࡮ࡌ࡞࠿࡯ࠗ᪞ࠍኻ⽎ߦ㧘ࠬࡍࠢ࠻࡞ⷐ⚛ᴺ ߦၮߠ޿ߡⷐ⚛ⴕ೉ࠍዉ಴ߔࠆ㧚

ゲᣇะᚑಽ

ゲᣇะߩᄌ૏ࠍݑሺݔǡ ݐሻ㧘ⷐ⚛ߩ㐳ߐ݈㧘ᢿ㕙Ⓧܣ㧘ࡗࡦ

ࠣ₸ܧ㧘න૏૕Ⓧ㊀㊂ߩߣߔࠆߣ㧘ㆇേᣇ⒟ᑼߪᰴߩࠃ߁ ߦ⴫ߐࠇࠆ㧚

ܧܣ߲^ଶݑሺݔǡ ݐሻ

߲ݔ^ଶ െ ߩܣ߲^ଶݑሺݔǡ ݐሻ

߲ݐ^ଶ ൌ Ͳ (2.1) ゲജܰ௧ሺݔǡ ݐሻߪ㧘ᰴᑼߩㅢࠅߢ޽ࠆ㧚

ܰ_௧ሺݔǡ ݐሻ ൌ ܧܣ߲ݑሺݔǡ ݐሻ

߲ݔ (2.2)

ᄌ૏ݑሺݔǡ ݐሻߩࡈ࡯࡝ࠛᄌ឵ࠍܷሺݔǡ ߱ሻߣߔࠆߣ㧘ᰴߩᑼ߇ ᚑࠅ┙ߟ㧚

ܷሺݔǡ ߱ሻ ൌͳ

ܶන ݑሺݔǡ ݐሻ݁^ି௜ఠ௧݀ݐ

்

଴

(2.3) ᑼ(2.1)ࠍ๟ᵄᢙ㗔ၞߢᦠ߈⴫ߔߣ㧘

ܧܣ݀^ଶܷሺݔǡ ߱ሻ

݀ݔ^ଶ ൅ ߱^ଶߩܣܷሺݔǡ ߱ሻ ൌ Ͳ (2.4) ߣߥࠆ㧚ߎߩ⸃ߪ㧘ᰴߩࠃ߁ߥᒻߢផቯߐࠇࠆ㧚

ܷሺݔǡ ߱ሻ ൌ ܽ݁^{ି௜௞ሺఠሻ௫} (2.5) ᑼ(2.5)ࠍᑼ(2.4)ߦઍ౉ߔࠆߎߣߦࠃࠅ㧘ᰴߩ㑐ଥ߇ᓧ ࠄࠇࠆ

݇^ଶെ ݇௅ଶൌ Ͳ (2.6) ߚߛߒ㧘݇_௅ߪ߱ߩ㑐ᢙߢ޽ࠆ㧚

݇௅ൌ ߱ටߩ

ܧ (2.7)

ࠃߞߡ㧘ᑼ(2.6)ߩ⸃ߪ㧘ᰴᑼߢ⴫ߐࠇࠆ㧚

݇ଵൌ െ݇ଶൌ ݇௅ (2.8) ߎߩᑼ߆ࠄ㧘ᑼ(2.5)ߩ▵ὐᄌ૏ܷሺݔǡ ߱ሻߪᰴߩࠃ߁ߦߥࠆ㧚

ܷሺݔǡ ߱ሻ ൌ ܽଵ݁^ି௜௞^ಽ^௫൅ ܽଶ݁^ା௜௞^ಽ^௫ൌ ࢋሺݔǡ ߱ሻࢇ (2.9) ߚߛߒ㧘

ࢋሺݔǡ ߱ሻ ൌ ሾ݁^ି௜௞^ಽ^௫ ݁^ା௜௞^ಽ^௫ሿ

(2.10)

ࢇ ൌ ሼܽଵ ܽଶሽ^்

ߢ޽ࠆ㧚ߎߎߢ㧘ⷐ⚛ߩႺ⇇᧦ઙࠃࠅᰴߩᑼ߇ᓧࠄࠇࠆ㧚

ࢊሺ߱ሻ ൌ ൜ܷଵ

ܷ_ଶൠ ൌ ൜ܷሺͲሻ

ܷሺ݈ሻൠ (2.11) ᑼ(2.9)ࠍᑼ(2.11)ߩฝㄝߦઍ౉ߔࠆߣ㧘ᰴᑼࠍᓧࠆ㧚

ࢊሺ߱ሻ ൌ ൤ࢋሺͲǡ ߱ሻ

ࢋሺ݈ǡ ߱ሻ൨ ࢇ ൌ ࡴ^ࡾሺ߱ሻࢇ (2.12) ߚߛߒ㧘

ࡴ_ࡾሺ߱ሻ ൌ ቂ ͳ ͳ

݁^ି௜௞^ಽ^௟ ݁^ା௜௞^ಽ^௟ቃ (2.13) ߢ޽ࠆ㧚ᑼ(2.12)ࠍ૶ߞߡᑼ(2.9)߆ࠄࡌࠢ࠻࡞aࠍᶖ෰ߔ ࠆߣ㧘ᰴᑼࠍᓧࠆ㧚

ܷሺݔǡ ߱ሻ ൌ ࡺ_ࡾሺݔǡ ߱ሻࢊሺ߱ሻ (2.14) ߚߛߒ㧘

ࡺ_ࡾሺݔǡ ߱ሻ ൌ ࢋሺݔǡ ߱ሻࡴ_ࡾ^ିଵሺ߱ሻ ൌ ሾܰோଵሺݔǡ ߱ሻ ܰோଶሺݔǡ ߱ሻሿ

ܰ_ோଵሺݔǡ ߱ሻ ൌ ሾ݇_௅ሺ݈ െ ݔሻሿȀ ሺ݇_௅݈ሻ

ܰ_ோଶሺݔǡ ߱ሻ ൌ ሺ݇_௅ݔሻ Ȁ ሺ݇_௅݈ሻ

(2.15)

ߢ޽ࠆ㧚ᑼ(2.2)ߩゲജࠍ㧘๟ᵄᢙ㗔ၞߢ⴫ߔߣ㧘ᰴߩᑼ ߢ⴫ߐࠇࠆ㧚

ܰሺݔǡ ߱ሻ ൌ ܧܣܷ݀ሺݔǡ ߱ሻ

݀ݔ (2.16)

ߎߩⷐ⚛ౝߩゲജߣ▵ὐߦ૞↪ߔࠆജߩ㑐ଥߪ㧘ᰴᑼߢ

⴫ߐࠇࠆ㧚

ࢌ_ࢉሺ߱ሻ ൌ ൜ܰଵ

ܰ_ଶൠ ൌ ൜െܰሺͲሻ

൅ܰሺ݈ሻൠ (2.17) ᑼ(2.14)ߣᑼ(2.16)ࠍᑼ(2.17)ߩฝㄝߦઍ౉ߔࠆߣᰴߩᑼ ߇ᓧࠄࠇࠆ㧚

ࡿࡾሺ߱ሻࢊሺ߱ሻ ൌ ࢌࢉሺ߱ሻ (2.18) ߚߛߒ㧘

ࡿࡾሺ߱ሻ ൌܧܣ

݈ ቂݏோଵଵ ݏோଵଶ

ݏ_ோଵଶ ݏ_ோଶଶቃ ൌ ࡿࡾሺ߱ሻ^் ݏோଵଵൌ ݏோଶଶൌ ሺ݇௅݈ሻȀ ሺ݇௅݈ሻ

ݏோଵଶൌ െሺ݇௅݈ሻȀ ሺ݇௅݈ሻ

݇௅ൌ ߱ඥߩ ܧΤ

(2.19)

ߢ޽ࠆ㧚

ߖࠎᢿ࡮ᦛߍᣇะᚑಽ

ߣหߓࠃ߁ߦ㧘ߖࠎᢿᣇะߩᄌ૏ࠍݒሺݔǡ ݐሻߣ⟎ߊ㧚 ܧܫ߲^ସݒሺݔǡ ݐሻ

߲ݔ^ସ െ ߩܣ߲^ଶݒሺݔǡ ݐሻ

߲ݐ^ଶ ൌ Ͳ (2.20) ߖࠎᢿജߣᦛߍࡕ࡯ࡔࡦ࠻ߪ㧘ᰴߩㅢࠅߢ޽ࠆ㧚

ܳ_௧ሺݔǡ ݐሻ ൌ െܧܫ߲^ଷݒሺݔǡ ݐሻ

߲ݔ^ଷ ܯ௧ሺݔǡ ݐሻ ൌ ܧܫ߲^ଶݒሺݔǡ ݐሻ

߲ݔ^ଶ

(2.21)

ߣห᭽ߦߔࠆߣ㧘ݒሺݔǡ ݐሻߩࡈ࡯࡝ࠛᄌ឵ܸሺݔǡ ߱ሻߪ㧘

ᰴߩᑼߢ⴫ߐࠇࠆ㧚

ܸሺݔǡ ߱ሻ ൌ ܽଵ݁^ି௜௞^ಷ^௫൅ ܽଶ݁^ି௞^ಷ^௫൅ ܽଷ݁^ା௜௞^ಷ^௫൅ ܽସ݁^ା௞^ಷ^௫ (2.22) ߚߛߒ㧘݇ிߪ߱ߩ㑐ᢙߢ޽ࠆ㧚

(3)

݇_ிൌ ξ߱ ඨߩܣ ܧܫ

ర (2.23)

ߎࠇࠄߩᑼ߆ࠄߣห᭽ߦߒߡ㧘ߖࠎᢿ࡮ᦛߍᣇะߩ

േ೰ᕈⴕ೉ࡿ_࡮ሺ߱ሻ߇ዉ಴ߐࠇࠆ㧚ߥ߅㧘ࠬࡍࠢ࠻࡞ⷐ⚛

ᴺߢߪ⾰㊂ߩᓇ㗀ߪേ೰ᕈⴕ೉ߦ฽߹ࠇߡ޿ࠆ㧚

᦭㒢ⷐ⚛ᴺߣߩᲧセ

଀ߣߒߡ㧘᦭㒢ⷐ⚛ᴺߩゲᣇะߩⷐ⚛೰ᕈⴕ೉ࠍ਄ߍ ࠆߣᰴߩࠃ߁ߦߥࠆ㧚

ࡷோൌܧܣ

݈ ቂ ͳ െͳ

െͳ ͳ ቃ (2.24)

৻ᣇ㧘ࠬࡍࠢ࠻࡞ⷐ⚛ᴺߩゲᣇะߩേ೰ᕈⴕ೉ߪᑼ(2.19) ࠃࠅએਅߩࠃ߁ߦߥࠆ㧚

ࡿ_ோሺ߱ሻ ൌܧܣ݇ሺ߱ሻ

݈ ۏێ ێۍ ͳ

݇ሺ߱ሻ െ ͳ

݇ሺ߱ሻ

െ ͳ

݇ሺ߱ሻ

ͳ

݇ሺ߱ሻ ےۑۑې

݇ሺ߱ሻ ൌ ݈߱ඥߩȀܧ

(2.25)

ⷐ⚛ౝߩᄌ૏ࠍ▵ὐᄌ૏ߢ⵬㑆ߔࠆ㓙㧘FEMߢߪᄙ㗄 ᑼߢ⵬㑆ߒߚ߇㧘SEMߢߪᝄേᢙߩ㑐ᢙߢ⵬㑆ߒߚ㧚㜞 ᝄേᢙߢ⿠ᝄߔࠆ႐วߪᛒ߁ᵄ㐳߇⍴޿ߚ߼㧘FEMߢߪ ⷐ⚛ಽഀᢙࠍᄙߊขࠄߥߌࠇ߫ߥࠄߥ޿ߩߢ㧘⸘▚ᤨ㑆 ߇⤘ᄢߦߥࠆߣ޿߁໧㗴߇޽ࠆߣ⠨߃ࠄࠇࠆ㧚ߘߩ৻ᣇ㧘 SEMߢߪᢿ㕙ᒻ⁁߇ᄌൻߔࠆὐ߿ᄖജࠍਈ߃ࠆὐ㧘ᔕ╵

ࠍ▚಴ߔࠆὐ╬ࠍ㒰޿ߡⷐ⚛ࠍಽഀߔࠆᔅⷐ߇ߥ޿ߣ⠨

߃ࠄࠇࠆ㧚ᧄ▵ߢߪ㧘ⷐ⚛ಽഀᢙ߇⸃ᨆ⚿ᨐߦߤߩࠃ߁ ߥᓇ㗀ࠍ෸߷ߔ߆ࠍFEMߣSEMߩᲧセࠍㅢߒߡᬌ⸽ߔ ࠆ㧚

⸃ᨆࠤ࡯ࠬ

ਔ┵࿕ቯߩ᪞ࠍ⠨߃ࠆ㧚ߎߩ᪞ㇱ᧚ߪ㍑࠻࡜ࠬᯅߩᢳ

᧚ࠍᗐቯߒߡ߅ࠅ㧘‛ᕈ୯ߪㇱ᧚㐳ߐ݈ ൌ ͹Ǥ͵ͺሾ݉ሿ㧘න૏

૕ Ⓧ ⾰㊂ߩ ൌ ͹ͺͲͲሾ݇݃ ݉Τ ^ଷሿ㧘 ࡗ ࡦ ࠣ ₸ܧ ൌ ʹǤʹͲ ൈ ͳͲ^ଵଵሾܰ ݉Τ ^ଶሿ㧘ᢿ㕙Ⓧܣ ൌ ͷǤͷͲ ൈ ͳͲ^ିଷሾ݉^ଶሿ㧘ᢿ㕙2ᰴࡕ

࡯ࡔࡦ࠻ܫ ൌ ͷǤͳͳ ൈ ͳͲ^ିହሾ݉^ସሿߣߒߚ㧚ᷫ⴮ቯᢙ݄ ൌ Ͳߩ 㕖ᷫ⴮♽ࠍ઒ቯߒߚ㧚⿠ᝄ▵ὐߪㇱ᧚ߩਛᄩߦ࿕ቯߒ㧘

⿠ᝄᣇะߪㇱ᧚ߦኻߒߡ⋥ⷺߣߒߡ㧘⺞๺ᄖജࠍ૞↪ߐ ߖࠆ㧚⿠ᝄὐߣหߓ▵ὐߢ๟ᵄᢙᔕ╵㑐ᢙࠍ⸘᷹ߔࠆ㧚

⸘᷹ߔࠆ๟ᵄᢙᔕ╵㑐ᢙࡴሺ߱ሻߪ㧘᦭㒢ⷐ⚛ᴺߢߪᑼ

(2.26)㧘ࠬࡍࠢ࠻࡞ⷐ⚛ᴺߢߪᑼ(2.27)ߢਈ߃ࠄࠇࠆ㧚᦭

㒢ⷐ⚛ᴺߩ⾰㊂ⴕ೉ߪᢛว⾰㊂ဳࠍ↪޿ߚ㧚ߎߎߢߩ

ࡷǡ ࡹǡ ࡿሺ߱ሻߪⷐ⚛ⴕ೉ࠍ⿷ߒวࠊߖߚో૕ⴕ೉ߢ޽ࠆ㧚

ࡴሺ߱ሻ ൌ ሾሺࡷ െ ߱^ଶࡹሻሿ^ିଵ (FEM) (2.26)

ࡴሺ߱ሻ ൌ ሾࡿሺ߱ሻሿ^ିଵ (SEM) (2.27)

⿠ᝄᝄേᢙࠍ1Hz߆ࠄ1000Hz߹ߢ1HzೞߺߢẋჇߐ ߖ๟ᵄᢙᔕ╵㑐ᢙࠍࡊࡠ࠶࠻ߒ㧘ⷐ⚛ಽഀᢙࠍᄌ߃ߡߘ ߩᄌൻࠍ᦭㒢ⷐ⚛ᴺߣࠬࡍࠢ࠻࡞ⷐ⚛ᴺߢᲧセߔࠆ㧚ಽ

ഀᢙߪ16㧘32㧘64㧘128㧘256ߦߟ޿ߡᬌ⸛ߔࠆ㧚

(a) ᦭㒢ⷐ⚛ᴺ

(b) ࠬࡍࠢ࠻࡞ⷐ⚛ᴺ

࿑-1 ⷐ⚛ಽഀᢙ߇⸃ᨆ⚿ᨐߦ෸߷ߔᓇ㗀ߩᲧセ

⸃ᨆ⚿ᨐ

⚿ᨐࠍ࿑-1ߦ␜ߔ㧚᦭㒢ⷐ⚛ᴺߢߩ⚿ᨐߪ࿑-1(a)㧘ࠬ

ࡍࠢ࠻࡞ⷐ⚛ᴺߢߩ⚿ᨐߪ࿑-1(b)ߢ޽ࠆ㧚ਔ࿑ߣ߽㧘ᮮ ゲߪᝄേᢙ㧔1㨪1000Hz㧕㧘❑ゲߪ๟ᵄᢙᔕ╵㑐ᢙ㧔FRF㧕 ߢ޽ࠆ㧚ಠ଀ߩᢙሼߪಽഀᢙࠍ␜ߒߡ޿ࠆ㧚

2 ߟߩ࿑ࠍᲧセߒ㧘⠨ኤߔࠆ㧚᦭㒢ⷐ⚛ᴺߢߪⷐ⚛ಽ

ഀᢙߦࠃߞߡFRF߇⇣ߥߞߡ߅ࠅ㧘㜞ᝄേᢙߦߥࠆ߶ߤ㧘 ಽഀᢙᲤߩ FRF ߩᏅ⇣߇ᄢ߈ߊߥߞߡ޿ࠆߎߣ߇ࠊ߆ ࠆ㧚৻ᣇ㧘ࠬࡍࠢ࠻࡞ⷐ⚛ᴺߢߪߤߩⷐ⚛ಽഀᢙߢ޽ߞ ߡ߽FRFߪ߶߷৻ቯߣߥߞߡ޿ࠆߎߣ߇ࠊ߆ࠆ㧚

࿑-1(b)ߩࠬࡍࠢ࠻࡞ⷐ⚛ᴺߩ⚿ᨐߦ߅޿ߡ㧘FRF߇ᱜ

߆ࠄ⽶߳ߣ╓ภߩᄌࠊࠆ㧘33Hz㧘180Hz㧘446Hz㧘830Hz ߪߘࠇߙࠇ1ᰴ㧘3ᰴ㧘5ᰴ㧘7ᰴߩ࿕᦭ᝄേᢙߦኻᔕߒ ߡ޿ࠆ㧚⿠ᝄὐࠍㇱ᧚ਛᄩߣߒߚߚ߼㧘஧ᢙᤨߩ࿕᦭ᝄ

േᢙߪ⃻ࠇߡ޿ߥ޿㧚࿑-1(a)ߩ᦭㒢ⷐ⚛ᴺߩ⚿ᨐߢߪ㧘1

ᰴ࿕᦭ᝄേᢙߩ▚ቯ୯ߪ޿ߕࠇߩⷐ⚛ಽഀߢ߽33Hzߢ

޽ࠆ㧚7ᰴߩ࿕᦭ᝄേᢙߪ㧘ಽഀᢙ16ߢߪ924Hz㧘ಽഀ

ᢙ256ߢߪ773Hzߢ޽ࠆ㧚ಽഀᢙ128ߣ256ߩ⚿ᨐߪ߶

߷৻⥌ߒߡ޿ࠆߎߣ߆ࠄ㧘⚂800Hzࠍᛒ߁႐ว㧘᦭㒢ⷐ

⚛ᴺߢᔅⷐߥⷐ⚛ಽഀᢙߪ64୘ߣ128୘ߩ㑆ߢ޽ࠆߎߣ ߇ࠊ߆ࠆ㧚ߥ߅㧘ࠬࡍࠢ࠻࡞ⷐ⚛ᴺߣ256ಽഀߩ᦭㒢ⷐ

⚛ᴺߢ㜞ᝄേᢙ߶ߤ FRF ෸߮࿕᦭ᝄേᢙߦ㆑޿߇޽ࠆ ߩߪ㧘⾰㊂ߩࡕ࠺࡞ൻ߇⇣ߥࠆߚ߼ߢ޽ࠆ㧚ࠬࡍࠢ࠻࡞

ⷐ⚛ᴺߢߪᝄേᢙଐሽߩᄌ૏㑐ᢙߢኒᐲߩᓇ㗀ࠍขࠅㄟ ࠎߢ߅ࠅ㧔ᑼ(2.25)㧕㧘ᝄേᢙߦᔕߓߚ⾰㊂ߩᓇ㗀ࠍ⹏ଔ ߢ߈ࠆߚ߼㧘᦭㒢ⷐ⚛ᴺߦ߅ߌࠆ㧘ᝄേᢙ0Hzߦ⋧ᒰߔ ࠆ⾰㊂ߦെ߱^ଶࠍਸ਼ߓߚࡕ࠺࡞ൻ㧔ᑼ(2.26)㧕ࠃࠅ㜞ᝄേᢙ 㗔ၞࠍᱜ⏕ߦ⴫⃻ߢ߈ࠆߣ⠨߃ࠄࠇࠆ㧚

એ਄ࠃࠅ㧘ࠬࡍࠢ࠻࡞ⷐ⚛ᴺߢߪᢿ㕙ᄌൻὐ߿ᄖജࠍ ਈ߃ࠆὐ㧘ᔕ╵ࠍ▚಴ߔࠆὐ╬ࠍ㒰޿ߡⷐ⚛ࠍಽഀߔࠆ ᔅⷐ߇ߥ޿ߚ߼㧘᦭㒢ⷐ⚛ᴺߦᲧߴߡ⸘▚ኈ㊂ࠍ▵⚂ߢ

䎓䎕䎓䎓䎗䎓䎓䎙䎓䎓䎛䎓䎓䎔䎓䎓䎓

䎐䎖䎐䎕䎐䎔䎓䎔䎕䎖䏛䎃䎔䎓^䎐䎚

ᝄേᢙ

䎩䎵䎩

䎃

䎔䎙䎖䎕䎙䎗䎔䎕䎛䎕䎘䎙

䎓䎕䎓䎓䎗䎓䎓䎙䎓䎓䎛䎓䎓䎔䎓䎓䎓

䎐䎖䎐䎕䎐䎔䎓䎔䎕䎖䏛䎃䎔䎓^䎐䎚

ᝄേᢙ

䎩䎵䎩

䎃

䎔䎙䎖䎕䎙䎗䎔䎕䎛䎕䎘䎙

(4)

߈㧘㜞ᝄേᢙ㗔ၞߢߪ․ߦ᦭೑ߢ޽ࠆߎߣ߇␜ߐࠇߚ㧚 ᧄ⺰ᢥߩ4┨ߢឭ᩺ߔࠆ⿠ᝄᝄേᢙᲤߩ๟ᵄᢙᔕ╵㑐ᢙ ߦ⌕⋡ߔࠆ៊்หቯᚻᴺߪ㧘߱Ფߦേ೰ᕈⴕ೉ࠍ૞ᚑߔ ࠆࠬࡍࠢ࠻࡞ⷐ⚛ᴺߣ⋧ᕈ߇ࠃ޿ߣ⸒߃ࠆ㧚ᰴ┨߆ࠄߪ㧘

ࠬࡍࠢ࠻࡞ⷐ⚛ᴺߦၮߠ޿ߡ⸃ᨆࠍⴕ߁߽ߩߣߔࠆ㧚

៊்߇㜞ᝄേᢙ㗔ၞߩᝄേ․ᕈߦ෸߷ߔᓇ㗀

៊்ߩࡕ࠺࡞ൻ

᭴ㅧ‛߇⠧᧎ൻߒߡ⣣㘩㧘∋ഭߥߤߦࠃࠅ៊்ߔࠆߣ㧘 ᢿ㕙ᰳ៊߇↢ߓᢿ㕙Ⓧߣᢿ㕙2ᰴࡕ࡯ࡔࡦ࠻߇ૐਅߔࠆ㧚 ᧄ⎇ⓥߢߪ㧘᭴ㅧ‛ߩ៊்ࠍᢿ㕙Ⓧܣߣᢿ㕙2 ᰴࡕ࡯ࡔ ࡦ࠻ܫߩᷫዋߣߒߡਈ߃㧘േ೰ᕈⴕ೉ࡿሺ߱ሻࠍ૞ᚑߔࠆߎ ߣߦࠃࠅ៊்ࠍࡕ࠺࡞ൻߔࠆ㧚

⸃ᨆࡕ࠺࡞

ਔ┵࿕ቯߩ᪞ࠍ⠨߃㧘ߎࠇࠍ╬㑆㓒ߦ132ಽഀߔࠆ㧚 Ꮐ஥ߩ┵߆ࠄⷐ⚛⇟ภߣ▵ὐ⇟ภࠍߟߌࠆ㧚ㇱ᧚ਛᄩߩ

▵ὐ⇟ภߪ67ߣߥࠆ㧚ߎߩ᪞ㇱ᧚ߪ㍑࠻࡜ࠬᯅߩᢳ᧚ࠍ ᗐቯߒߡ߅ࠅ㧘‛ᕈ୯ߪߘࠇߙࠇ㧘ㇱ᧚㐳ߐ݈ ൌ ͹Ǥ͵ͺሾ݉ሿ㧘 න૏૕Ⓧ㊀㊂ߩ ൌ ͹ͺͲͲሾ݇݃ ݉Τ ^ଷሿ㧘ࡗࡦࠣ₸ܧ ൌ ʹǤʹͲ ൈ ͳͲ^ଵଵሾܰ ݉Τ ^ଶሿ㧘ᢿ㕙Ⓧܣ ൌ ͷǤͷͲ ൈ ͳͲ^ିଷሾ݉^ଶሿ㧘ᢿ㕙2ᰴࡕ

࡯ࡔࡦ࠻ܫ ൌ ͷǤͳͳ ൈ ͳͲ^ିହሾ݉^ସሿߣߒߚ㧚ᷫ⴮ቯᢙߪ݄ ൌ Ͳ ߣ઒ቯߒߚ㧚⿠ᝄ▵ὐߪㇱ᧚ߩਛᄩߦ࿕ቯߒ㧘⿠ᝄᣇะ ߪㇱ᧚ߦኻߒߡ⋥ⷺߣߔࠆ㧚

⸃ᨆࠤ࡯ࠬࠍ⴫-1ߦ␜ߔ㧚៊்ߩਈ߃ᣇߣ៊்ߩ૏⟎

ߩ⇣ߥࠆ4ࠤ࡯ࠬࠍᗐቯߒߚ㧚៊்ߩਈ߃ᣇߪ㧘ᢿ㕙2

ᰴࡕ࡯ࡔࡦ࠻I߇50%ૐਅߒߚ߽ߩߣᢿ㕙2ᰴࡕ࡯ࡔࡦ

࠻Iߣᢿ㕙ⓍA߇ߣ߽ߦ50%ૐਅߒߚ߽ߩߩ2⒳㘃ࠍ⠨

߃ߚ㧚ࠬࡍࠢ࠻࡞ⷐ⚛ᴺߦ߅޿ߡ㧘⾰㊂ߩᓇ㗀ߪᢿ㕙Ⓧ

ߦଐሽߔࠆ߇ᢿ㕙2ᰴࡕ࡯ࡔࡦ࠻ߦߪଐሽߒߥ޿ߩߢ㧘 ᢿ㕙2ᰴࡕ࡯ࡔࡦ࠻ߛߌ߇50%ૐਅߔࠆࠤ࡯ࠬߪ៊்೨ ߢ⾰㊂ߪਇᄌߢ޽ࠆ㧚ᢿ㕙2ᰴࡕ࡯ࡔࡦ࠻ߣᢿ㕙Ⓧ߇ߣ

߽ߦᷫዋߔࠆࠤ࡯ࠬߪ㧘ᢿ㕙ᰳ៊ࠍᗐቯߒߡ߅ࠅ㧘ᢿ㕙 2 ᰴࡕ࡯ࡔࡦ࠻ߩߺᷫዋߔࠆࠤ࡯ࠬߪ੉ⵚߩࠃ߁ߥ៊்

ࠍᗐቯߒߡ޿ࠆ㧚៊்ߩ૏⟎ߪㇱ᧚ਛᄩ࡮ㇱ᧚┵ߩ2ࡄ

࠲࡯ࡦࠍ⠨߃ࠆ㧔࿑-2㧕㧚࿑-2ߩᢙሼߪⷐ⚛⇟ภࠍ⴫ߒߡ

޿ࠆ㧚ㇱ᧚ਛᄩߣߪⷐ⚛⇟ภ66ߣ67ߩⷐ⚛ߩᢿ㕙Ⓧߣ ᢿ㕙2ᰴࡕ࡯ࡔࡦ࠻ࠍૐᷫߐߖߚࠤ࡯ࠬ㧔࿑-2(a)ෳᾖ㧕㧘ㇱ᧚┵ߣߪⷐ⚛⇟ภ131ߣ132ߩⷐ⚛ߩᢿ㕙Ⓧߣᢿ㕙2

ᰴࡕ࡯ࡔࡦ࠻ࠍૐᷫߐߖߚࠤ࡯ࠬ㧔࿑-2(b)ෳᾖ㧕ߢ޽ࠆ㧚 50%ߣ޿߁ᄢ߈ߥ៊்ࠍ઒ቯߒߚߩߪ៊்ߦࠃࠆᝄേ․

ᕈߩᄌൻ߇ࠊ߆ࠅ߿ߔߊߥࠆߚ߼ߢ޽ࠆ㧚

⸃ᨆౝኈ

៊்ߦࠃࠆ࿕᦭ᝄേᢙߩᄌൻ

⿠ᝄὐ࡮⸘᷹ὐ࡮ߘࠇࠄߩᣇะࠍ࿕ቯߒ㧘⿠ᝄᝄേᢙ Ȧ ࠍẋჇߐߖ㧘ᑼ(2.27)ߢਈ߃ࠄࠇࠆ๟ᵄᢙᔕ╵㑐ᢙ

ࡴሺ߱ሻࠍ⸘▚ߔࠆߣ㧘ߘߩࡇ࡯ࠢ߇⃻ࠇࠆᝄേᢙ߇࿕᦭

ᝄേᢙߣߥࠆ㧚

⴫-1 ⸃ᨆࠤ࡯ࠬ

⸃ᨆCase ៊்ߩᄢ߈ߐ ៊்୘ᚲ

1 AЈA

IЈI/2

ਛᄩ

2 ┵

3 AЈA/2

IЈI/2

ਛᄩ

4 ┵

(a) ៊்߇ㇱ᧚ਛᄩߦ޽ࠆ႐ว

(b) ៊்߇ㇱ᧚┵ߦ޽ࠆ႐ว

࿑-2 ⸃ᨆࡕ࠺࡞㧔ਔ┵࿕ቯ᪞㧕

៊்ߦࠃࠆ๟ᵄᢙᔕ╵㑐ᢙߩᄌൻ

⿠ᝄὐ࡮⿠ᝄᝄേᢙࠍ࿕ቯߒో▵ὐߦ߅ߌࠆࡴሺ߱ሻࠍ

⸘▚ߔࠆ㧚ߎࠇࠍ࿑␜ߔࠆߎߣߦࠃࠅ㧘ฦᝄേᢙߦ߅ߌ ࠆㇱ᧚ߩᝄേᒻ⁁߇ಽ߆ࠆ㧚ߟ߹ࠅ㧘៊்ߦࠃࠆ๟ᵄᢙ ᔕ╵㑐ᢙߩᄌൻࠍᝄേᢙߦᔕߓߡⷞⷡ⊛ߦℂ⸃ߒᲧセߔ ࠆߎߣ߇ߢ߈ࠆ㧚

⸃ᨆ⚿ᨐ

࿕᦭ᝄേᢙߩᄌൻ

⸃ᨆ⚿ᨐߪ࿑-3㧘࿑-4ߩㅢࠅߢ޽ࠆ㧚ฦ࿑ߩ(a)㨪(d)ߪ

ߘࠇߙࠇCase1㨪4ߦኻᔕߔࠆ㧚ᮮゲߪᝄേᢙ㧘❑ゲߪ๟

ᵄᢙᔕ╵㑐ᢙ㧔FRF㧕ߢ޽ࠆ㧚1ᰴ࿕᦭ᝄേᢙઃㄭ㧔31Hz 㨪34Hz㧦0.01Hz ೞߺ㧕ࠍࡊࡠ࠶࠻ߒߚ߽ߩ㧔࿑-3㧕ߣ㧘 9ᰴ࿕᦭ᝄേᢙઃㄭ㧔1250Hz㨪1350Hz㧦0.1Hzೞߺ㧕ࠍ ࡊࡠ࠶࠻ߒߚ߽ߩ㧔࿑-4㧕ߩ2⒳㘃ߩࠣ࡜ࡈࠍ␜ߔ㧚FRF ߩ╓ภ߇ᱜ߆ࠄ⽶ߦᄌൻߔࠆߣ߈ߩᝄേᢙ߇࿕᦭ᝄേᢙ ߢ޽ࠅ㧘ஜోᤨߣ៊்ᤨߣߢᲧセߔࠆ㧚࿑-3㧘࿑-4߆ࠄ㧘

៊்ߦࠃࠅ࿕᦭ᝄേᢙ߇ᷫዋߔࠆߣ޿߁ߎߣ߇ࠊ߆ࠆ㧚 ߎࠇߪ㧘៊்ߦࠃࠅᢿ㕙Ⓧ߿ᢿ㕙2ᰴࡕ࡯ࡔࡦ࠻߇ᷫዋ ߔࠆߣ೰ᕈ߇ૐਅߔࠆߚ߼ߢ޽ࠆߣ⠨߃ࠄࠇࠆ㧚߹ߚ㧘㜞ᝄേᢙߢ⿠ᝄߒߚ߶߁߇៊்ߦࠃࠆ࿕᦭ᝄേᢙߩᄌൻ ߇ᄢ߈޿ߣ޿߁ߎߣ߇ࠊ߆ࠆ㧚ߎࠇࠃࠅ㧘㜞ᝄേᢙߩ߶

߁߇៊்ߦኻߔࠆᗵᐲ߇㜞޿ߣ޿߃ࠆ㧚࿑-3(a)(b)ߣ࿑

-3(c)(d)߿ ࿑-4(a)(b)ߣ࿑-4(c)(d)ࠍᲧセߒߡࠊ߆ࠆߎߣߪ㧘 ᢿ㕙Ⓧߩᷫዋߩᓇ㗀ߦࠃߞߡ㧘ᢿ㕙2ᰴࡕ࡯ࡔࡦ࠻ߩߺ ૐᷫߒߚ႐วߣᲧߴߡ㧘࿕᦭ᝄേᢙ߇Ⴧടߔࠆߣ޿߁ߎ ߣߢ޽ࠆ㧚ߎࠇߪᢿ㕙ᰳ៊ߦࠃࠆ⾰㊂ߩᷫዋ߇ᝄേ․ᕈ ߦᓇ㗀ࠍਈ߃ߚߚ߼ߢ޽ࠆߣ⠨߃ࠄࠇࠆ㧚

(5)

(a) Case1

(b) Case2

(c) Case3

(d) Case4

࿑-3 1ᰴ࿕᦭ᝄേᢙ

(a) Case1

(b) Case2

(c) Case3

(d) Case4

࿑-5 ᝄേᢙ1Hz

(a) Case1

(b) Case2

(c) Case3

(d) Case4

࿑-4 9ᰴ࿕᦭ᝄേᢙ

(a) Case1

(b) Case2

(c) Case3

(d) Case4

࿑-6 ᝄേᢙ1500Hz

䎖䎔䎖䎔䎑䎘䎖䎕䎖䎕䎑䎘䎖䎖䎖䎖䎑䎘䎖䎗

䎐䎕䎐䎔䎓䎔䎕䏛䎃䎔䎓^䎐䎗

ᝄേᢙ

䎩䎵䎩

䎃

ஜోᤨ

៊்ᓟ

ᝄേᢙ

䎩䎵䎩

䎃

ஜోᤨ

៊்ᓟ

ᝄേᢙ

䎩䎵䎩

䎃

ஜోᤨ

៊்ᓟ

ᝄേᢙ

䎩䎵䎩

䎃

ஜోᤨ

៊்ᓟ

䎓䎕䎓䎗䎓䎙䎓䎛䎓䎔䎓䎓䎔䎕䎓

䎐䎕䎐䎔䎓䎔䎕

䏛䎃䎔䎓^䎐䎚

▵ὐ⇟ภ

䎩䎵䎩

䎃

ஜోᤨ

៊்ᓟ

䏛䎃䎔䎓^䎐䎚

▵ὐ⇟ภ

䎩䎵䎩

䎃

䎃 ஜోᤨ

៊்ᓟ

䏛䎃䎔䎓^䎐䎚

▵ὐ⇟ภ

䎩䎵䎩

䎃

䎃 ஜోᤨ

៊்ᓟ

䏛䎃䎔䎓^䎐䎚

▵ὐ⇟ภ

䎩䎵䎩

䎃

䎃 ஜోᤨ

៊்ᓟ

䎔䎕䎘䎓䎔䎖䎓䎓䎔䎖䎘䎓

䎐䎕䎐䎔䎓䎔䎕䏛䎃䎔䎓^䎐䎚

ᝄേᢙ

䎩䎵䎩

䎃

ஜోᤨ

៊்ᓟ

ᝄേᢙ

䎩䎵䎩

䎃

ஜోᤨ

៊்ᓟ

ᝄേᢙ

䎩䎵䎩

䎃

ஜోᤨ

៊்ᓟ

ᝄേᢙ

䎩䎵䎩

䎃

ஜోᤨ

៊்ᓟ

䎐䎙䎐䎗䎐䎕䎓䎕䎗

䏛䎃䎔䎓^䎐䎔䎓

▵ὐ⇟ภ

䎩䎵䎩

䎃

ஜోᤨ

៊்ᓟ

▵ὐ⇟ภ

䎩䎵䎩

䎃

䎃 ஜోᤨ

៊்ᓟ

▵ὐ⇟ภ

䎩䎵䎩

䎃

ஜోᤨ

៊்ᓟ

▵ὐ⇟ภ

䎩䎵䎩

䎃

䎃 ஜోᤨ

៊்ᓟ

(6)

๟ᵄᢙᔕ╵㑐ᢙߩᄌൻ

⸃ᨆ⚿ᨐߪ࿑-5㧘࿑-6ߩㅢࠅߢ޽ࠆ㧚ฦ࿑ߩ(a)㨪(d)ߪ

ߘࠇߙࠇCase1㨪4ߦኻᔕߔࠆ㧚ᮮゲߪ▵ὐ⇟ภߢ޽ࠅ㧘

❑ゲߪ๟ᵄᢙᔕ╵㑐ᢙ㧔FRF㧕ߢ޽ࠆ㧚⿠ᝄᝄേᢙߪૐ ᝄേᢙߩ଀ߣߒߡ1Hzߣ㧘㜞ᝄേᢙߩ଀ߣߒߡ1500Hz ࠍㆬᛯߒߘࠇߙࠇࠍᲧセߔࠆ㧚޿ߕࠇ߽ஜోᤨߦ߅޿ߡ ᝄേᒻ⁁߇Ꮐฝኻ⒓ߣߥࠆᝄേᢙߢ޽ࠆ㧚

1Hzߣ1500Hzߩ⚿ᨐࠍᲧߴࠆߣ㧘ᝄേᢙߩ㜞޿߶߁

߇๟ᵄᢙᔕ╵㑐ᢙߩᒻ⁁ߩᄌൻ߇ࠃࠅᄢ߈޿௑ะ߇ߺ ࠄࠇࠆ㧚߹ߚ㧘៊்ߩ૏⟎߇┵ߦ޽ࠆ㧔Case2㧘4㧕߶߁ ߇๟ᵄᢙᔕ╵㑐ᢙߩᒻ⁁ߪࠃࠅᄢ߈ߥᄌൻࠍฃߌࠆߣ

޿߁ߎߣ߇ࠊ߆ࠆ㧚1500Hz⿠ᝄᤨߩCase1ߩᔕ╵߇៊்

ߦࠃߞߡ߶ߣࠎߤᄌൻߒߥ޿ߩߪ㧘Case1 ߢߪ⾰㊂߇ਇ ᄌߢ޽ࠅ㧘߆ߟㇱ᧚ਛᄩߩᢿ㕙2ᰴࡕ࡯ࡔࡦ࠻ߩᷫዋߪ ᝄേ․ᕈߩᄌൻߦᓇ㗀ࠍਈ߃ߦߊ޿ߚ߼ߢ޽ࠆߣ⠨߃ ࠄࠇࠆ㧚࿑-6(a)ࠃࠅ㧘ㇱ᧚ਛᄩߩ೰ᕈૐਅߩᓇ㗀ߪ߶ߣ ࠎߤ⴫ࠇߥ޿ߎߣ߇ࠊ߆ߞߡ޿ࠆߩߢ㧘࿑-6 ߩ(a)ߣ(c) ߩᏅߪㇱ᧚ਛᄩߩ⾰㊂ᄌൻߩᓇ㗀߇⴫ࠇߚ߽ߩߣ⠨߃ ࠄࠇࠆ㧚ㇱ᧚ਛᄩߦᢿ㕙ᰳ៊߇↢ߓߚ႐ว㧘㜞ᝄേᢙ㗔

ၞߩ FRF ߩᄌൻߦᓇ㗀ࠍਈ߃ࠆߩߪ೰ᕈࠃࠅ߽߻ߒࠈ

⾰㊂ߢ޽ࠆߚ߼㧘ߎߩࠃ߁ߥ៊்ࠍᱜߒߊᝒ߃ࠆߦߪ㧘

⾰㊂ߩᓇ㗀ࠍ⠨ᘦߒߚ៊்หቯᚻᴺߩ᭴▽߇ᔅⷐਇน

ᰳߢ޽ࠅ㧘ߎࠇࠍ⥄േߢขࠅㄟ߼ࠆࠬࡍࠢ࠻࡞ⷐ⚛ᴺߪ

᦭㒢ⷐ⚛ᴺߦᲧߴߡൎߞߡ޿ࠆߣ⠨߃ࠄࠇࠆ㧚

ᢿ㕙ᰳ៊ߦࠃࠅᢿ㕙Ⓧ߇ᷫዋߔࠆߣ㧘೰ᕈߛߌߢߥߊ

⾰㊂߽ᷫዋߔࠆ㧚એ਄ߩᬌ⸛ࠃࠅ㧘࿕᦭ᝄേᢙߦኻߔࠆ

೰ᕈᄌൻߣ⾰㊂ᄌൻߩᓇ㗀ᐲߪ㧘៊்૏⟎ߦࠃߞߡ⇣ߥ ࠆߎߣ߇ࠊ߆ߞߚ㧚⾰㊂ᄌൻߩᓇ㗀ࠍήⷞߒ㧘࿕᦭ᝄേ

ᢙߩᄌൻ߆ࠄ៊்ᐲࠍផቯߔࠆ⹜ߺ߽ߥߐࠇߡ޿ࠆ߇㧘 ᢿ㕙ᰳ៊ߦࠃࠅᝄേᢙ߇Ⴧടߔࠆߣ޿߁ߎߣ߇ࠊ߆ߞߚ ߩߢ㧘ᝄേᢙߩᄌൻࠍᜰᮡߦߔࠆߣ៊்ࠍ⷗⪭ߣߔෂ㒾 ᕈ߇޽ࠆߎߣ߇ࠊ߆ߞߚ㧚߹ߚ㧘៊்૏⟎߇┵ߦⴕߊ߶

ߤ៊்ߦࠃࠆᝄേᢙߩૐਅ㊂߇ᄢ߈ߊߥࠆߚ߼㧘หߓᢿ 㕙ᰳ៊ߢ߽ㇱ᧚ਛᄩߦ޽ࠆࠃࠅ┵ߦ޽ࠆ߶߁߇㧘៊்߇ ᄢ߈ߊ⷗Ⓧ߽ࠄࠇߡߒ߹߁ߎߣ߇ࠊ߆ࠆ㧚

៊்หቯᚻᴺ

ቯᑼൻ

៊்ߩࡕ࠺࡞ൻ

᭴ㅧ‛ߩ៊்ࠍᢿ㕙ⓍAߩᷫዋ෸߮ᢿ㕙2ᰴࡕ࡯ࡔࡦ

࠻ I ߩᷫዋߣߒߡ⹏ଔߔࠆ㧚᭴ㅧ‛ో૕ߩേ೰ᕈⴕ೉

ࡿሺ߱ሻߪฦⷐ⚛ߩേ೰ᕈⴕ೉ߩ㓸ว૕ߣߒߡᰴᑼߩࠃ߁ ߦࡕ࠺࡞ൻߢ߈ࠆ㧚

ࡿሺ߱ሻ ൌ ෍ ࡿ^௘ሺ߱ሻ

௡

௘ୀଵ

(4.1)

ߎߎߢ㧘nߪ᪞ⷐ⚛ߩ✚ᢙߢ޽ࠅ㧘ࡿ^௘ሺ߱ሻߪe⇟⋡ߩ᪞ⷐ

⚛ߩേ೰ᕈⴕ೉ߢ޽ࠆ㧚e⇟⋡ߩ᪞ⷐ⚛ߩᢿ㕙Ⓧߣᢿ㕙2

ᰴࡕ࡯ࡔࡦ࠻߇ߜܣ௘㧘ߜܫ௘ᷫዋߒߚߣߔࠆߣ㧘e⇟⋡ߩ᪞

ⷐ⚛ߩേ೰ᕈⴕ೉ߩᷫዋಽߜࡿ^௘ሺ߱ሻߪ㧘

ߜࡿ^௘ሺ߱ሻ ൌ ߜܣ_௘ࡷ_࡭^௘ሺ߱ሻ ൅ ߜܫ_௘ࡷ_ࡵ^௘ሺ߱ሻ (4.2) ߚߛߒ㧘

ࡷ_࡭^௘ሺ߱ሻ ൌߜࡿ^௘ሺ߱ሻ

ߜܣ_௘ ǡ ࡷ_ࡵ^௘ሺ߱ሻ ൌߜࡿ^௘ሺ߱ሻ

ߜܫ_௘ (4.3) ߣ⴫ߐࠇࠆ㧚ࠃߞߡ㧘ో૕േ೰ᕈⴕ೉ߩᷫዋಽߪ㧘ᰴᑼ ߢ⴫ߐࠇࠆ㧚

ߜࡿሺ߱ሻ ൌ ෍ ߜܣ_௘

௡

௘ୀଵ

ࡷ_࡭^௘ሺ߱ሻ ൅෍ ߜܫ_௘ࡷ_ࡵ^௘

௡

௘ୀଵ

ሺ߱ሻ (4.4)

៊்หቯᣇ⒟ᑼߩዉ಴

៊்೨ߩ๟ᵄᢙ㗔ၞߦ߅ߌࠆㆇേᣇ⒟ᑼߪ㧘

ࡿሺ߱ሻࢄሺ߱ሻ ൌ ࡲሺ߱ሻ (4.5) ߢ޽ࠆ㧚ࡿሺ߱ሻߪേ೰ᕈߢ޽ࠅ㧘ࢄሺ߱ሻߣࡲሺ߱ሻߪߘࠇߙࠇ ᄌ૏ߣᄖജߩࡈ࡯࡝ࠛᝄ᏷ߢ޽ࠆ㧚ᄌ૏ᔕ╵ࢄሺ߱ሻߪᰴᑼ ߩㅢࠅߢ޽ࠆ㧚

ࢄሺ߱ሻ ൌ ࡴሺ߱ሻࡲሺ߱ሻ (4.6)

ߥ߅㧘ࡴሺ߱ሻߪᑼ(2.27)ࠃࠅ㧘๟ᵄᢙᔕ╵㑐ᢙߢ޽ࠆ㧚ᰴ

ߦ㧘៊்ᓟߩㆇേᣇ⒟ᑼߪ

ሺࡿሺ߱ሻ െ ߜࡿሺ߱ሻሻሺࢄሺ߱ሻ ൅ ߜࢄሺ߱ሻሻ ൌ ࡲሺ߱ሻ (4.7) ߢ޽ࠆ㧚ߜࢄሺ߱ሻߪᄌ૏ߩჇಽߢ޽ࠅ㧘ߜࡿሺ߱ሻߪᑼ(4.4)ࠃ ࠅേ೰ᕈߩᷫዋಽߢ޽ࠆ㧚

ᑼ(4.7)ߦᑼ(4.5)ߣᑼ(4.4)ࠍઍ౉ߒߡ㧘ᰴᑼࠍᓧࠆ㧚 ߜࢄሺ߱ሻ ൌ ࡴௗሺ߱ሻߜࡿሺ߱ሻࡴሺ߱ሻࡲሺ߱ሻ (4.8)

ࡴௗሺ߱ሻߪ៊்ᓟߩ๟ᵄᢙᔕ╵㑐ᢙߢ޽ࠅ㧘

ࡴௗሺ߱ሻ ൌ ሾࡿሺ߱ሻ െ ߜࡿሺ߱ሻሿ^ି૚ (4.9) ߣ⴫ߐࠇࠆ㧚ᑼ(4.4)ࠃࠅ㧘ᄌ૏ߩჇಽߜࢄሺ߱ሻߪ㧘

ߜࢄሺ߱ሻ ൌ ෍ ࡴ_ௗሺ߱ሻࡷ࡭௘ሺ߱ሻࡴሺ߱ሻࡲሺ߱ሻߜܣ௘

௡

௘ୀଵ

൅ ෍ ࡴௗሺ߱ሻࡷࡵ௘ሺ߱ሻࡴሺ߱ሻࡲሺ߱ሻߜܫ௘

௡

௘ୀଵ

(4.10)

ߢ޽ࠆ㧚ߎߎߢ㧘

ࢁ஺௘ሺ߱ሻ ൌ ࡴ_ௗሺ߱ሻࡷ_࡭^௘ሺ߱ሻࡴሺ߱ሻ

ࢁ_ூ^௘ሺ߱ሻ ൌ ࡴ_ௗሺ߱ሻࡷ_ࡵ^௘ሺ߱ሻࡴሺ߱ሻ (4.11) ߣ⟎ߊ㧚ᑼ(4.6)ߦ␜ߒߚ៊்೨ߩᄌ૏ࢄሺ߱ሻߦ㧘ᑼ(4.10) ߢ᳞߹ߞߚ៊்ߦࠃࠆᄌ૏Ⴧಽߜࢄሺ߱ሻࠍട߃ࠆߎߣߦ ࠃࠅ㧘៊்ᓟߩᔕ╵ࢄԢሺ߱ሻ߇᳞߹ࠆ㧚

ࢄ^ᇱሺ߱ሻ ൌ ࢄሺ߱ሻ ൅ ߜࢄሺ߱ሻ

ൌ ࡴሺ߱ሻࡲሺ߱ሻ ൅ ෍ ࢁ_஺^௘ሺ߱ሻࡲሺ߱ሻߜܣ_௘

௡

௘ୀଵ

൅ ෍ ࢁ_ூ^௘ሺ߱ሻࡲሺ߱ሻߜܫ_௘

௡

௘ୀଵ

(4.12)

๟ᵄᢙᔕ╵㑐ᢙࠍ㧘⿠ᝄᝄേᢙߦ߅ߌࠆടㅦᐲᔕ╵ߩ ࡈ࡯࡝ࠛᝄ᏷ࠍ౉ജߢ޽ࠆ⺞๺ᄖജߩᝄ᏷ߢ㒰ߒߚ߽ߩ ߢ޽ࠆߣ⠨߃ࠆ㧚⸘᷹ὐࠍࡁ࡯࠼݅㧘⿠ᝄὐࠍࡁ࡯࠼݆㧘

⿠ᝄᝄേᢙࠍ߱ߣߒߚߣ߈㧘๟ᵄᢙᔕ╵㑐ᢙܽሺ݅ǡ ݆ǡ ߱ሻߪ

ᰴᑼߩࠃ߁ߦ⴫ߐࠇࠆ㧚

(7)

ܽሺ݅ǡ ݆ǡ ߱ሻ ൌെ߱^ଶࢄԢሺ߱ሻ

ࡲሺ߱ሻ

ൌ െ߱^ଶ൭ࡴ_௜௝ሺ߱ሻ ൅ ෍ ࢁ_஺^௘_௜௝ሺ߱ሻߜܣ_௘

௡

௘ୀଵ

൅ ෍ ࢁ_ூ^௘_௜௝ሺ߱ሻߜܫ_௘

௡

௘ୀଵ

൱

(4.13)

਄ᑼߦ߅޿ߡ㧘ܽሺ݅ǡ ݆ǡ ߱ሻߪ៊்ᓟߩ๟ᵄᢙᔕ╵㑐ᢙߢ޽

ࠅ㧘⸘᷹ߦࠃࠅᓧࠄࠇࠆ୯ߢ޽ࠆ㧚ࡴ_௜௝ሺ߱ሻߪ៊்೨ߩ๟

ᵄᢙᔕ╵㑐ᢙߢ޽ࠅ㧘ᣢ⍮ߩ୯ߢ޽ࠆ㧚৻ᣇ㧘ࢁ_஺௜௝^௘ ሺ߱ሻߣ

ࢁ_ூ௜௝^௘ ሺ߱ሻߪ៊்೨ߩ᭴ㅧ࠺࡯࠲ߣ⿠ᝄᝄേᢙ෸߮ᧂ⍮ߩ ࡄ࡜ࡔ࡯࠲ߜܣ௘㧘ߜܫ௘߆ࠄ᳿߹ࠆ୯ߢ޽ࠆ㧚

ᑼ(4.13)ࠍᢛℂߒ㧘Ꮐㄝߦᧂ⍮ߩ㗄㧘ฝㄝߦᣢ⍮ߩ㗄ࠍ

⒖㗄ߔࠆߣ㧘ᰴߩᑼ߇ᓧࠄࠇࠆ㧚

െ߱^ଶ෍ ࢁ_஺^௘_௜௝ሺ߱ሻߜܣ_௘

௡

௘ୀଵ

െ ߱^ଶ෍ ࢁ_ூ^௘_௜௝ሺ߱ሻߜܫ_௘

௡

௘ୀଵ

ൌ ܽሺ݅ǡ ݆ǡ ߱ሻ ൅ ߱^ଶࡴ_௜௝ሺ߱ሻ

(4.14)

ߎߩᑼߪ㧘⸘᷹ὐ݅㧘⿠ᝄὐ݆㧘⿠ᝄᝄേᢙߩ⚵ߺวࠊߖ ߏߣߦᚑࠅ┙ߟᣇ⒟ᑼߢ޽ࠆ㧚݅㧘݆㧘߱ߩ⚵วߖࠍ᭽ޘ ߦᄌ߃㧘݉⒳㘃ߩ⸘᷹ࠍⴕ߁ߣ㧘ᰴᑼߦ␜ߔࠃ߁ߥㅪ┙

ᣇ⒟ᑼ߇ᚑ┙ߔࠆ㧚

ሾࢄሺߜ࡭ǡ ߜࡵሻሿሼࢇሽ ൌ ሼ࢟ሽ (4.15) ߎߎߢ㧘

ࢄ௟ǡ௘ሺߜ࡭ǡ ߜࡵሻ ൌ െ߱^ଶࢁ_஺௜௝^௘ ሺ߱ሻ

ࢄ௟ǡ௡ା௘ሺߜ࡭ǡ ߜࡵሻ ൌ െ߱^ଶࢁ_ூ௜௝^௘ ሺ߱ሻ

ሼࢇሽ ൌ ሼߜܣ_ଵǡ ڮ ǡ ߜܣ௡ǡ ߜܫଵǡ ڮ ǡ ߜܫ௡ሽ^்

ሼ࢟ሽ ൌ ܽሺ݅ǡ ݆ǡ ߱ሻ ൅ ߱^ଶࡴ௜௝ሺ߱ሻ

(4.16)

ߢ޽ࠆ㧚݈ሺ݈ ൌ ͳǡ ڮ ǡ ݉ሻߪ⇣ߥࠆ݅㧘݆㧘߱ߩ⚵วߖߦኻᔕ ߔࠆ⸘᷹࠺࡯࠲⇟ภߢ޽ࠆ㧚ᑼ(4.15)ߪᧂ⍮ᢙʹ݊୘ߦኻ ߔࠆ݉୘ߩㅪ┙ᣇ⒟ᑼߣߥࠅ㧘ߎࠇࠍ៊்หቯᣇ⒟ᑼߣ

๭߱㧚ߎߩᑼࠍ⸃ߊߎߣߦࠃࠅ㧘៊்୘ᚲߣ៊்ߩ⒟ᐲ ࠍ⴫ߔሼࢇሽࠍ᳞߼ࠆߎߣ߇ߢ߈ࠆ㧚ᑼ(4.15)ߪࡑ࠻࡝ࠢࠬ

ሾࢄሺߜ࡭ǡ ߜࡵሻሿ߇ᧂ⍮ߩࡄ࡜ࡔ࡯࠲ߜܣ_௘㧘ߜܫ_௘ࠍ฽߻ߚ߼㧘➅ ࠅ㄰ߒ⸘▚߇ᔅⷐߢ޽ࠆ㧚

⸃ᨆࡕ࠺࡞

╙3┨ߣหߓ‛ᕈ୯ߩਔ┵࿕ቯ᪞ߦߟ޿ߡ⠨߃㧘ㇱ᧚ ࠍ10╬ಽߔࠆ㧔࿑-7㧕㧚ㇱ᧚ਛᄩߪ▵ὐ⇟ภ6ߢ޽ࠅ㧘 ߘߩਔ஥ߩⷐ⚛㧔ⷐ⚛⇟ภ 5㧘6㧕ߦᢿ㕙Ⓧ A ߩૐਅ₸

20%㧘ᢿ㕙2ᰴࡕ࡯ࡔࡦ࠻Iߩૐਅ₸20%ߩ៊்ࠍ઒ቯ ߔࠆ㧚઒ቯߒߚ៊்ߩ⌀୯ߪ࿑-8ߩࠃ߁ߦߥࠆ㧚

⸃ᨆࠤ࡯ࠬ

ㇱ᧚ਛᄩߩ▵ὐ㧔▵ὐ⇟ภ 6㧕ߢ⿠ᝄߒ㧘ਔ┵એᄖߩ

▵ὐߢ⸘᷹ߔࠆ㧚⿠ᝄᝄേᢙߣߒߡ㧘1Hzߣ2000Hzࠍ ㆬᛯߒ⸃ᨆ⚿ᨐߩᲧセࠍⴕ߁㧚2000Hzߪ࿕᦭ᝄേᢙߦㄭ ߊ㧘៊்ߦࠃߞߡ๟ᵄᢙᔕ╵㑐ᢙ߇ᄌൻߒ߿ߔ޿ᝄേᢙ ߢ޽ࠆ㧚߹ߚ㧘⿠ᝄ࡮⸘᷹ᣇะࠍゲᣇะ࡮ゲ⋥ⷺᣇะߢ Ყセߔࠆ㧚߹ߚ㧘3%ߩ⸘᷹ࡁࠗ࠭ࠍ⠨ᘦߔࠆ㧚એ਄ߩ᧦

ઙߩ߽ߣߢ៊்หቯ⸃ᨆࠍⴕ߁㧚

࿑-7 ⸃ᨆࡕ࠺࡞

(a) ᢿ㕙Ⓧૐਅ₸

(b) ᢿ㕙2ᰴࡕ࡯ࡔࡦ࠻ૐਅ₸

࿑-8 ઒ቯߒߚ៊்⌀୯

⸃ᨆ⚿ᨐ

ᝄേᢙ 1Hz ߩ⸃ᨆ⚿ᨐࠍ࿑-9㧘10 ߦ␜ߒ㧘ᝄേᢙ

2000Hzߩ⚿ᨐࠍ࿑-11㧘12ߦ␜ߔ㧚࿑-9㧘11ߪゲᣇะߦ

⿠ᝄߒߚ႐วߢ޽ࠅ㧘࿑-10㧘12 ߪゲ⋥ⷺᣇะߦ⿠ᝄߒ ߚ႐วߢ޽ࠆ㧚ฦ࿑ߩ(a)ߪᢿ㕙Ⓧૐਅ₸ߩหቯ⚿ᨐ㧘(b) ߪᢿ㕙2ᰴࡕ࡯ࡔࡦ࠻ߩหቯ⚿ᨐࠍ⴫ߔ㧚

߹ߕ㧘⿠ᝄᝄേᢙ1Hzߣ2000HzࠍᲧセߔࠆߣ㧘ⷐ⚛

⇟ภ5㧘6ߩ៊்ࠍ1Hzߢߪᬌ಴ߢ߈ߕ㧘2000Hzߢߪᬌ

಴ߢ߈ߡ޿ࠆߎߣ߇ಽ߆ࠆ㧚1Hz ߢߪ 3%ߩ⸘᷹ࡁࠗ࠭

ߦࠃࠆᓇ㗀ࠍήⷞߢ߈ߕ㧘⺋ᬌ಴ߒߡߒ߹߁ߣ޿߁⚿ᨐ ߦߥߞߚ㧚৻ᣇ㧘2000Hzߢߪࡁࠗ࠭ߩᓇ㗀ߪዊߐߊ㧘઒

ቯߒߚ៊்ࠍหቯߔࠆߎߣ߇ߢ߈ߚ㧚⸘᷹ࡁࠗ࠭߇ߥ޿

႐ว߽೎ㅜ⸃ᨆࠍⴕߞߡ߅ࠅ㧘1Hz㧘2000Hzߣ߽หቯߢ ߈ߚ㧚ߎߩߎߣ߆ࠄ㧘㜞ᝄേᢙߢ⿠ᝄߔࠆ߶߁߇ࡁࠗ࠭

ߦᒝߊ㧘ࠃࠅ᦭ലߢ޽ࠆߣ޿߃ࠆ㧚

ᰴߦ㧘⿠ᝄ࡮⸘᷹ᣇะߩ㆑޿ߦߟ޿ߡᬌ⸛ࠍⴕ߁ߣ㧘ゲᣇะߦ⿠ᝄ࡮⸘᷹ߔࠆߣᢿ㕙Ⓧߩหቯ♖ᐲ߇㜞ߊ㧘ゲ

⋥ⷺᣇะߦ⿠ᝄ࡮⸘᷹ߔࠆߣᢿ㕙2ᰴࡕ࡯ࡔࡦ࠻ߩหቯ

♖ᐲ߇㜞޿ߎߣ߇ಽ߆ߞߚ㧚ゲᣇะߦ⿠ᝄߔࠆߣゲᣇะ ߩᝄേ߇ථ⿧ߒ㧘ᢿ㕙Ⓧߩૐਅ߇ᬌ಴ߐࠇ߿ߔߊߥࠅ㧘ゲ⋥ⷺᣇะߦ⿠ᝄߔࠆߣᦛߍᣇะߩᝄേ߇ථ⿧ߒ㧘ᢿ㕙 2 ᰴࡕ࡯ࡔࡦ࠻ߩૐਅ߇ᬌ಴ߐࠇ߿ߔߊߥߞߚ߽ߩߣ⠨

߃ࠄࠇࠆ㧚

㪈㪉㪊㪋㪌㪍㪎㪏㪐㪈㪇

㪈㪉㪊㪋㪌㪍㪎㪏㪐㪈㪇㪈㪈

ⷐ

ⷐ⚛⇟ภ

▵ὐ⇟ภ

䎔䎕䎖䎗䎘䎙䎚䎛䎜䎔䎓

䎐䎓䎑䎓䎘䎓䎓䎑䎓䎘䎓䎑䎔䎓䎑䎔䎘䎓䎑䎕䎓䎑䎕䎘䎓䎑䎖

ⷐ⚛⇟ภ

ᢿ㕙Ⓧૐਅ₸

ⷐ⚛⇟ภ

ᢿ㕙䎕ᰴ䮩䯃䮨䮺䮏ૐਅ₸

(8)

࿑-9 1Hzߢゲᣇะߦ⿠ᝄߒߚ႐ว

࿑-10 1Hzߢゲ⋥ⷺᣇะߦ⿠ᝄߒߚ႐ว ߹ߣ߼

ᧄ⎇ⓥߢߪ㧘㜞ᝄേᢙ㗔ၞߩ⸃ᨆߦㆡߒߚࠬࡍࠢ࠻࡞

ⷐ⚛ᴺߦၮߠ޿ߡkHz࡟ࡌ࡞ߩ㜞ᝄേᢙߢ⿠ᝄߒ㧘៊்

ߦࠃࠆ๟ᵄᢙᔕ╵㑐ᢙߩᄌൻߦ⌕⋡ߒߡ៊்ࠍᬌ಴ߔࠆ ᚻᴺߩឭ᩺ࠍⴕߞߚ㧚ਔ┵࿕ቯ᪞ࠍኻ⽎ߣߒߚᢙ୯ࠪࡒ ࡘ࡟࡯࡚ࠪࡦߦࠃߞߡឭ᩺ᚻᴺߩ᦭↪ᕈࠍᬌ⸽ߒߚ㧚

㜞ᝄേᢙ㗔ၞߦ߅ߌࠆⷐ⚛ಽഀᢙߦࠃࠆ๟ᵄᢙᔕ╵

㑐ᢙߩ㆑޿ࠍᬌ⸽ߒߚ㧚᦭㒢ⷐ⚛ᴺߢߪⷐ⚛ಽഀᢙ߇ዋ ߥ޿ߣ⸃ᨆ⚿ᨐߦ⺋Ꮕ߇↢ߓߚ߇㧘ࠬࡍࠢ࠻࡞ⷐ⚛ᴺߢ ߪ㧘ⷐ⚛ಽഀᢙߦࠃࠄߕ৻ቯߣߥࠅ㧘㜞ᝄേᢙ⿠ᝄߦ߅ ߌࠆࠬࡍࠢ࠻࡞ⷐ⚛ᴺߩ᦭ലᕈ߇␜ߐࠇߚ㧚

៊்ߦࠃࠆᝄേ․ᕈߩᄌൻߦ㑐ߒߡ㧘ૐᝄേᢙߦᲧߴ㧘㜞ᝄേᢙߩ߶߁߇៊்ߦኻߔࠆᗵᐲ߇㜞޿ߎߣ߇ಽ߆ߞ ߚ㧚ᢿ㕙ᰳ៊ߩ᦭ήߦࠃࠆᝄേ․ᕈߩᄌൻߦኻߔࠆᓇ㗀 ࠍ⺞ߴߚߣߎࠈ㧘⾰㊂ߩᷫዋߦࠃࠅ࿕᦭ᝄേᢙ߇Ⴧടߔ ࠆߎߣ߇ಽ߆ࠅ㧘࿕᦭ᝄേᢙߩᄌൻߦࠃࠅ៊்ࠍᬌ಴ߔ ࠆߣ㧘⺋ᬌ಴ߩෂ㒾ᕈ߇޽ࠆߎߣ߇ಽ߆ߞߚ㧚⸘᷹ࡁࠗ

࠭ࠍ⠨ᘦߒߡ៊்หቯ⸃ᨆࠍⴕߞߚߣߎࠈ㧘㜞ᝄേᢙߩ

߶߁߇ૐᝄേᢙߦᲧߴ㧘៊்หቯߩ♖ᐲ߇ࠃ޿ߎߣ߇ಽ ߆ߞߚ㧚߹ߚ㧘ゲᣇะߦ⿠ᝄ࡮⸘᷹ߔࠆߣᢿ㕙Ⓧ߇หቯ ߐࠇ߿ߔߊ㧘ゲ⋥ⷺᣇะߦ⿠ᝄ࡮⸘᷹ߔࠆߣᢿ㕙2ᰴࡕ

࡯ࡔࡦ࠻߇หቯߐࠇ߿ߔ޿ߎߣ߇ಽ߆ߞߚ㧚

࿑-11 2000Hzߢゲᣇะߦ⿠ᝄߒߚ႐ว

࿑-12 2000Hzߢゲ⋥ⷺᣇะߦ⿠ᝄߒߚ႐ว

੹ᓟߪ㧘㍑࠻࡜ࠬᯅࠍኻ⽎ߣߒߚᢙ୯ࠪࡒࡘ࡟࡯࡚ࠪ

ࡦࠍⴕ޿㧘ዪᚲ⊛ߦዊߐߥ៊்ࠍᬌ಴ߢ߈ࠆ߆ᬌ⸽ߔࠆ

੍ቯߢ޽ࠆ㧚

ෳ⠨ᢥ₂

1) ศጟീ࡮ጊญብ᮸㧦㍑࠻࡜ࠬᯅࠍਥߣߒߚᝄേ․ᕈ ᄌൻߦၮߠߊ᭴ㅧࡋ࡞ࠬࡕ࠾࠲࡝ࡦࠣ㧘ၯ₹ᄢቇᄢ ቇ㒮ℂᎿቇ⎇ⓥ⑼ඳ჻⺰ᢥ, 2010

2) ฎᎹᗲሶ࡮ᄢႦਭື࡮᪢ᨋ⑔ᄥ㇢㧦᭴ㅧ‛ߩ៊்ߦ

઻߁ᝄേ․ᕈߩᄌൻߦ㑐ߔࠆታ㛎⊛⠨ኤ㧘࿯ᧁቇળ

࿾㔡Ꮏቇ⺰ᢥ㓸, ╙28Ꮞ, No.19, 2005

3) ਛ᧛ల࡮቟੗⼑㧦ᓸേ᷹ቯߦၮߠߊ࿾㔡ⵍἴ㋕㛽ᑪ

‛ߩጀ៊்⹏ଔ㧘ᣣᧄᑪ▽ቇળ᭴ㅧ♽⺰ᢥ㓸, ╙517 ภ, pp.61-68, 1999

4) ศጟീ࡮ේ↰᡽ᒾ࡮ጊญብ᮸࡮દ⮮ା㧦ᢳ᧚ߩታ៊

்ߦࠃࠆ㍑࠻࡜ࠬᯅߩᝄേ․ᕈᄌൻߦ㑐ߔࠆ৻ᬌ⸛㧘

᭴ㅧᎿቇ⺰ᢥ㓸Vol.54A, pp.199-208, 2007

5) ฎᎹᗲሶ࡮ᄢႦਭື㧦㜞ᝄേᢙ㗔ၞߩࡈ࡯࡝ࠛᝄ᏷

ࠍ↪޿ߚዪᚲ៊்หቯ㧘ᔕ↪ജቇ⺰ᢥ㓸 Vol.11, pp.27-37, 2008

6) U. Lee㧦Spectral Element Method in Structural Dynamics, John Wiley & Sons (Asia) Pte Ltd, 2009

ⷐ⚛⇟ภ

ᢿ㕙Ⓧૐਅ₸

䎃

ⷐ⚛⇟ภ

䎃

ⷐ⚛⇟ภ

ᢿ㕙Ⓧૐਅ₸

䎃

ⷐ⚛⇟ภ

䎃

ⷐ⚛⇟ภ

ᢿ㕙Ⓧૐਅ₸

䎃

ⷐ⚛⇟ภ

䎃

ⷐ⚛⇟ภ

ᢿ㕙Ⓧૐਅ₸

䎃

ⷐ⚛⇟ภ

䎃

(2.8) ߎߩᑼ߆ࠄ㧘ᑼ(2.5)ߩ▵ὐᄌ૏ܷሺݔǡ ߱ሻߪᰴߩࠃ߁ߦߥࠆ㧚 ܷሺݔǡ ߱ሻ ൌ ܽଵ݁ି௜௞ಽ௫൅ ܽଶ݁ା௜௞ಽ௫ൌ ࢋሺݔǡ ߱ሻࢇ (2.9) ߚߛߒ㧘 ࢋሺݔǡ ߱ሻ ൌ ሾ݁ି௜௞ಽ௫ ݁ା௜௞ಽ௫ሿ (2.10

ࠬࡍࠢ࠻࡞ⷐ⚛ᴺߦၮߠߊ㜞ᝄേᢙ⿠ᝄߦࠃࠆ᭴ㅧ‛ߩ៊்หቯߦߟ޿ߡ

ࠠ࡯ࡢ࡯࠼㧦៊்หቯ㧘ࠬࡍࠢ࠻࡞ⷐ⚛ᴺ㧘㜞ᝄേᢙ㧘๟ᵄᢙᔕ╵㑐ᢙ

䎩䎵 䎩

䎩䎵䎩

䎩䎵 䎩

䎩䎵 䎩

䎩䎵 䎩

䎩䎵 䎩

䎩䎵 䎩

䎩䎵 䎩

䎩䎵 䎩

䎩䎵 䎩

䎩䎵 䎩

䎩䎵 䎩

䎩䎵 䎩

䎩䎵 䎩

䎩䎵 䎩

䎩䎵 䎩

䎩䎵 䎩

䎩䎵 䎩

㪈 㪉 㪊 㪋 㪌 㪍 㪎 㪏 㪐 㪈㪇

㪈 㪉 㪊 㪋 㪌 㪍 㪎 㪏 㪐 㪈㪇 㪈㪈

ⷐ⚛⇟ภ

▵ὐ⇟ภ

䎩䎵䎩

䎩䎵䎩

䎩䎵䎩

䎩䎵䎩

䎩䎵䎩

䎩䎵䎩

䎩䎵䎩

䎩䎵䎩

䎩䎵䎩

䎩䎵䎩

䎩䎵䎩

䎩䎵䎩

䎩䎵䎩

䎩䎵䎩

䎩䎵䎩

䎩䎵䎩

䎩䎵䎩

㪈㪉㪊㪋㪌㪍㪎㪏㪐㪈㪇

㪈㪉㪊㪋㪌㪍㪎㪏㪐㪈㪇㪈㪈