A Study on Identification Method for Basic Dynamic Characteristics of the Buildings
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(2) ĭþÀÃìº^QA@ÿźŐśMeNgŐśº® Vol.32 2018 Ø. 45. 1H,?M'I5/ *.7FBT . A Study on Identification Method for Basic Dynamic Characteristics of the Buildings īt ƹŇljdž ĕÏ °ÄNJdž «Ń ƯžNJdž Yuto Kawai, Kazuhiro Suezaki and Nagayuki Yoshida ljdž. ĭþÀÃÀÃƵQIBeÑÃŐśŖÚťÃÈý ĭþÀÃQIBeÑÃƪÚťÃŖ. NJdž. The structural model should be constructed with high accuracy for exactly redesigning the earthquake resistance ability of old buildings. For this, the procedures for identifying the basic characteristic of the building such as natural frequencies and damping factors are intensively required nowadays. This could be done by measuring the vibration of buildings caused by microtremors of the ground and identifying the vibrational characteristics of buildings. In this study it is investigated whether these dynamic characteristics could be extracted from observed data on small vibration by using MOESP method that is the basic method in subspace identification methods. Keywords : Microtremor, MOESP, Subspace identification ¬Åñĭ,¦Żë>ø# 5,'
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(5) : ,Ƹ ÚĻ,ĝƤÞÙ>ĝƤ_ >ĜƋ& : Qb(&Ʃ+Ɛ:(ŸƽƂÞ>Ē+ :i',ƬƄ*ú(*: hŽ+-ƍƊ´ď6 :'=N2J6=N2"$%=N2 Ŀ»Ƒǂ+7:ţÅ ĊŸƽƆÅ+# ùÅ*) ĝƤ_Qb~ïČ,ñ9(*: ŸƽƂÞƍ Ɗ-,ĝƤ_Qb+Ƒžň*ĝƤĤ>&Ÿ ljƘķŧ_Qb; ĝƤĻ·ƽ,ƣÙ ƽƉĘ>Æć ,Ēë>ĜƋ:Ŵ9ƟXc 𝑧𝑧̈# (𝑡𝑡)>¤:(: ;>÷ĆŗÛ'ſ MK,o'Ʀž: , 4 ƂÞƍƊ,¹ķ( ( *:ĝƤ_Qb-}8,ĝƤõğ+7#& ,Á (1) 𝑚𝑚𝑧𝑧̈ (𝑡𝑡) + 𝑑𝑑𝑧𝑧̇ (𝑡𝑡) + 𝑘𝑘𝑘𝑘(𝑡𝑡) = −𝑚𝑚𝑧𝑧̈# (𝑡𝑡) ßëĜƏ;& *;.*8* Ď+- Ÿ (*: ' 𝑧𝑧(𝑡𝑡)-Ƙķ,Ħ×½{'
(6) : ƽƂÞ,ęćÑã Œ+ÆĿ; ,ĜƏ ;> 1 Ʒ,çĆŗÛ+ďû:( 5éƄ(*: ;8,ĜƏ>¦Ż+:h$,Ć {𝑥𝑥̇ (𝑡𝑡)} = [𝐴𝐴∗ ]{𝑥𝑥(𝑡𝑡)} + [𝐵𝐵∗ ]𝑧𝑧̈# (𝑡𝑡) (2) ĭ(& ÕČçƇĵ>Ƣ ĝƤļëõğ,¬ ' ÅĜƏö8;: ĖŐś-çƇĵQgN8ĝƤļëõğ(& vſň*µĒ¯ē(ĴƀÅā>ò:ŦÙ,ǃ ¡ř¤u 2018 Ø 3 đ 20 ĉ ņž 2018 Ø 6 đ 1 ĉ Copyright © 2018 Hosei University.
(7) 46. 0 −𝑘𝑘/𝑚𝑚 [𝐵𝐵∗ ] = < 0 = −1 𝑧𝑧(𝑡𝑡) {𝑥𝑥(𝑡𝑡)} = > ? 𝑧𝑧̇ (𝑡𝑡) [𝐴𝐴∗ ] = 6. 1 : −𝑑𝑑/𝑚𝑚. (3). {𝑥𝑥(𝑡𝑡)}-Ľî½ā(7.; ;+7#&ƌƠ. ; Û(2)>ĽîĆŗÛ( Ľî½ā-ƇĵƁŵ >Ƣ&*?8,Ʈ{𝑦𝑦(𝑡𝑡)}(&Ɗĵ;: . ŭÇƣÙ𝑥𝑥̈ (𝑡𝑡) + 𝑧𝑧̈# (𝑡𝑡)Ʈ,»ª-. Û(1)79. 𝑦𝑦(𝑡𝑡) = [𝐶𝐶 ]𝑥𝑥(𝑡𝑡) 𝑘𝑘 𝑑𝑑 [𝐶𝐶 ] = 6− − : 𝑚𝑚 𝑚𝑚. (4). (ſ;: iÛ>ĆŗÛ(70 ƥŮČƲ𝑡𝑡 'ſ; ĽîĆŗÛ>ƼĀČƲſĿ :( {𝑥𝑥(𝑘𝑘 + 1)} = [𝐴𝐴]{𝑥𝑥(𝑘𝑘)} + [𝐵𝐵]𝑧𝑧̈# (𝑡𝑡) (5) '. [𝐴𝐴] = 𝑒𝑒. [C∗]∆E ∆E. (6). ∗. [𝐵𝐵] = F 𝑒𝑒 [C ]G 𝑑𝑑𝑑𝑑 ∙ [𝐵𝐵∗ ] #. [RaDK𝐴𝐴∗ Ĥ*8 ,Ś-ģ,7 +*: ∗. [𝐵𝐵] = [𝐴𝐴∗ ]JK L𝑒𝑒 [C ]∆E − [𝐼𝐼 ]N[𝐵𝐵∗ ] ∗ = L𝑒𝑒 [C ]∆E − [𝐼𝐼 ]N[𝐴𝐴∗ ]JK [𝐵𝐵∗ ]. (7). ĆŗÛ5ƼĀČƲſĿ:( wj,7+ *: (8) 𝑦𝑦(𝑘𝑘) = [𝐶𝐶 ]{𝑥𝑥(𝑘𝑘)} Û(5)(Û(8)8*:,7*JKP] >ŲàČk½JKP](70[1] +># [RaDK[𝐴𝐴∗ ],µĒ±ǀ- [𝐴𝐴∗ ],µĒ>𝜆𝜆∗. µĒYDRb>{𝑥𝑥 ∗ }(:(ģ,7+ď: (9) [𝐴𝐴∗ ]{𝑥𝑥 ∗ } = 𝜆𝜆∗ {𝑥𝑥 ∗ } µĒλ>ĩÅ:+- µĒĆŗÛ Q[𝐴𝐴∗ ] − 𝜆𝜆∗ [𝐼𝐼]R = 0>Ɖ(+*: 1 Ƙķŧ'-. 𝑚𝑚𝜆𝜆∗ S + 𝑑𝑑𝜆𝜆∗ + 𝑘𝑘 = 0. (10). ,Ɖ- ģÛ'ſ;:. λK∗ = −𝜔𝜔ℎ + iW1 − ℎS 𝜔𝜔 λS∗ = −𝜔𝜔ℎ − iW1 − ℎS 𝜔𝜔. (11). '. µĒ÷āNj𝜔𝜔 = X. Y. Z. ,. ĴƀÅāNjℎ =. [. (12). S√ZY. (<' ÷ŧ,ĽîŜƲſĿ-Ľî,Ĥ½ û,ā!ĸƴ,żńÙ
(8) : *=" yí ,Ĥ[RaDK[𝑇𝑇]>ł &Ľî½ā> (13) {𝑥𝑥^(𝑘𝑘)} = [𝑇𝑇]JK {𝑥𝑥(𝑘𝑘)} ,7+½û:( ĽîĆŗÛ(ĆŗÛ-. ģ,7+*: . {𝑥𝑥^(𝑘𝑘 + 1)} = Q𝐴𝐴_R{𝑥𝑥^(𝑘𝑘)} + Q𝐵𝐵`R𝑧𝑧̈# (𝑘𝑘). 𝑦𝑦(𝑘𝑘) = Q𝐶𝐶_ R{𝑥𝑥^(𝑘𝑘)}. (14). ' . Q𝐴𝐴_R = [𝑇𝑇]JK [𝐴𝐴][𝑇𝑇]. Q𝐵𝐵`R = [𝑇𝑇]JK [𝐵𝐵]. Q𝐶𝐶_ R = [𝐶𝐶 ][𝑇𝑇]. (15). ¬Å±ǀ+ &- L[𝐴𝐴] [𝐵𝐵] [𝐶𝐶]N '-*. LQ𝐴𝐴_R Q𝐵𝐵`R Q𝐶𝐶_ RN ¬Å;: [RaDKQ𝐴𝐴_R ,µĒ±ǀ. Q𝐴𝐴_R{𝑥𝑥^ } = [𝑇𝑇]JK [𝐴𝐴][𝑇𝑇]{𝑥𝑥^ } = 𝜆𝜆_{𝑥𝑥^ }. (16). '- Û(13)8. [𝐴𝐴]{𝑥𝑥 } = 𝜆𝜆_{𝑥𝑥 }. (17) _ (*: *="[RaDKQ𝐴𝐴R([RaDK[𝐴𝐴]µĒ_gSŅ*#&5 ¬h,µĒ𝜆𝜆_>Ē: ,(8 QgN,ƨ +7#&),7 *[RaDKQ𝐴𝐴_R¬Å;&5 µĒ-¬h* ,' ţÅ;:µĒ÷ā6ĴƀÅā,-½ =8* 1H'I59D ÚĻ,ļë>ſ¹Ėň*õğ-µĒ÷ā 𝜔𝜔3 -µĒ¯ē𝑇𝑇( ĴƀÅāℎ'
(9) : '-. ;8>Û(6),ŠljÛ8Ĩ4:Ćĭ>ăľ[2]+ ä#&Ơ2: [RaDK[𝐴𝐴]DžÆƸ+-Q𝐴𝐴_Rdž- ,µĒ𝜆𝜆a >Ç ƈ+n2 µĒ[RaDK[Λ](µĒ_gS, YDRb{𝑥𝑥a }>n2 µĒ[RaDK[𝑈𝑈]+7#&. ģ,7+ſ(': [𝐴𝐴] = [𝑈𝑈][Λ][𝑈𝑈]JK (18) ƥŮČƲſĿ; ĽîĆŗÛ,[𝐴𝐴∗ ]5¬Ğ+µ ĒƉĘ:(' (;. [𝐴𝐴∗ ] = [𝑈𝑈 ∗ ][Λ∗ ][𝑈𝑈 ∗ ]JK (19) (ſ : ,( ģÛïŝ: ∗ ∗ (20) 𝑒𝑒 [C ]∆E = [𝑈𝑈 ∗ ]𝑒𝑒 [d ]∆E [𝑈𝑈 ∗ ]JK Û(6),Š Û79 i,Û(18)(Û(20)- ŵ' : . [𝑈𝑈][Λ][𝑈𝑈]JK = [𝑈𝑈 ∗ ]𝑒𝑒 [d. ∗ ]∆E. [𝑈𝑈 ∗ ]JK. (21) (<' ŲàČk½JKP]',Ľî½ā,µ. Copyright © 2018 Hosei University ĭþÀÃìº^QA@ÿźŐśMeNgŐśº® Vol.32.
(10) 47 ĒYDRb-ƥŮČƲ,Č+=8 k½'
(11) :8 ƼĀČƲ, *:Č+ &5k½'
(12) : #& [𝑈𝑈] ∝ [𝑈𝑈 ∗ ](:(': ,' ģÛå8;: . 6. [Λ] = 𝑒𝑒 [d. ↓. 𝜆𝜆K. 𝜆𝜆S. ;79 . ∗ ]∆E ∗. gh ∆E : = 6𝑒𝑒. . (22). 𝑒𝑒. g∗i ∆E. :. |ln 𝜆𝜆K | = |𝜆𝜆∗K ∆𝑡𝑡| = W𝜔𝜔ℎ + (1 − ℎ)𝜔𝜔∆𝑡𝑡 = 𝜔𝜔∆𝑡𝑡. ↓. 3. 𝜔𝜔 =. . ∗. |ln 𝜆𝜆K | ∆𝑡𝑡. ∗. |𝜆𝜆K | = m𝑒𝑒 𝜆𝜆h∆E m = 𝑒𝑒 no(𝜆𝜆h )∆E = 𝑒𝑒 Jpq∆E. 79 . ln|𝜆𝜆K | = −𝜔𝜔ℎ∆𝑡𝑡. ↓. ln|𝜆𝜆K | ln|𝜆𝜆K | ℎ=− =− |ln 𝜆𝜆K | 𝜔𝜔∆𝑡𝑡. (23). (24). (25). wi8 [RaDK[𝐴𝐴](3 -Q𝐴𝐴_R),µĒ 8ÚĻ,µĒ÷ā(ĴƀÅā>ò:( ':
(13) F LCY*. Û(14),ĽîĆŗÛ(ĆŗÛ+3;:©[ RaDKĔŎ'
(14) :(: QgN8 ;8ĔŎ,[RaDK>ùÅ:(>¬Å( ƞØ ¬Åĭ(&ƪŜƲĭƱņ; ©ƭ 'ıņ*Őśž=;& : ,o'5 ¹Ėň *Ćĭ'
(15) :MOESPĭ+İŋ ;>ł: (+79çƇĵĢ³8å8;:QgN 8ÚĻĝƤ>¬Å:Ćĭ>ĜƋ: wj+ [ RaDKQ𝐴𝐴_R(Q𝐶𝐶_ R>¬Å:ñƿ>Ƅũ&Ŕ (1) QgN(&Ħ×·ƣÙ𝑢𝑢(𝑘𝑘) = 𝑧𝑧̈# (𝑘𝑘) 𝑘𝑘 = 0 1 2 ⋯ 𝑞𝑞 − 1 QgN( &ÚĻ,yíǃ+:Ħ×ŭÇƣÙ 𝑦𝑦(𝑘𝑘) = 𝑥𝑥̈ (𝑘𝑘) + 𝑧𝑧̈# (𝑘𝑘) 𝑘𝑘 = 0 1 2 ⋯ 𝑞𝑞 − 1 ,7+©𝑞𝑞 $å8;& :(: ' ģ,7*QgN[RaDK(Qg N[RaDK>ÅŶ: . [𝑈𝑈]. 𝑢𝑢(0) 𝑢𝑢(1) ⋯ 𝑢𝑢(𝐿𝐿 − 1) 𝑢𝑢(1) 𝑢𝑢(2) ⋯ 𝑢𝑢(𝐿𝐿) z (26) =v ⋮ ⋮ ⋮ 𝑢𝑢(𝑟𝑟 − 1) 𝑢𝑢(𝑟𝑟) ⋯ 𝑢𝑢(𝐿𝐿 + 𝑟𝑟 − 1). ∈ 𝑅𝑅~×Ä. . [𝑌𝑌]. 𝑦𝑦(0) 𝑦𝑦(1) ⋯ 𝑦𝑦(𝐿𝐿 − 1) ⎡ ⎤ 𝑦𝑦(1) 𝑦𝑦(2) ⋯ 𝑦𝑦(𝐿𝐿) ⎥ (27) =⎢ ⋮ ⋮ ⎢ ⋮ ⎥ ⎣𝑦𝑦(𝑟𝑟 − 1) 𝑦𝑦(𝑟𝑟) ⋯ 𝑦𝑦(𝐿𝐿 + 𝑟𝑟 − 1)⎦. ∈ 𝑅𝑅~∙K×Ä. . ,7+QgN>h$ $Ò+ 8& ©ž+hÅā(𝐿𝐿)n2 [RaDK>VeF bf[RaDK( 𝑟𝑟-WcODVeFbf [RaDK,WcODžā'
(16) : WcODljž ,QgNā-ČƲÖ(𝐿𝐿 − 1)∆𝑡𝑡 ,mş( ,ķ Č+HeXaeE; QgN,űā'
(17) : ;WcODž+&𝑟𝑟L= 𝑞𝑞 − (𝑟𝑟 − 1)Nžƫŵ ; VeFbf[RaDKQgN[R aDK'
(18) : ,( 𝑟𝑟 𝐿𝐿,À-kÅ'
(19) : (2) ' QgN[RaDK(QgN[ RaDK>ų+n2 QgN[RaDK. [𝐺𝐺 ] = 6. [𝑈𝑈] : ∈ 𝑅𝑅 (~ä~∙K)×Ä [𝑌𝑌]. (28). >~9 ģ,7+LQƉ: . 6. [𝐿𝐿 ] [𝑄𝑄 ] [𝑈𝑈] ∙ : = 6 KK : 6 K : [𝑌𝑌] [𝐿𝐿SK ] [𝐿𝐿SS ] [𝑄𝑄S ]. (29). '. [𝐿𝐿KS ] ∈ 𝑅𝑅~×~ [𝐿𝐿SK ] ∈ 𝑅𝑅~∙K×~. [𝐿𝐿SS ] ∈ 𝑅𝑅~∙K×~∙K. [𝑄𝑄K ] ∈ 𝑅𝑅~×Ä [𝑄𝑄S ] ∈ 𝑅𝑅~∙K×Ä. iÛ§Ɲ- ÆƸ+-QgN[RaDK,ƛŵ [RaDK[𝐺𝐺]å >QRƉ ;>Ùƛŵ& å8;: (3) [𝐿𝐿SS ]>ļŅƉ: . [𝐿𝐿22 ]. (30). Copyright © 2018 Hosei University ĭþÀÃìº^QA@ÿźŐśMeNgŐśº® Vol.32.
(20) 48. [Σç ] [𝑉𝑉ç ]å ∙ : 6 : [Σêç ] [𝑉𝑉êç ]å ∙ éç ][Σêç ][𝑉𝑉êç ]å = [𝑈𝑈ç ][Σç ][𝑉𝑉ç ]å + [𝑈𝑈 å ≅ [𝑈𝑈ç ][Σç ][𝑉𝑉ç ] éç ]] 6 = [[𝑈𝑈ç ] [𝑈𝑈. {𝑥𝑥(𝑡𝑡)} = >. ' [𝐿𝐿SS ],`eD(Ʒā)𝑛𝑛'
(21) :*8 . [Σç ] = 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑ó𝜎𝜎K ⋯ 𝜎𝜎ç ô [Σêç ] = 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑ó𝜎𝜎çäK 𝜎𝜎çäS ⋯ 𝜎𝜎~ ô (31) L𝜎𝜎ö ≅ 0 𝑗𝑗 ≧ 𝑛𝑛 + 1N. (*: ,7*ļŅ,Ôå8; »ª - ƇĵÇƗ,żńÙ>𝑛𝑛 = 2(Å:ƉĘŬ ę8𝑛𝑛 = 2(Å':»ª- ƇĵÇƗ,ż ńÙ>1(ùÅ: (4) [𝑈𝑈ç ] -𝑟𝑟ž× 𝑛𝑛,[RaDK'
(22) : ,Š𝑖𝑖 ž8Š𝑗𝑗ž3'£9 ƪ[RaDK> [ a:ö 𝑈𝑈ç ](ſƌ:( Šljž>£9&. Q𝐶𝐶_ R = Q K:K𝑈𝑈ç R. (32). (:(': (5) ,( ĐūŠ𝑟𝑟ž>£9ƶ Q K:~JK𝑈𝑈ç R(Š ljž>£9ƶ Q S:~𝑈𝑈ç R(-ģ,Ƴ . Q K:~JK𝑈𝑈ç RQ𝐴𝐴_R = Q S:~ 𝑈𝑈ç R. (33) _
(23) :,'Q𝐴𝐴R-ĐÊsqĭ+7#&ģ,7+ Ĩ48;: . Q𝐴𝐴_R. JK. (34). = L[ K:ûJK𝑈𝑈ç ]å [ K:ûJK𝑈𝑈ç ]N [ K:ûJK𝑈𝑈ç ]å [ S:~𝑈𝑈ç ] (6) Q𝐴𝐴_R,µĒ±ǀNjÛ(34) 3 -µĒĆŗÛ mQ𝐴𝐴_R − 𝜆𝜆[𝐼𝐼]m>Ɖ &µĒ𝜆𝜆a (𝑖𝑖 = 1 ⋯ 𝑛𝑛/2)>. Ĩ4 ©_gS,µĒ÷ā𝜔𝜔a 3 -µĒ¯ē 𝑇𝑇a = 2π/𝜔𝜔a 7/ĴƀÅāℎa >ţÅ:[1] -WGP. !83. ;3',ƌƠ'- ŀƉ6 7+ljƘķ ŧ_Qb>ÇƗ( hŽ,¿Ƙķŧ_Qb'-. Û(1)ģÛ+v=:. [𝑀𝑀]{𝑧𝑧̈ } + [𝐷𝐷]{𝑧𝑧̇ } + [𝐾𝐾 ]{𝑧𝑧} = −[𝑀𝑀]{1}𝑧𝑧̈#. ( 35). Û(3)(Û(4)'Ŕ ĽîĆŗÛ(ĆŗÛ, ©[RaDK6YDRb5wj,7+v=:. 𝑂𝑂§ 𝐼𝐼§ : JK −𝑀𝑀 𝐾𝐾 −𝑀𝑀JK 𝐷𝐷 {0} [𝐵𝐵∗ ] = 6 : −{1}. [𝐴𝐴∗ ] = 6. {𝑧𝑧(𝑡𝑡)} ? {𝑧𝑧̇ (𝑡𝑡)}. (36). [𝐶𝐶 ] = [−[𝑀𝑀]JK [𝐾𝐾] −[𝑀𝑀]JK [𝐷𝐷]]. (37) & N Ƙķŧ,»ª-𝑛𝑛 = 2𝑁𝑁(*: Ť 3',ƌƠ- ,33Ē'
(24) : ;3'- ŭÇƣÙêŢ,Ƈĵķā ℓ -lj'
(25) :(&Ɩ& ƃāķℓ > 1,ƇĵQgN> ł :»ª'- Û(27),[RaDK,KC`g Ʈ-wj,7+YDRbƮ(*9 ſƌ𝑟𝑟 ∙ 1-ſ ƌ𝑟𝑟 ∙ ℓ+½=:. [𝑌𝑌]. {𝑦𝑦(0)} {𝑦𝑦(1)} ⎡ {𝑦𝑦(1)} {𝑦𝑦(2)} =⎢ ⋮ ⋮ ⎢ ⎣{𝑦𝑦(𝑟𝑟 − 1)} {𝑦𝑦(𝑟𝑟)} . ∈ 𝑅𝑅~∙ℓ×Ä. '. ⋯ ⋯. ⋯. {𝑦𝑦(𝐿𝐿 − 1)} ⎤ {𝑦𝑦(𝐿𝐿)} ⎥ (38) ⋮ ⎥ {𝑦𝑦(𝐿𝐿 + 𝑟𝑟 − 1)}⎦. 𝑦𝑦K (𝑘𝑘) ( ) {𝑦𝑦(𝑘𝑘)} = ™𝑦𝑦S 𝑘𝑘 ´ ⋮ 𝑦𝑦ℓ (𝑘𝑘). (39). E;4'&X0. ç-ĖėƇĵƮ'
(26) : ƇĵƮ8,ĒíŶ *QgN>ò:ñĭ,ƱņŐś+ł : 4Ġ üçƣÙ𝑧𝑧̈# >~ï:[3] Ġüç>ÅÕkƆƧŗ(:(ģ,7+Å Û': . 𝑦𝑦̈ # (𝑡𝑡) = 𝑔𝑔(𝑡𝑡) ∙ 𝑧𝑧̈ 0 L𝑡𝑡𝑗𝑗 N. (40). ¥. 2𝑆𝑆(𝜔𝜔a )∆𝜔𝜔 𝑧𝑧̈# L𝑡𝑡ö N = ¨ ≠ cos(𝜔𝜔a 𝑡𝑡 + 𝜑𝜑a ) 𝜋𝜋. '. aµK. 𝑆𝑆(𝜔𝜔)Nj ∆𝜔𝜔 =. 𝑗𝑗 = 1, ⋯ , n∑. i pi ∫pi Kä∏qπ π. i Nä∏q i pi ∫pi LKJpi ∫pπ π π. 𝜔𝜔ª Nj·Ŋ,ljģµĒ÷ā. pºΩΩæø Jp¿¡¬æø ¥ p. 1≤. ƒ. . (41). (42). (43). ≤ 100 . 𝑁𝑁:Ƭªā(300 ŗÙ) K. 𝜔𝜔a = 𝜔𝜔Ä + ≈𝑖𝑖 − S∆ ∆𝜔𝜔 𝜑𝜑a : 0~2𝜋𝜋,hĞrā. (44) (45). Copyright © 2018 Hosei University ĭþÀÃìº^QA@ÿźŐśMeNgŐśº® Vol.32.
(27) 49 Ƭª ã ƣÙĮà,ĐÀðƄ,ā+* :7ƕĂ: ½{,÷Ö𝑎𝑎,»ª ƣÙĮà-𝑎𝑎(2𝜋𝜋/𝑇𝑇)S ( *: 𝑎𝑎 = 1𝜇𝜇𝜇𝜇( 𝑇𝑇>ĐÊ'0.02𝑠𝑠(= 2∆𝑡𝑡)(: ( ƣÙ÷Ö-7 0.1m/𝑠𝑠 S'
(28) : ·Ŋ,µĒ¯ē𝑇𝑇à = 2𝜋𝜋/𝜔𝜔𝑔𝑔-ſ 1 +7#&l: ſ 1 ·Ŋ,Řǁ(µĒ¯ē𝑇𝑇à (𝑠𝑠) Table 1 Type of ground and Natural Period 𝑇𝑇à (𝑠𝑠) Š 1 Ř·Ŋ ÌŊ őƘŏœË p(& 0.4 Š 3 Ũw,·Ë*) 0.6 Š 2 Ř·Ŋ Š 1 3 Ř·Ŋw¾,5, Š 3 Ř·Ŋ ƚÜ*ĪŚË 30m wi,5 0.8 , 3 - įĬ įIJÍ> 3m wi¸4ŝ& ã 30 ØĔ Ķ,5,š. S@QA. \WG. ! BUS@QA. Ū*ljƘķŧ_Qb>ÇƗ+ wi+Ơ2 MOESP ĭ>ł µĒ¯ē(ĴƀÅā,òñĭ +$ &ĜƋ:[4] [5] [6] 3 Û(26)(27)+:QgN[RaDK,ųġ ĥ+$ &5ĜƋ>ž Ƙķ_Qb>´.1 +Ŕ. QgNāƉĘČƲs. ſ 2 ,7+ QgNfQgNā ; ; 50 5
(29) ;.ǃ ŦÙ'µĒ¯ē(ĴƀÅā> ò:(' ~ï:QgN[RaDK,àĽ- 3 Ƣ9'ĜƏ Ŭę+À*Ó-ƅ8;*# 4 Ú Ļ(·Ŋ,QgNā+ê&yí'ĝ=* (ŷ8;: . ſ 2 QgN[RaDK,ųġĥ+7:ĥƜ Table 2 Comparison of the Data Matrix Aspect Ratio.. µĒ¯ē(t). 0.05. 0.3209295. 0.06267000. 𝑚𝑚 × 2𝑚𝑚. 0.3358009. 0.07902643. 0.0028194. 0.99990000. 𝑚𝑚 × 𝑚𝑚. 0.4007251. 0.04920188. 𝑚𝑚 × 2𝑚𝑚. 0.4003544. 0.04943078. 𝑚𝑚 × 3𝑚𝑚. 0.4000680. 0.04996341. 𝑚𝑚 × 𝑚𝑚. 0.3999954. 0.05000024. 0.3999995. 0.04999714. 𝑚𝑚 × 3𝑚𝑚. 0.3999941. 0.04999702. 𝑚𝑚 × 𝑚𝑚. 10Dž0.1sdž . 𝑚𝑚 × 3𝑚𝑚. 50Dž0.5sdž . 500Dž5sdž . ĴƀÅā. 0.4. Lj. 𝑚𝑚 × 2𝑚𝑚. ]WG. !)Z[/ O0BU ģ+ ÇƗÚĻ>¿ƘķĝƤĻ1óÝ: 4. ´.2 ,7*NJƘķ_Qb',ĜƏ>ž 3. ljƘķ+ &*ŦÙŒƒ' 4 wj ,7*ƻƾ,ij>xÅŬę,ĥƜ>ž fƊĵ³ƓÓfff©Č,ƣÙ𝑥𝑥̈ (𝑡𝑡)+ & |𝑥𝑥̈ (𝑡𝑡)| × α(%),UBL>: fŁ¼ƓÓfffƣÙQgN,ĐÀ|𝑥𝑥̈ |ZŒœ ,α(%) >ĐÀ÷Ö(:ZdBRUBL>:. 𝑇𝑇K = 0.5(𝑠𝑠) 𝑇𝑇S = 0.2(s). 𝑇𝑇K = 0.4(𝑠𝑠) ℎK = 0.05 ´.1 ljƘķŧ_Qb Fig.1 Single-Degree-of-Freedom Model.. ųġĥ. ~ï _Qb. ℎK = 0.05 ℎS = 0.08. ´.2 NJƘķŧ_Qb Fig.2 2-Degree-of-Freedom Model. ſ 3 ƻƾ,ª+7:ĥƜ Table 3 Comparison of the Noise Ratio É ƻƾ ª . QgNā ƉĘČƲ . _Qb. . ģ_gS. ģ_gS. µĒ¯ē(t). ĴƀÅā. µĒ¯ē(t). ĴƀÅā. 0.5. 0.05. 0.2. 0.08. 500(5). 0.49999849. 0.04999723. 0.20020135. 0.07998501. . 1000(10). 0.50001824. 0.05008015. 0.20035986. 0.07701294. 5. 1000(10). 0.49992202. 0.04998565. 0.20377790. 0.06104071. 1000(10). 0.49989092. 0.05008231. 0.02816362. 0.00025840. 3000(30). 0.49989761. 0.05029855. 0.02269004. 0.00121618. 6000(60). 0.49964426. 0.05006224. 0.52015925. 0.00236592. *. 10. ſ 3 +Ł¼ƓÓƻƾ> QgN+7: ƉĘŬę>Ŕ ƻƾ 5DŽŗÙ,»ª 1000 ŗ, QgNå8;& ;.ljģ_gS,µĒ¯ē(Ĵ. Copyright © 2018 Hosei University ĭþÀÃìº^QA@ÿźŐśMeNgŐśº® Vol.32.
(30) 50 ƀÅā NJģ_gS,µĒ¯ē3'ŦÙ7ţ ¦Ż'
(31) # hĆ' 10DŽ>ƙƻƾ,»ª ljģ _gS',ŦÙ-ůô& : NJģ_gS'ā,r;ƅ8; QV. ĖŐś'-ƉĘÇƗ(&Ġüç>¤:ljƘ ķ¢/ 2 Ƙķŧ_Qb>~ï ƪŜƲJKP] ¬Åĭ,o'5¹Ėň*Ćĭ'
(32) : MOESP ĭ>¹ + ÚĻ,ļë>ò:ñĭ+$ &ĜƋ fƣÙ¢/êŢƣÙ8~ï:QgN[ RaDK-àĽ+78 ƉĘ>ž(': fƻƾĿÆň*ª'3;:»ª+ &5. ljģ_gS+$ &-ŦÙ7ò' ƪŜƲ JKP]¬Åĭ- ,Ēë>ô& :. (R<K [1] À|č, “ĝƤĻ,JKP]æ”, ěĹ, 2013 Ø [2] ŹŃLJħƭĤž, “ƪŜƲĭ+¹%J KP]¬Å+7:ÚĻ,µĒ÷ā(ĴƀÅ ā,ùÅŦÙ”LJĉĖÚťÃzĝƤŧƖăƺLJŠ 701 ¨, pp.923-932, 2014.7 [3] ĚŃċè, “ĐąŸƽĝƤƉĘ” ,Š 3 Ĺ, Š 7 Ş, ěĹ, 2014 Ø [4] Ð¥h, “hŽơž(ĝƤÑÃ1,êł”, GcTŕ, 2011 Ø [5] ÀÏƿá, “Úť÷ŀƖ”,â¶ŕ, 1996 Ø [6] ĺÎŌ, “āƊţ, 4, Fortran90/95 Xc E`\eEư”, ěĹ, 2007 Ø. Copyright © 2018 Hosei University ĭþÀÃìº^QA@ÿźŐśMeNgŐśº® Vol.32.
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