)5$*,/,7<$66(660(172)815(,1)25&('0$6215<:$//6
81'(5*2,1*($57+48$.(,1'8&('/2&$/)$,/85(
0(&+$1,606
0DUFR1DOH
$QGUHD&KLR]]L
5LFFDUGR/DPEURJKLQL
)DELR0LQJKLQL
0DUFR5LJR
OLQ
DQG$QWRQLR7UDOOL
'HSDUWPHQWRI(QJLQHHULQJ8QLYHUVLW\RI)HUUDUD
9LD6DUDJDW)HUUDUD,WDO\
HPDLO^PDUFRQDOHDQGUHDFKLR]]LIDELRPLQJKLQLDQWRQLRPLFKHOHWUDOOL`#XQLIHLW
^ULFFDUGODPERUJKLQLPDUFRULJROLQ`#VWXGHQWXQLIHLW
.H\ZRUGV)UDJLOLW\IXQFWLRQV0DVRQU\/RFDOIDLOXUHPHFKDQLVPV6HLVPLFYXOQHUDELOLW\
$EVWUDFW 'DPDJH REVHUYDWLRQV IURP VWURQJ HDUWKTXDNHV VKRZ WKDW XQUHLQIRUFHG PDVRQU\
EXLOGLQJV KDYH H[KLELWHG UHFXUUHQW ORFDO IDLOXUH PHFKDQLVPV DQG FRQVWLWXWH D VHULRXV OLIH
VDIHW\KD]DUG7KLVFRQWULEXWLRQLVDLPHGDWHYDOXDWLQJWKHIUDJLOLW\IXQFWLRQVIRUXQUHLQIRUFHG
PDVRQU\ZDOOVLQWKHSUHVHQFHRIORFDOIDLOXUHPHFKDQLVPVLQGXFHGE\RXWRISODQHORDGLQJ
7KHRXWRISODQHUHVSRQVHFRQVLVWVRIWKHRYHUWXUQLQJRIWKHHQWLUHRUDSDUWRIWKHZDOOLQVXI
ILFLHQWO\FRQQHFWHGWRWKHUHVWRIWKHVWUXFWXUH7KHZDOOFDQEHLGHDOL]HGDVDQXPEHURIULJLG
ERGLHVXQGHUJRLQJURFNLQJPRWLRQ7KH\DUHDVVXPHGWRXQGHUJRRQHVLGHGURFNLQJRUYHUWL
FDOVSDQQLQJVWULSZDOOGLVSODFLQJDVDQDVVHPEO\RIDFRXSOHGULJLGERG\,QWKLVVWXG\ZH
XVHDVHWRIJURXQGPRWLRQVIURP HDUWKTXDNHHYHQWVWKDWRFFXUUHGLQ,WDO\IURPWR
)RUDQ\JLYHQZDOOXQGHUJRLQJDVSHFLILF FROODSVHPHFKDQLVPWKHSUREDELOLW\RIFRO
ODSVHLVHYDOXDWHGWKURXJKD0XOWLSOH6WULSH$QDO\VLV06$7KHQDIUDJLOLW\FXUYHLVILWWHG
WRWKH06$GDWDSRLQWV7KHSURFHGXUHRXWOLQHGPD\EHH[WHQGHGWRREWDLQW\SRORJLFDOIUDJLOL
W\IXQFWLRQVDVDFRPELQDWLRQRIWKHIUDJLOLW\FXUYHVFRUUHVSRQGLQJWRWKHYDULRXVPHFKDQLVPV
DQDO\]HG$SUHOLPLQDU\DSSOLFDWLRQRIWKHSURFHGXUHWRWKHKLVWRULFDOFHQWUHRI)HUUDUD,WDO\
LVGHVFULEHG
4311
EURODYN 2020
XI International Conference on Structural Dynamics
M. Papadrakakis, M. Fragiadakis, C. Papadimitriou (eds.)
Athens, Greece, 23–26 November 2020
Available online at www.easdprocedia.org
EASD Procedia EURODYN (2020) 4311-4317
ISSN:2311-
9020 © 2020 The Authors. Published by EASD Procedia.
Peer-review under responsibility of the Organizing Committee of EURODYN 2020.
doi: 10.47964/1120.9353.20305
0DUFR1DOH$QGUHD&KLR]]L5LFFDUGR/DPERUJKLQL)DELR0LQJKLQL0DUFR5LJROLQDQG$QWRQLR7UDOOL
,1752'8&7,21
7KH RXWRISODQH EHKDYLRU RI 8Q5HLQIRUFHG 0DVRQU\ LQ WKH IROORZLQJ 850 VWUXFWXUHV
VXEMHFWHGWRJURXQGPRWLRQH[FLWDWLRQVKDVEHHQ ZLGHO\LQYHVWLJDWHG5HFHQW VHLVPLF HYHQWV
KDYHVKRZQWKDWRYHUWXUQLQJRIHQWLUHRUSDUWVRIZDOOVUHSUHVHQWVRQHRIWKHPRVWVHULRXVOLIH
KD]DUGV>@$QFLHQWEXLOGLQJVQRWFRQFHLYHGZLWKVSHFLILFGHVLJQFULWHULDDJDLQVWHDUWKTXDNH
DFWLRQVDUHJHQHUDOO\PRUHYXOQHUDEOHWKDQQHZEXLOGLQJVEHFDXVHRIWKHLQDGHTXDF\RIFRQ
QHFWLRQVRIZDOOVWRWUDQVYHUVHVWDELOL]LQJZDOOVDQGIORRUVWUXFWXUHV
,Q ,WDO\ WKH VHLVPLF DQDO\VLV RI PDVRQU\ VWUXFWXUHV EDVHG RQ WKH VWXG\ RI ORFDO FROODSVH
PHFKDQLVPVVWDUWVZLWK*LXIIUq>@DQGDGHVLJQPHWKRGEDVHGRQNLQHPDWLFDQDO\VLVLVFXU
UHQWO\UHSRUWHGE\WKH,WDOLDQEXLOGLQJFRGH>@$QRWKHUDSSURDFKRIWHQPRUHDFFXUDWHPDNHV
XVHRIWKHPRWLRQHTXDWLRQVRIURFNLQJULJLGEORFNVVXEMHFWHGWRDJLYHQDFFHOHUDWLRQWLPHKLV
WRU\,QWKLVFRQWH[WWKHVWXG\RIURFNLQJRVFLOODWRUVVWDUWVZLWKWKHVHPLQDOSDSHUE\+RXVQHU
>@ZKLFKGHULYHVWKHRXWRISODQHUHVSRQVHRIDSDUDSHWZDOOFRQVLGHUHGDVDVLQJOHGHJUHHRI
IUHHGRP6'2)V\VWHP)ROORZLQJ+RXVQHUWKHUHVHDUFKIRFXVHVRQWKHG\QDPLFUHVSRQVH
RIULJLGEORFNVVXEMHFWHGWRSXOVHRUHDUWKTXDNHVH[FLWDWLRQV>@,QSDUWLFXODULWLVVKRZQWKDW
WKLVUHVSRQVHLVFKDUDFWHUL]HGE\VWURQJQRQOLQHDULW\DQGG\QDPLFLQVWDELOLW\
/DWHURWKHUPRGHOVDUHGHYHORSHGWRDSSUR[LPDWHWKHURFNLQJUHVSRQVHRIFRPSOH[PXOWL
EORFNV\VWHPVZLWKDQHTXLYDOHQW6'2)V\VWHP>@,QSDUWLFXODUDXVHIXO6'2)LGHDOL]DWLRQ
IRUWKHGLVSODFHPHQWEDVHGDQDO\VLVRIWKHRXWRISODQHEHQGLQJRI850ZDOOVLVSURSRVHGLQ
>@
7KHLQFUHDVLQJLQWHUHVWLQDSUREDELOLVWLFDSSURDFKWKDWDOORZVWDNLQJDFFRXQWRIXQFHUWDLQ
WLHVYXOQHUDELOLWLHVDQGULVNLQHDUWKTXDNHHQJLQHHULQJSURYLGHVDGHVFULSWLRQRIWKHVWUXFWXUDO
UHVSRQVHE\PHDQV RI G\QDPLF DQDO\VHV ,Q3((53%((IUDPHZRUN>@WKHIUDJLOLW\FXUYH
UHSUHVHQWV RQH RI WKH PDLQ NH\ WRROV 6HYHUDO VWXGLHV SURYLGH IUDJLOLW\ FXUYHV IRU URFNLQJ
EORFNVDVDIXQFWLRQRIYDULRXVLQWHQVLW\PHDVXUHV>@
7KHDLPRIWKHSUHVHQWVWXG\LVWRSURSRVHDG\QDPLFDSSURDFKXVLQJULJLGEORFNPRGHOLQJ
WRGHULYHIUDJLOLW\FXUYHVIRUWZRW\SHVRIYHU\IUHTXHQWORFDOIDLOXUHPHFKDQLVPV,QSDUWLFXODU
ZHDQDO\]HRQHVLGHGURFNLQJDQGRQHZD\YHUWLFDOVSDQQLQJVWULSZDOOV966:GLVSODFLQJ
DVDQDVVHPEO\RIWZRULJLGERGLHV6HFWLRQUHYLHZVWKHPHFKDQLFDOPRGHOVXVHGWRUHSUR
GXFHWKHRXWRISODQHEHKDYLRU 6HFWLRQ SUHVHQWVWKHSURFHGXUHIRUHYDOXDWLQJWKHIUDJLOLW\
FXUYHVDQG UHSRUWV VRPHUHVXOWV $V D FDVH VWXG\DSUHOLPLQDU\ DSSOLFDWLRQ WR WKH KLVWRULFDO
FHQWUHRI)HUUDUD)LJXUH,WDO\LVSUHVHQWHG
D
E
)LJXUH7\SLFDO850EXLOGLQJVLQWKHKLVWRULFDOFHQWUHRI)HUUDUD
4312
0DUFR1DOH$QGUHD&KLR]]L5LFFDUGR/DPERUJKLQL)DELR0LQJKLQL0DUFR5LJROLQDQG$QWRQLR7UDOOL
0(&+$1,&$/02'(/65(9,(:6
7KLV VHFWLRQ SUHVHQWV WKH HTXDWLRQV RI PRWLRQ IRU WKH RQHVLGHG URFNLQJ DQG WZREORFN
URFNLQJ PHFKDQLVPV 7KH G\QDPLF UHVSRQVH RI WKH ULJLG EORFNV WR SUHVFULEHG DFFHOHUDWLRQ
WLPHKLVWRULHVLVREWDLQHGIURPDVSHFLILFDOO\VXLWHG0$7/$% FRGHWKDWQXPHULFDOO\ VROYHV
WKHQRQOLQHDUHTXDWLRQVZLWKD
WK
WK
RUGHU5XQJH.XWWDLQWHJUDWLRQWHFKQLTXH
2QHVLGHGURFNLQJ
$UHFWDQJXODU EORFN UHVWLQJ RQ DKRUL]RQWDOSODQHDQG SUHVHQWLQJ DYHUWLFDO RQHVLGHGUH
VWUDLQWLVFRQVLGHUHG)LJXUH7KHIULFWLRQFRHIILFLHQWLVDVVXPHGODUJHHQRXJKWRDYRLGVOLG
LQJEHWZHHQWKHEORFNDQGWKHSODQH
)LJXUH2QHVLGHGURFNLQJXQGHUJURXQGPRWLRQ
7KHHTXDWLRQRIPRWLRQWKDWJRYHUQVWKHRQHVLGHGURFNLQJUHVSRQVHFDQEHZULWWHQDVIRO
ORZV
TD TDT FRVVLQ
JEE
X505J0,
ZLWK5EHLQJWKHGLVWDQFHEHWZHHQEORFNFHQWURLGDQGURWDWLRQFHQWUH2TWKHDQJXODUURWDWLRQ
,
WKHSRODUVHFRQGPRPHQWRIDUHDĮWKHDQJOHEHWZHHQ5DQGWKHYHUWLFDOHGJHRIWKHEORFN
0
E
WKHEORFNPDVVRIWKHEORFNDQGJWKHJUDYLW\7KHSUHVHQFHRIDYHUWLFDOUHVWUDLQWPDNHV
URWDWLRQTUHPDLQSRVLWLYH
,QWKLVSDSHUDFRHIILFLHQWRIUHVWLWXWLRQLVDFFRXQWHGIRUWRHVWLPDWHWKHHQHUJ\GLVVLSDWLRQ
7KLVFRHIILFLHQWGHILQHGDVWKHUDWLREHWZHHQDQJXODUYHORFLWLHVDIWHU
T
DQGEHIRUH
T
WKH
JHQHULFLPSDFWWDNHVWKHIROORZLQJIRUP>@
VLQ FRV
V
K
DD
§·§ ·
¨¸¨ ¸
©¹© ¹
7ZREORFNPHFKDQLVP
$ZDOOZLWKDGHIRUPHGVKDSHFRUUHVSRQGLQJWRWKHIRUPDWLRQRISLYRWLQWHUIDFHVDWWKHWRS
WKH ERWWRP DQG DQ LQWHUPHGLDWH KHLJKW LV QRZ FRQVLGHUHG )LJXUH 7KH PDLQ SDUDPHWHUV
WKDWGHVFULEHWKHPHFKDQLVPDUHDQJOHVĮ
DQGĮ
GHILQLQJWKHVOHQGHUQHVVRIWKHWZREORFNV
0
E
DQG0
E
UHSUHVHQWWKHPDVVHVRIWKHEORFNVDQG,
DQG,
WKHLUSRODUVHFRQGPRPHQWVRI
DUHD
4313
0DUFR1DOH$QGUHD&KLR]]L5LFFDUGR/DPERUJKLQL)DELR0LQJKLQL0DUFR5LJROLQDQG$QWRQLR7UDOOL
)LJXUHWZREORFNPHFKDQLVPXQGHUJURXQGPRWLRQ
7KHHTXDWLRQRIPRWLRQFDQQRZEHZULWWHQLQWKHIROORZLQJIRUPWKHLQWHUHVWHGUHDGHULV
UHIHUUHGWR>@IRUPRUHGHWDLOV
FRW
EEEE
EE J
%
,%,%05 &,&05 J$500
$
$0 0 5 X 4
II
DI
ªº
§·
¨¸
«»
©¹
¬¼
7KHFRHIILFLHQWRIUHVWLWXWLRQIRUWKLVPHFKDQLVPGHSHQGLQJRIWKHEORFNVOHQGHUQHVVHVLV
GHILQHGDV>@
WDQ VLQ FRV WDQ
VLQ VLQ
WDQ WDQ WDQ
WDQ
VLQ FRV WDQ
WDQ WDQ
EEE
WE
EE
05 , 05 05
05 , , 05
DDDD
DD
DDD
K
D
DD D
DD
ªº
§·
«»
¨¸
©¹
¬¼
ªº
§·
«»
¨¸
©¹
¬¼
7KLV FRHIILFLHQW GHFUHDVHVZLWK ZDOO VOHQGHUQHVV DQG HOHYDWLRQRIWKHLQWHUPHGLDWH KLQJH
7KHH[SHULPHQWDOHYLGHQFHVKRZVWKDWWKHFRHIILFLHQWRIUHVWLWXWLRQUDQJHVEHWZHHQDQG
RIWKHSUHGLFWHGYDOXH>@
)5$*,/,7<$1$/<6,6
7KHIUDJLOLW\FXUYHLVGHILQHGDVDFRQGLWLRQDOSUREDELOLW\RIIDLOXUH
OQ [
3&,0 [
T
E
§·
)
¨¸
©¹
ZKHUH[LVWKHPHGLDQYDOXHRIWKHVHOHFWHG(QJLQHHULQJ'HPDQG3DUDPHWHU('3ZKLOHșLV
WKHFDSDFLW\UHODWHGZLWKWKHFROODSVHGDPDJHVWDWH&RHIILFLHQWȕLVWKHORJDULWKPLFVWDQGDUG
GHYLDWLRQRIWKHGHPDQGFRQGLWLRQHGRQWKH,QWHQVLW\0HDVXUH,0)UDJLOLW\SDUDPHWHUVPD\
EH HVWLPDWHG IURP DQ ,QFUHPHQWDO'\QDPLF$QDO\VLV,'$RUD0XOWLSOH 6WULSH $QDO\VLV
06$,QWKLVFRQWULEXWLRQWKHVHFRQGDSSURDFKLVFKRVHQ
4314
0DUFR1DOH$QGUHD&KLR]]L5LFFDUGR/DPERUJKLQL)DELR0LQJKLQL0DUFR5LJROLQDQG$QWRQLR7UDOOL
*URXQGPRWLRQVHOHFWLRQ
$VHWRIQDWXUDOJURXQGPRWLRQVIURPWKH,7$&$>@LVXVHG7KHJURXQGPRWLRQVHW
FROOHFWVWKHKRUL]RQWDO FRPSRQHQWVRIDFFHOHUDWLRQWLPHKLVWRULHVUHFRUGHGLQ,WDO\GXULQJ
HDUWKTXDNHHYHQWVRFFXUUHGIURPWR7KHJURXQGPRWLRQVDUHVHOHFWHGZLWKDODUJH
UDQJH RI SHDN JURXQG DFFHOHUDWLRQ 3*$ DQG SHDN JURXQG YHORFLW\ 3*9 7KH LQWHQVLW\
PHDVXUHXVHGIRUWKHIUDJLOLW\FXUYHVLVWKH3*$ZKLFKLVWKHNH\VWURQJPRWLRQSDUDPHWHUIRU
VHLVPLFGHVLJQLQ,WDO\>@
(QJLQHHULQJ'HPDQG3DUDPHWHU
$QDSSURSULDWHFKRLFHRIWKH('3VLVQHFHVVDU\IRUWKHIUDJLOLW\DQDO\VLV7KH('3IRUDQ
RYHUWXUQLQJEORFNPD\EHFKRVHQDVWKHUDWLREHWZHHQEORFNURWDWLRQ
TDQGVOHQGHUQHVVDQJOH
ĮVHH)LJXUH
('3
TĮ
9DOXHVRIWKH('3ODUJHUWKDQ]HURLPSO\WKDWWKHVWUXFWXUHVWDUWVWRURFN:KHQWKH('3
H[FHHGVWKHRYHUWXUQLQJRFFXUV7KLVGHILQLWLRQRIWKHRYHUWXUQLQJFRQGLWLRQLVDVLPSOLILFD
WLRQRQWKHVDIHVLGH,QIDFWDURFNLQJEORFNPLJKWH[KLELWDKLJKHU('3ZLWKRXWRYHUWXUQLQJ
>@
0XOWLSOH6WULSH$QDO\VLV06$
7KLVW\SHRIDQDO\VLVFRQVLVWVRIDVHULHVRIWLPHKLVWRU\DQDO\VHVIRUDVSHFLILHGVHWRI,0
OHYHOV >@ &RPSDUHG ZLWK WKH ,'$ WKH 06$ RIIHUV WKH DGYDQWDJH RI D UHGXFHG FRPSXWD
WLRQDO HIIRUW 7KH PD[LPXP OLNHOLKRRG FULWHULRQ LV WKHQ XVHG WR ILW WKH FRPSXWHG IUDJLOLWLHV
ZLWKVXLWDEOHDQDO\WLFDOIXQFWLRQV)LJXUH
('3
D
E
)LJXUHDH[DPSOHRI06$UHVXOWVEFROODSVHSUREDELOLW\DVDIXQFWLRQRI,0DQGHVWLPDWHGIUDJLOLW\FXUYH
)UDJLOLW\FXUYHV
$VXUYH\RIDQDJJUHJDWHRIEXLOGLQJVLQWKHKLVWRULFFHQWUHRI)HUUDUD,WDO\KDVEHHQSUH
OLPLQDU\FDUULHGRXWWRIRUPD³SRSXODWLRQ´RIPDVRQU\ZDOOV7KHSUREDELOLW\RIRFFXUUHQFH
RIWKHRQHVLGHGURFNLQJDQGWZREORFNPHFKDQLVPLVHVWLPDWHGEDVHGRQSHFXOLDUFKDUDFWHULV
WLFVRIWKHWKHVXUYH\HGEXLOGLQJV7KHFRUUHVSRQGLQJIUDJLOLW\FXUYHVDUHHYDOXDWHG)LJXUH
7KHVHFXUYHVGHVFULEHWKHYXOQHUDELOLW\RIWKHDJJUHJDWHDFFRUGLQJZLWKWKHDQDO\]HGPHFKD
QLVPV,WLVZRUWKQRWLQJWKDWWKHURFNLQJPHFKDQLVPLVPRUHYXOQHUDEOHWKDQWKHWZREORFN
PHFKDQLVP7KLVJUHDWHUYXOQHUDELOLW\UHOLHVXSRQWKHQDWXUHRIWKHURFNLQJPHFKDQLVPZKLFK
KDVDWULJJHUDFFHOHUDWLRQORZHUWKDQWKDWRIWKHWZREORFNVPHFKDQLVP
4315