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时间:2019-08-01
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1、同济大学DynamicsofStructuresProjectMiguelAngelHidalgoCalvoID:1375464th7January2014DynamicsofStructuresProjectGeneralStatementOurproblemistheclassicalmulti-storiedbuildingbutwithalead-corerubber-bearingisolationsystemplacedinthebasement.Inadditionwehavetoconsidereran
2、on-linearrestoringforceinoursystemstiffnessmatrix.??̈+??̇+??=?(?)HystereticcomponentIfweconsiderthatthetimederivativeofthehystereticcomponentisonlytimedependentwiththetimederivativeofthebasementdisplacementwecanconcludethefollowingrelation:?̇?=???−1[???̇?−??
3、?̇?
4、
5、
6、??
7、??−1??−???̇?
8、??
9、??]??≈???−1[????−??
10、??
11、
12、??
13、??−1??−????
14、??
15、??]Substitutingtheparametersvalues:??=20[??−2
16、??
17、
18、??
19、??−??
20、??
21、2]=??(??)Inordertosolvetheimplicitrelationthefollowingstaticinitialconditionsaresupposed:??(0)=0?????(0)=0Bouc-WenmodelOnceconsideredtheh
22、ystereticcomponentapproximationwehavedeterminedthestiffnessrestoringforceofthelead-corerubber-bearing.Fortheinitialconditionsourstiffnessmustbekb.???=??????+(1−??)???????Substitutingtheparametersvalues:???=0.6∗180.5∗??+(1−0.6)∗180.5∗0.05?????=108.3??+3.61??Basem
23、entmodelWhenevertheearthquakemotionstartsthestiffnessofourbasementbecomesnon-linearandwehavetouseatime-stepmethodfornon-linearsystems.m?̈?+??̇?+????=0????m?̈?+??̇?+??=−??̈?(?)???SystemMatricesThesystemmassanddampingmatriceshavetobemodelledforafive-storiedbuildin
24、g,whichmeansa5x5matrixwithanon-linearcomponentduetotheBouc-Wenmodel.Ontheotherhandwehavethenon-linearstiffnessmatrixthatwillbeachievedusingtheNewmark’smethod.?100004500000⎡⎤⎡⎤⎢0?2000⎥⎢0345.6000⎥?=⎢00?300⎥=⎢00345.600⎥⎢000?40⎥⎢000345.60⎥⎣0000?5⎦⎣0000345.6⎦?1+?2−?2
25、000⎡−?2?2+?3−?300⎤?=⎢0−?3?+?−?40⎥=⎢34⎥⎢00−?4?4+?5−?5⎥⎣000−?5?5⎦26.17+490−490000⎡⎤−490490+467−46700⎢⎥=⎢0−467467+410−4100⎥=⎢00−410410+386−386⎥⎣000−386386⎦516.17−490000⎡⎤−490957−46700⎢⎥=⎢0−467877−4100⎥⎢00−410796−386⎥⎣000−386386⎦?1+?2−?2000⎡⎤⎢−?2?2+?3−?300⎥?=⎢0−?3?3
26、+?4−?40⎥=⎢00−?4?4+?5−?5⎥⎣000−?5?5⎦?1+340.4−340.4000⎡⎤−340.4340.4+325.7−325.700⎢⎥=⎢0−325.7325.7+284.9−284.90⎥=⎢00−284.9284.9+268.6−268.6⎥⎣000−268.6268.6⎦?1+340.4−340.4
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