重慶大學(xué)-結(jié)構(gòu)動(dòng)力學(xué)大作業(yè)

1、 研究生課程考核試卷科目：結(jié)構(gòu)動(dòng)力學(xué)大作業(yè)教師姓名：學(xué)號(hào)專業(yè)：土木工程類別適用于課程論文、提交報(bào)告）劉綱學(xué)術(shù)上課時(shí)間：2016年9月至2016年12月考生成績：卷面成績平時(shí)成績課程綜合成績閱卷評語：閱卷教師（簽名）重慶大學(xué)研究生院制土木工程學(xué)院2016級(jí)碩士研究生考試試題科目名稱：結(jié)構(gòu)動(dòng)力學(xué)考試日期：2016年12月總分：20分1、按規(guī)定設(shè)計(jì)一個(gè)2跨3層鋼筋混凝土平面框架結(jié)構(gòu)（部分要求如附件名單所示；未作規(guī)定部分自定）。根據(jù)所設(shè)計(jì)的結(jié)構(gòu)參數(shù)，求該結(jié)構(gòu)的一致質(zhì)量矩陣、一致剛度矩陣；2、至少采用兩種方法求該框架結(jié)構(gòu)的頻率和振型；3、輸入地震波（地震波要求如附件名單所示），采用時(shí)程分析法，利用有限元

2、軟件或自編程序求出該框架結(jié)構(gòu)各層的線性位移時(shí)程反應(yīng)。要求給出：（1）框架結(jié)構(gòu)圖，并給出一致質(zhì)量矩陣和一致剛度矩陣；（2）寫出兩種方法名稱及對應(yīng)的頻率和振型；（3）輸入地震波的波形圖，計(jì)算所得各樓層位移反應(yīng)時(shí)程圖。第1頁共1頁框架概況框架截面尺寸框架立面圖如圖1.1所示，各跨跨度為L二3900mm，各層建筑層高均為1L二3700mm，對應(yīng)的梁截面分別為200 x400mm2，柱截面均為300 x300mm2。3設(shè)樓層進(jìn)深為L二4200mm，板厚為100mm，頂層板厚取最小值120mm。2b&a苛？013+403bt!Dn20000bBQN?0000beDN?00-*0BbBQM?0000DeDn

3、200f0B圖1.1框架立面圖動(dòng)力自由度框架結(jié)構(gòu)可以理想化為在節(jié)點(diǎn)處相互連接的單元（梁和柱）的集合。設(shè)梁、柱的軸向變形均忽略不計(jì)，只考慮橫向平面位移，則該框架有3平動(dòng)自由度和9角自由度，共12自由度。自由度編號(hào)及梁柱單元編號(hào)如圖1.2所示。1.3力學(xué)參數(shù)計(jì)算梁柱混凝土都采用C30，其彈性模量為E二3.0 x104N/mm212200 x400mm2梁截面慣性矩：I=n=x400mm2梁的單位長度質(zhì)量（按照計(jì)算重力荷載代表值的方法計(jì)算）:x4003mm412300 x300mm2柱截面慣性矩：丁等=型注mm4200 x400mm2梁剛度：EI=3.0 x104x200 x400=3.2x104k

4、N-m2112300 x300mm2柱剛度：EI=3.0 x104x300 x300=2.025x104kN-m2212一二層（考慮樓板恒載及樓面活載作用）：m=（0.2x0.4x2500+4.2x0.1x2500+4.2x200）=2090kg/m1頂層（僅考慮樓板恒載不考慮屋面活載作用）：m=（0.2x0.4x2500+4.2x0.12x2500）=1460kg/m2300 x300mm2柱的單位長度質(zhì)量m=bh=0.3x0.3x2500kg/m=225kg/m3根據(jù)以上計(jì)算結(jié)果，將其列入表中，如下表1.3所示：表1.3梁柱力學(xué)參數(shù)截面尺寸（mm2）“200 x400300 x300力學(xué)參

5、數(shù)截面慣性矩I（mm4）1.067x1096.75x108剛度EI(kN-m2)3.2x1042.025x104單位長度質(zhì)量m(kg/m)一、二層2090頂層1460225一致質(zhì)量矩陣、一致剛度矩陣一致質(zhì)量矩陣在節(jié)點(diǎn)位移作用下框架梁和柱上所引起的變形形狀采用Hermite多項(xiàng)式。因此均布質(zhì)量梁特殊情形中的一致質(zhì)量矩陣為-1565422L13LmL5415613L22LMe42022L13L4L23L213L22L3L24L2計(jì)算梁單元（單位：kg）水平位移自由度產(chǎn)生的質(zhì)量影響系數(shù)m.ii轉(zhuǎn)角自由度產(chǎn)生的質(zhì)量影響系數(shù)mijm=mL=1-1214-45-5420 x4L2=1460 x3.9二56

6、94=m45544201460420 x(3L2)=x4x3.93二824.821460420 x3x3.93=-618.61m=mL=1-1211460 x3.9二56945556=m66=m65420420 x4L2=1460420 x(3L2)=x4x3.93=824.821460420 x3x3.93=618.61m=mL=2-2112090 x3.9二81517778=m88=m87420420 x4L2=2090420 x(3L2)=x4x3.93=1180.732090420 x3x3.93=885.55m=mL=2-2112090 x3.9二81519998=m88=m8942

7、04202090420 x(3L2)=x4x3.93=1180.732090420 x3x3.93=885.55m=mL=3-3112090 x3.9二8151=m10101111420=m10111110420 x4L22090420 x(3L2)=x4x3.93=1180.732090420 x3x3.93=885.55m=mL=3-3112090 x3.9二815111111112=m1212=m1211420420 x4L2=2090420 x(3L2)=x4x3.93=1180.732090420 x3x3.93=885.552.1.2計(jì)算柱單元（單位：kg）質(zhì)量影響系數(shù)m11m12

8、m14m17二m22二m21二m41二m71m24m27m44m47m11m12m15m18m25m28m55m58m11m12m16二x156二225x3.7x156二309.21420420二m42二m72二m77二m74二m22二m21二m51二m81二m52二m82二m88二m85二m22二m21二m61mL_A225x3.733x54=x54=107.04420420mL225x3.7,33x22Lx22x3.7161.354203420mL225x37x(13L)5x(13x3.7)95.344203mL33x(13L)4203mL33x(22L)4203420mL,T225x3.

9、733x4L2x4x3.72108.544203420mL225x3.7、8133x(3L2)x(3x3.72)81.414203420mL225x3.73092133x156x156309.21420420mL一225x3.733x54x54107.04420420mL225x3.7,3x22Lx22x3.7161.354203420mL(225x3.7(34203420mL225x3.7333x(13L)x(13x3.7)95.344203420mL225x3.733x(22L)x(22x3.7)161.354203420mLAT225x3.733x4L2x4x3.72108.544203

10、420mL()225x3.7、8133x(3L2)x(3x3.72)81.414203420mL225x3.73092133x156x156309.21420420mL一225x3.733x54x54107.04420420mL225x3.7,33x22Lx22x3.7161.354203420420225x3.713379534x13x3.7=95.34420225x3.7x(22x3.7)=161.35質(zhì)量影響系數(shù)元mL225x3.7/-小小、2”mmCC33x(13L)x(13x3.7)95.3429924203420mL225x3.7小小、2”mmcC33x(13L)(13x3.7)9

11、5.3426624203420mL225x3.7/-mm33x(22L)x(22x3.7)161.3529924203420mL225x3.7_mm33x4L24x3.72108.5466994203420mL225x3.7/小小、八mmCC33x(3L2)(3x3.72)81.4169964203420柱層柱單號(hào)單m22二m33m3L3X156二225X3.7X156二309.21420420m32m27二m23二m72m210m24m310m77mL225x3.7x54=x54=107.04420420mL225x3.716135=t3x22L=x22x3.7=161.354203420m

12、L225X37二T_3X(13L)二5X(13X3.7)二95.344203420mx(13L)二225X3.7x(13x3.7)二95.344203420 x(22L)二225X3.7x(22x3.7)=161.354203420mL,T225x3.733x4L2=x4x3.72=108.544203420mL(225x3.737、_814133x(3L2)x(3x3.72)81.414203420二m102二m42二m103二m1010m710m22m32m28二m107二m33二m23二m82m211m38mL225x3.73092133x156x156309.21420420mL一22

13、5x3.733x54x54107.04420420mL225x3.7,33x22Lx22x3.7161.354203420mL(225x3.7(1333x(13L)x(13x3.7)95.344203420mL225x3.79533x(13L)x(13x3.7)95.344203420mL225x3.733x(22L)x(22x3.7)161.354203420mLAT225x3.733x4L2x4x3.72108.544203420二m112二m83m311二m113m二m881111mL()225x3.7(337)qim=m=33x(3L2)=x(3x3.72)=81.41q1111q42

14、03420mL225x3.7=33x156=x156=309.21420420mL225x3.7-33x54=x54=107.04420420mL225x3.7,4x22L=x22x3.7=161.354203420mL(225x3.7(95=33x(13L)=x(13x3.7)=95.344203420mL225x3.79533x(13L)=x(13x3.7)=95.344203420m22m23m29二m33二m32二m92m212m二m122二mm=m=ml33八420(22L)3=225x3.7x(22x3.7)=161.35420312123mL225x3.7m=m=33x4L=-x

15、4x3.72=108.549912124203420mL225x3.7m=m=33x(3L2)=x(3x3.72)81.419121294203420層柱單質(zhì)量影響系數(shù)號(hào)兀ml225x3.7m33x156=x156309.213342042013ml225x3.7m=moo33x22L=x22x3.7161.353101034203420mL225x3.7maa-x4Lx4x3.72108.5410104203420mL225x3.7m33x156=x156309.2133420420一ml225x3.7m=mcc一33x22L=-x22x3.7161.35層3111134203420mL22

16、5x3.7mcc33x4L-二x4x3.72108.5411114203420mL225x3.7m33x156=x156309.213342042015mL225x3.7m=maa33x22L=x22x3.7161.353121234203420mL225x3.7m=33-x4L=x4x3.72108.541212420342039932.1.3計(jì)算整體坐標(biāo)系的mij根據(jù)m=m（m）+m（n）+m（卩）+.可矢口ijijijij第一行：m=2x5694+3x309.21=12315.63kgi-im=3x107.4=321.12kg1-2m=0kgm=m=m=161.35kgTOC o 1-5

17、 h z1-31-41-51-6m=m=-95.34kgm=m=m=m=0kg；71-81-91-101-111-12第二行：m=2x8151+6x309.21=18157.26kg2m=3x107.04=321.12kg2-3m=m=m=95.34kgm=m=m=161.352-42-52-62-72-82-9m=-95.342-10m=m=02-112-12第三行：m=2x8151+6x309.21=18157.26kg3-3m=m=m=0kgm3-43-53-63-7m=m=m=0103-113-12第四行：m=824.82+108.54=933.36kg4m=-618.61kgm=0k

18、g4-54-6m=m=m=m=m4-84-94-104-114-12第五行：=m=m=95.34kg3-93-8m4-7=0kg；=-81.41kgm=824.82x2+108.54=1758.18kg5m=-618.61kgm=0kgTOC o 1-5 h z5-65-7m=-81.41kg5-8m=m=m=m=0kg；95-105-115-12第六行：m=824.82+108.54=933.36kg6m=0m=0kg6-76-8m=-81.41kgm=m=m=0kg96-106-116-12第七行：m=1180.73+108.54x2=1397.81kgm=-885.55kg77-8m=-

19、81.41kgm=m=m=0kg；7-107-97-117-12第八行：m二1180.73x2+108.54x2二2578.54kg8m=885.55kgm二0kg98-10m=-81.41kgm二0kg8-118-12第九行：m二1180.73+1108.54x2二1397.81kg9m二m二0kgm=81.41kg；TOC o 1-5 h z109-119-12第十行：m二1180.73+108.54x2二1397.81kg10m=885.55kgm二0kg1110-12第十一行：m二1180.73x2+108.54x2二2578.54kg11m=885.55kg12第十二行：m二1180

20、.73+108.54x2二1397.81kg120000161.3595.340095.340000000000081.4100081.41000885.55081.4101397.810081.411397.81885.5502578.54885.551397.8112315.63321.120161.35161.35161.3595.3495.3418157.26321.1295.3495.3495.34161.35161.3518157.2600095.3495.34933.36618.61081.4101758.18618.61081.41一致質(zhì)量矩陣M是對稱矩陣，故只寫出上三角（單位

21、：kg）933.3600M=1397.81-885.552578.54一致剛度矩陣在節(jié)點(diǎn)位移作用下框架梁和柱上所引起的變形形狀采用Hermite多項(xiàng)式。因此，等截面梁的一致剛度矩陣為：663L3L663L3L3L3L2L2L23L3LL22L22EIL32.2.1計(jì)算梁單元(單位：kN-m2)層梁單號(hào)元相應(yīng)剛度系數(shù)(L1=3.9m)k=k44552EI2x3.2x1041x2L=x2=3.2821x104L313.91k=k45542EI2x3.2x1051xL=1.6410 x104L313.91k55=k662EI2x3.2x1041x2L=x2=3.2821x104L313.91k65=

22、k562EI2x3.2x1051xL=1.6410 x104L313.91k77=k882EI2x3.2x1041x2L=x2=3.2821x104L313.91k78=k872EI2x3.2x1051xL=1.6410 x104L313.91k88=k992EI2x3.2x1041x2L=x2=3.2821x104L313.91k89=k982EI2x3.2x105ixL=1.6410 x104L3113.9k1010=k11112EIix2LL112232x14x2=3.2821x1043.92EI2x3.2x104k=k=1x2L-x2-3.2821x10411-1112-12L313.

23、912EI2x3.2x105k=k-1xL-=1.6410 x10411-1212-11L313.9k=k10-1111-102EI2x3.2x1051xL=L313.911=1.6410 x104柱單元層號(hào)相應(yīng)剛度系數(shù)（L二3加）2.2.2計(jì)算柱單元（單位：kN-m2）3.73k=k=竺x1-22-1k二k二k1-44-11-7k2-4二k4-2L337-1=k=kk4-42-7二k7-7k4-7(-6)二-12x2.025x104二-0.4797x1043.732EI6x2.025x1043x3L=0.8875x104L3337-2L33二k7-4k二k1-1k二k1-22-13.72込x

24、(-3L)=-6x2325x104=-0.8875x10432EI3x2LL3332EI3xLL332EI二3x6二2-2L333.724x彳025x104二2.1892x1043.72X2曲14二1.0946x1043.712xWO4二0.4797x1043.73竺x(-6)=-12x2025x104=-0.4797x104L333.73k二k二k二k5-11-88-11-52EI6x2.025x1043x3L=0.8875x104L3333.72k二k2-55-22EI-6x2.025x1043.72二k二k二3x(3L)二=0.8875x10488-2L3333 柱單元層號(hào)k5-5=k8

25、-8k5-8=k8-52EI3x2LL3332EI3xLL3332EIk=k1-12-2L33k=k1-22-1k=k=k1-66-11-9k=k2-66-24x225x14=3.1892x1043.72x2.25x14=1.0946x1043.7x6=12x2025x104=0.4797x1043.732EI3x(-6)=-12x2.025x104=-0.4797x104L333.73=k9-1=k=kk6-62-9=k9-9k6-9=k9-6k二k2-23-3k二k2-33-22EI6x2.025x1043x3L=0.8875x104L3339-2L333.72竺x(-3L)=-6x2.0

26、25x104=-0.8875x10432EI3x2LL3332EI3xLL3333.724x225x14=2.1892x1043.72x225x104=1.0946x1043.7相應(yīng)剛度系數(shù)（l二3.m）2EI,12x2.025x1043x6二L33.733二0.4797x1042EI-12x2.025x1043x(-6)二L33.733=-0.4797x104k=k=k=k2-77-22-1010-22EI6x2.025x1043x3L=L33.723=0.8875x104k=k=k=k3-77-33-1010-32EI-6x2.025x1043x(-3L)=L333.723=-0.8875

27、x1042EIk=k=3x2L7-710-10L334x2.025x10437=2.1892x104 柱單元層號(hào)k二k7-1010-7k二k3-3k2-32-2二k3-2k二k2-88-2二k2-11k3-82EI3XLL3332EI3x6二L332EI3XL33二k11-2=k=k=kk2-98-33-11k8-8二k11-11k8-112X2.025X104二1.0946x1043.712X2025X104二0.4797x1043.73(-6)=-12X2.025X104=-0.4797x1043.732EI6X2.025X1043x3L二二0.8875x104L33311-3L33二k1

28、1-8k二k3-3k2-32-2二k3-2二k9-2二k2-123.722EI3x(-3L)=-6X225X104=-0.8875x10432EI3x2LL332EI3XLL3332EI3x6二L332EI3XL33二k12-23.724X2025X104二2.1892X1043.72X2.025X104二1.0946x1043.712X2025X104二0.4797x1043.73(-6)=-12X2.025X104=-0.4797x1043.732EI6x2.025x1043x3L二二0.8875x104L3333.72k二k3-99-3=k=kk9-93-12二k12-12k9-1212

29、-3L33二k12-9竺x(-3L)6X225X104=-0.8875x10432EI3x2LL3332EI3XLL3333.724X2025二2.1892X1043.72X2.025X104二1.0946X1043.7相應(yīng)剛度系數(shù)（l二3.m）層1415k3-3k3-10竺x6二12X2.025X104二0.4797X104L333.73二k10-3k10-102EIk3-3k3-112EI6X2.025X1043x3L=0.8875x104L3433.724X2.025X104x2L二二2.1892X104L3333.7込X6二12X2.025X104二0.4797X104L333.73二

30、k11-32EI3L33x3L=6X2.025X104二0.8875x10433.72k11-11k3-3k3-122EI3XL32L234X沁二2.1892X1043.7竺x6二12X2.025X104二0.4797X104L333.73二k12-32EI6X2.025X1043x3L二二0.8875X104L3333.72k12-122EI4X2.025X104x2L二二2.1892X104L3333.72.2.3計(jì)算整體坐標(biāo)系的kij八八八ydi根據(jù)k=k（m）+k（n）+k（p）+.可知.（單位：kNm2）ijijijij:（）第一行：k=3X0.4797X104=1.4391X104

31、1k=3k(10)=3x(-0.4797x104)=-1.4391x104TOC o 1-5 h z1-21-2k=0k=k=k=k=k=k=0.8875X10431-41-51-61-71-81-9k=k=k=01-101-111-12第二行：k=3X0.4797X104=1.4391X1042k=3X(-0.4797X104)=-1.4391X1042-3=k=-0.8875X104k=k2-42-52-6k=k=k=0.8875X104k=k=k=02-72-82-92-102-112-12第三行：k=6x0.4797x104=2.8782x1043k=k=k=0k=k=k=0.8875

32、x104TOC o 1-5 h z43-53-63-73-83-9k=k=k=0.8875x104；10311312第四行：k=3.2821x104+2.1892x104=5.4713x1044k=1.6410 x104k=1.0946x104547k=k=k=k=k=k=0；64849410411412第五行：k=3.2821x104+2.1892x104=5.4713x1045k=1.0946x104k=1.6410 x104658k=k=k=k=k=0;759510511512第六行：k=3.2821x104+2.1892x104=5.4713x1046k=1.0946x1049k=k=

33、k=k=k=0;768610611612第七行：k=3.2821x104+2x2.1892x104=7.66054k=1.6410 x104778k=1.0946x104k=k=k=0；71079711712第八行：k=2x3.2821x104+2x2.1892x104=10.9426x10488k=1.6410 x104k=089810k=1.0946x104811k=0；812第九行：TOC o 1-5 h zk=3.2821x104+2x2.1892x104=7.6605x1049k=k=010911k=1.0946x104；12第十行：k=3.2821x104+2x2.1892x104

34、=7.6605x104k=1.6410 x104；101011k=012第十一行：k=2x3.2821x104+2x2.1892x104=10.9426x10411k=1.6410 x10412第十二行：k=3.2821x104+2x2.1892x104=7.6605x10412一致質(zhì)量矩陣K是對稱矩陣，故只寫出上三角（單位：kN/m）1.4391-1.439100.88750.88750.88750.88750.88750.8875000、1.4391-1.4391-0.8875-0.8875-0.88750.88750.88750.8875000.2.8782000-0.8875-0.88

35、75-0.88750.88750.88750.8875.5.47131.641001.094600000.5.47131.094601.64100005.4713001.0946000.0.7.66051.641001.094600010.94261.641001.09467.6605000.1.0946.7.66051.64100.x10410.94261.64107.6605.頻率與振型簡化的質(zhì)量矩陣和剛度矩陣的計(jì)算將結(jié)構(gòu)質(zhì)量集中到各層，此結(jié)構(gòu)用層剪切模型簡化為框架等效多質(zhì)點(diǎn)體系，如圖3.1所示。lLakikziiijki圖3.1框架等效多質(zhì)點(diǎn)體系計(jì)算簡化的質(zhì)量矩陣根據(jù)簡化的方式，如圖3.

36、1所示可知m二225x3.7x3x0.5+1460 x3.9x2二12636.75kg1m=225x3.7x3+2090 x3.9x2=18799.5kg2m=225x3.7x3+2090 x3.9x2=18799.5kg3由于結(jié)構(gòu)的質(zhì)量集中到各層，因此結(jié)構(gòu)的質(zhì)量矩陣為對角矩陣。質(zhì)量矩陣如下所示：12636.7500)00、M二018799.50kg二01.487701.2636.75x104kg0018799.5丿001.4877丿3.1.2計(jì)算簡化的剛度矩陣(1)利用“D值法”計(jì)算柱的側(cè)向剛度。各梁、柱構(gòu)件的線剛度計(jì)算如下，其中在求梁截面的慣性矩是考慮現(xiàn)澆板的作用時(shí)，取I=21(1為不考慮

37、樓板翼緣作用的梁截面慣性矩)。00框架梁的線剛度：2EIi二-1bL12x3.2x10439二1.6410 x104kN-m框架柱線剛度：EI2.025x104i二20.5473x104kN-mcL3.73二三層柱的D值為：2i1.6410 x104邊柱：K=f二二2.998，a2i0.5473x104cc二Kb二060則D二a竺二0.60 x12x0.5473x104二0.2878x104kN/m邊ch2j3.722i+2i2x1.6410 x104中柱：K二Tb二二5.997，2ic0.5473x104a二Kb二0.7512icch2j二0.75x12x5473x1043.72二0.359

38、8x104kN/m底層柱的D值為：邊柱：i1.6000 x104K二-bic0.5473x104_2.998ac中柱：則D1邊12i12x0.5473x104=ac二0.636x二0.3052x104kN-mch2j3.72少i+i2x1.6410 x104K=-bb二二5.997ic0.5473x104則D1中12i二acch2j=0.7646x12x.5473x1043.720.3668x104kN/m從而得到各層的側(cè)向剛度為:k=2(D+D)=2x(0.3052+0.3668)x104=1.3440 x104kN/m31邊1中k=k=2(D+D)=2x(0.2878+0.3598)x10

39、4=1.2952x104kN/m21邊中2)計(jì)算剛度矩陣剛度矩陣計(jì)算如圖3.2所示：因此XXXVsXX圖3.2剛度計(jì)算1.2952-1.29520、1-1K=-1.29522.5904-1.2952x104kN/m=-12,0-1.29522.6392丿,0-10、-1x1.2952x107N/m2.0376丿頻率和振型計(jì)算行列式方程法結(jié)構(gòu)的運(yùn)動(dòng)微分方程為：mK3+IcKJ+kh=p(t) 1 其中,m為結(jié)構(gòu)質(zhì)量矩陣;k為結(jié)構(gòu)剛度矩陣;c為結(jié)構(gòu)阻尼矩陣；v、v、v分別為結(jié)構(gòu)加速度、速度和位移;；p(t)為作用荷載。對于無阻尼自由振動(dòng),則矩陣方程(1)式可化為：(Ikw2(M血二(2)實(shí)際上：一

40、個(gè)結(jié)構(gòu)體系的振動(dòng)分析就是矩陣代數(shù)求特征值的問題,即求特征值和特征向量;而特征值就是頻率的平方項(xiàng),特征向量就是振型形式。引入符號(hào)：則有:m102k1仃.263675x104)O2(1.2952x107丿1.2636751.2952X10-3Io2(1.295211.263675x103n丿(1n11x1.2952x107kN/m=0Ko2mL|121.4877n2.03761.4877n丿解行列式得：n33.75432+3.530血0.4982=0解得上式三根為：n=0.16468,n=1.22458,1解得：232(168.788(12.歹|1I=|1255.130II|1I=|35.4II|

41、o2I2|oI2|o2I.2382.633.|oI、48.8,l3丿7l3丿i丿n=2.32464。31求主振型：0_Y一01i1Y02i2.03761.4877n一iY3i0121.4877ni1(Ko2M)Y(i)=0iL一1ni1.2952x107x1L0解得振型為：111.324640.93234二0.835320.22458L0.465981.040733.2.2Stodola法1)三層框架的第一振型分析根據(jù)體系的質(zhì)量和剛度矩陣計(jì)算結(jié)構(gòu)的動(dòng)力矩陣D:D=fm=km=占x2.28821.51610.744050.74405111.263675000.744051101.8799500.

42、744051L001.879951.51611.51610.74405x2.8915104x=1.91591030.94022.85022.85021.39881.39881.39881.3988按式v二Dv(o)進(jìn)行迭代。假設(shè)本題目中的三層框架的第一振型為*二，則求第一振型的迭代過程如下:11032.89151.91590.94022.85022.85021.39881.39881.398811.3988(1丿v(o)1V1(7.1405=6.1649、3.7378v(1)11.00000.86340.5235v16.08465.10902.8802v(2)11.00000.83970.47

43、34V(3)15.94704.97142.7770v(3)11.00000.83600.4670V(4)V115.927511.00004.95190.83542.76280.4661V(5)15.92451.00004.94890.83532.76070.4660所得最終的形狀如v14)所示對比行列式方程法所求結(jié)果已經(jīng)精確到小數(shù)點(diǎn)后三位。V(s_1)根據(jù)32=仝1求第一振型頻率可得,1V(s)k1V(4)32二+11V(5)111035.9245二168.793廣1299(2)三層框架的第二振型分析第一振型淘汰矩陣的形式如下(QtM)-i(QtM)S二1s1r1Li這個(gè)結(jié)構(gòu)的0t=11.00

44、0000.83530.4660，M是質(zhì)量矩陣的第一列：1s233233 32 Mt二12636.7500。M表示質(zhì)量矩陣剩下的各列：sr_00M=18799.50r018799.5那么(0tM)-i(QtM)=1.24270.6932，故第一振型的淘汰矩陣為s1r1.24270.6932S=1.00000101.0000第二振型的動(dòng)力矩陣是0.74310.60561D=DS=一x0.41180.0707TOC o 1-5 h z11030.23040.7471以下計(jì)算第二振型的方法與就算第一振型方法相同，采用同樣的格式。因?yàn)轫攲游灰苬由正交條件控制，顯然這里的試探向量v(0)中只需要包含vt=

45、vv。直到v的解122r2232r收斂時(shí)，才需要計(jì)算v12值。D2v(0)2v2v(1)2v2v(2)2v21X/0.74310.6056-11-1030.41180.070710.48250.49360.27400.31830.20180.23040.747110.97751.00000.860811.00000.8204v(3)vv(4)v(5)v(5)v(6)v(6)v(7)22222222x0.24600.17200.21400.15880.19940.15280.19270.15001.00000.80381.00000.79641.00000.79301.00000.7915v(7)v(8)v(8)2220.74640.94391.0000 x0.18950.14870.1880-0.19921.00000.79081.0000-1.059所得最終的形狀如v所示，對比行列式方程法所求結(jié)果已經(jīng)精確到小數(shù)點(diǎn)后二位，精2TOC o 1-5 h z確度較第一振型差。v(s1)根據(jù)2=W求第二振型頻率可得：1v(s)v(7)1000o2=32=1264.542v(8)0.790832o