克拉夫結(jié)構(gòu)動(dòng)力學(xué)習(xí)題復(fù)習(xí)資料匯總

1、第二章自由振動(dòng)分析2-1(a)由例2因此max(t)其中k=0、1、(KTd)2TD=0.64sec 如果 很小，Td=T22 200kipsk ()2 J 49.9kips/in0.64sec 386in/seck 50kips/in(b)Vn 1V121.2ln 一 0.333 0.860.05290.33320.0530(a)Td .149.922 50kips / in (c)c2m4-gt gTd .1W 2g 2 g40.0529 200kipsg g：20.64sec .1 0.05292 386in /sec0.539kips sec/inT=Tdc 0.538kips sec

2、/inc 0.54kips sec/in4.47 (1/sec)40gv(0) v(0)sin Dtv(0) cosDtg(t)gv(0)v(0)sinDtgv(0) v(0)v(0) cosDtg(t)gv(0) cosgv(0)c2m(a) c=0v(t 1)gv(t 1)v(1)Dt(b)c=2.8g(t)g(t)c2(2)(4.47)gv(0)cosgv(0)cos0.0559c5.6 .八sin 4.47 0.7cos4.474.475.6cos 4.47 4.47(0.7)sin 4.47g1.4in , v(1) 1.7in /sec0.0559(2.8) 0.157D 4.47

3、 1 0.1572 4.41 (1/sec)(t 1) e (0.157)(4.41)DtDt2D2 v(0) singv(0)gv(0)1.38in1.69in / secDtv(0)v(0)sin-sinDtDDt5.6 0.7(0.157)(4.47) sin4.41 0.7cos4.414.41(t 1)0.764ing(t 1)(0.157)(4.41)e5.6cos 4.410.157(5.6) 4.41(0.7),1 0.1572sin 4.41g(t 1) 1.10in / secgv(1)0.76in ,v(1) 1.1in / sec第三章諧振荷載反應(yīng)3-11根據(jù)公式有7

4、sinwt sin wt120.8w 1.25wR t 2.778 sin wt 0.8sin1.25 wt將一t以80°為增量計(jì)算R(t)并繪制曲線如下:080°160° 240°320°400°480 °560°640°720°800°R(t) 00.5471.71-0.481 -3.214 0.3574.33-0.19 -4.92404.924R (t)II、 xIi/ILa:a at 口某DSi0 M。7(tyhi0班/ /3-2解：由題意得:m 2kips s2 . ink

5、20kips/in ,苗0) v(0) 0 , wk 20.w : 3.162 rad secWt 8(a) c 0R t sin wt wt coswt 2將wt 8代入上式得：R(t) 412.566(b) c 0.5k s/incccc2mw0.52 2 3.1620.0395expwt 1 coswtexp wt sin wt將wt 8代入上式得：R(t) 7.967(c) c 2.0k s in2.0cc 2mw 2 2 3.1620.158wt 1 coswtexp wt sin wt_1R t exp2將wt 8代入上式得：R(t) 3.1053-3解：(a)：依據(jù)共振條件可知：

6、-V w w .m1000.08400038610.983rad secL 2wL 10.983 36由 T 得：V 62.960ft/sV w22(b)：21212axvgo21220.4Vgo1.2in代入公式可得：vmax 1.921in(c):V 45min h 66 ft s2 V 266亡 11.513rad.sec11.5131.04810.9830.4代入數(shù)據(jù)得t vmaxvgo12=1.855in3-4解：按照實(shí)際情況，當(dāng)設(shè)計(jì)一個(gè)隔振系統(tǒng)時(shí),將使其在高于臨界頻率比TR又因?yàn)?TRtvmax0.005vgo0.03在這種情況下，隔振體系可能有小的阻尼。對(duì)于小阻尼聯(lián)立求的:201

7、25.6 rad1, sec又因?yàn)?wkwmwkg W聯(lián)立得:一 一2 一125.62 800386 74.670 kips, inJa下運(yùn)行,TR又因?yàn)?TRtvmax50vgo700聯(lián)立求的:151275.36 rad . sec又因?yàn)?聯(lián)立得:W2W75.362 6500386 156.376 kips, in解：按照實(shí)際情況，當(dāng)設(shè)計(jì)一個(gè)隔振系統(tǒng)時(shí)，將使其在高于臨界頻率比 在這種情況下，隔振體系可能有小的阻尼。對(duì)于小阻尼3-6(a)由圖 3-17 有，k f smax， 則f 390lbf k3x2600lbf /in0.15in(b)由方程3-66有eqED 2 ,由圖 3-17 有

8、Es 1k 22 k2eqEd4 Es26lbf in4 (29lbf in)0.0713因?yàn)閏 -一，所以2meq恐又因?yàn)閑q ° ED2 2,故2 mEdZZ-22612f in2 36.78lbf rad/(s in)10rad /s(0.15in)(c)由方程3-78有0.0713 0.1426 14.2%3-7(a)公式同題3.6(b)eqEd4 Es26lbf in 0.0713 4 (29lbf in)(b)公式同題3.6(c)Ed22612f in2 18.391bf rad/(sin)20rad /s(0.15in)22 0.0713 0.1426 14.2%(c)

9、通過(guò)題3.6與題3.7的比較可知，與 無(wú)關(guān)，故滯變阻尼機(jī)理更合理。3-8(原版英文書(shū)中為求ed的值)由方程3-66有Ed eq 2 k 2,當(dāng)k與 不變時(shí)，若eqeq( 一),則Ed Ed),由題3.7可知Ed Ed(一)第五章對(duì)沖擊荷載的反應(yīng)5-1解:1000 38660025.36 rad/sec2t10.15T=0.248 sec - 0.605 0.5T 0.24820.94 rad/sect10.1520.94*2= =0.826 t =0.136 sec25.3620.94 1 25.36/20.94Po 1*vmax2 (sin tk 1(b)-*5001sin t )2 sin

10、(20.94 0.136)0.8489 infS,max1000 1 (0.826)2kvmax 1000 0.8489 848.9 1b又上 0.605Vmax 色 D 0.85 inTk5-2解：設(shè)無(wú)阻尼(a)m般 kv p(t)P0(t/ti)0< t t1(1)Vc Acos t Bsin tVp Et F帶入(1)得：k(Et F) p0 - F 0 E Rt1kt1vpPo tk t1V=Vc VpAcos t Bsin t -p0- k t1V(0) B3 0 B -旦kt1k t1v(t) §(； -y sin t)k t1 t1當(dāng)t t1v(t)p0* 2.

11、2 t1sin sin(t t1k t121(b)tt1 :V(t) E 1 cos t kt12P0 . 2t1-sin 一 kt12sin 0 n n 0, 1, 222RmaxVmaxp0/k1 . 32 、sin(匕)3t13金o5OcoIO曜o(hù) gEu 6 coso<ex 乂u6H-»ooE飛oCXIu 萬(wàn)9 6Clu aCXIs4u aH-»XosCD>H-»CXI百太£出H-»(N1 H-»X EX|看1 H-»XcCDl | C|8(ZOzs解:上0.15，查表得：D=0.5 工fS,maxVma

12、xDp0D 0.395 4015.8（b）Vmaxt10 P（t）dt(2P0t1） P0L2kP。2k2 一0.15T T0.353,maxVmaxk 0.353207.06 k5-5解:Vmax0 P（t）dtt0 P（t）dtt10 P（t）dt（P0 4d 2 P2 4 P3 3P4）Vmax.40 4=0.395,maxvmaxk=0.395 40 15.8 kMmaxmax 150 15.8 2370,1 maxk ft第六章6-1Solution:歸 2,m(a)簡(jiǎn)單求和tN(1)P(N)(2)Sin(co tN) (3)Cos( cM)(4)Y (N-1)(5)An/F(6)Y

13、 (N-1)(7)Bn/F(8)(9)(10)(11)(12)(13)0000.001.000.000.000.000.000.000.000.000.000.0010.1500.590.8140.4540.4529.4029.4023.7823.780.000.000.0020.286.60.950.3126.7667.2182.36111.7663.9234.5329.381.8718.4630.31000.95-0.31-30.9036.3195.10206.8634.53-63.9298.456.2761.8640.486.60.59-0.81-70.06-33.7550.92257.

14、78-19.85-208.54188.7012.01118.5650.5500.00-1.00-50.00-83.750.00257.780.00-257.78257.7816.41161.9660.60-0.59-0.810.00-83.750.00257.7849.25-208.54257.7916.41161.97F 010.06366in/lb0.1seck 2lb/inm0.25 21(5)(2)(4)(11)(9)(10)(7) (2)(3)(12)F(11)v(t)(9) (6)(3)(13)K(12)fs(t)(10) (8) (4)(b)梯形法則)P(N) (2)Sin(co

15、 tN) (3)COS( 3Nt) (4)(5)? An/F(6)An/F(7)(8)?Bn/F(9)Bn/F (10)(11)(00.001.000.000.000.000.000.0001500.590.8140.4540.4540.4529.4029.4029.400.000286.60.950.3126.7667.21107.6682.36111.76141.1658.77131000.95-0.31-30.90-4.14103.5295.10177.46318.61196.906486.60.59-0.81-70.06-100.962.5650.92146.02464.63377.3

16、9125500.00-1.00-50.00-120.06-117.500.0050.92515.55515.551660-0.59-0.810.00-50.00-167.500.000.00515.55515.57160 10.1sec0.1 0.03183n/lb0.25 22k2lb/in(5) (2) (4)(2) (3)(11) (7) 3- (10) 4(12) F (11) v(t)(13) K (12) fs(t)P(N)(2)Sin(wtN)(3)Cos( 3N)(4)M(5)(6)? An/F(7)An/F(8)(9)?Bn/F (10)Bn/F(11)(12)00.001.

17、0010.000.000.000.000.00500.590.814161.80188.56117.60199.9686.60.950.31126.76188.5682.36199.96117.531000.95-0.314-123.60-166.90380.40513.6886.60.59-0.811-70.0621.6650.92713.63590.07500.00-1.004-200.00-270.060.0050.920-0.59-0.8110.00-248.400.00764.55764.58(c)Simpson 法則0.1F0.02122in/lb0.1sec0.25 23k 2l

18、b/in(6) (2) (4) (5)(2) (3) (5)(12) (8) 3- (11) 4(13) F (12) v(t)(14) K (13)fs(t)6-2Solution:30rad /s2T 0.209s0.005,F 0.000277ft / kipsm 3 30 2tN(1)P(N)(2)Sin(co tN) (3)Cos( 3Nt)(4)y(N)(5)y(N-1)(6)An-1 /F(7)An/F(8)y(N)(9)y(N- 1)(10)Bn-1/F(11)Bn/F(12)(13)(14)(15)0000.0001.0000.0010.00519.320.1490.9891

19、9.110.000.0019.112.880.000.002.880.000.00000.0020.0138.640.2960.95536.9019.1119.1175.1211.442.882.8817.195.810.00020.4430.01557.960.4350.90052.1636.9075.12164.1825.2111.4417.1953.8422.960.00061.7240.0277.280.5650.82563.7652.16164.18280.1043.6625.2153.84122.7257.010.00164.2850.02596.60.6820.73270.716

20、3.76280.10414.5765.8843.66122.72232.27112.720.00318.4560.0377.280.7830.62248.0770.71414.57533.3560.5165.88232.27358.66194.530.005414s70.03557.960.8670.49828.8648.07533.35610.2850.2560.51358.66469.42295.340.008222.180.0438.640.9320.36213.9928.86610.28653.1336.0150.25469.42555.68407.560.011330590.0451

21、9.320.9760.2194.2313.99653.13671.3518.8636.01555.68610.55521.530.014539.1100.0500.9970.0710.004.23671.35675.580.0018.86610.55629.41629.050.017547.1(5)(4)(14)F (13)v(t)(3)(15)K (14)fs(t)(13)(8)3- (12)46-3Solution:=5%=0.05K 2700kips / ft2Mult exp( t) 0.99250.005,F 0.000277ft / kipsm 3 30 2P(N)Sin(wN)

22、(3)Cos( 9 N) (4)(5)(5)+A(6)M*(6)(7)A(8)(9)(9)+B(10)M*(9)(11)B(12)(13)00.0001.0000.009.320.1490.98919.1138.2237.9319.112.885.765.712.880.008.640.2960.95536.90112.02111.1874.6011.4428.6328.4217.195.677.960.4350.90052.16216.34214.72164.1825.2179.0678.4653.8422.967.280.5650.82563.76343.86341.28280.1043.

23、66166.38165.14122.7257.0196.60.6820.73270.71485.28481.64404.5765.88298.15295.91232.27105.907.280.7830.62248.07581.42577.06525.1060.51419.17416.02358.66188.077.960.8670.49828.86639.14634.35597.4150.25519.67515.77469.42284.188.640.9320.36213.99667.12662.12635.3436.01591.69587.26547.9393.809.320.9760.2

24、194.23675.58670.51648.7018.86629.41624.69594.4502.9600.9970.0710.00648.700.00594.4604.55(5) (2)(4)(9) (2)(13) (8)3-(12) 4(14) F(13)v(t)(15) K(14)fs(t)6-4Solution:6.325rad /s_ c 2m0.42 0.2 6.3250.158exp( 2t) exp(-2 0.158 6.325 0.12) 0.7874exp( t) 4 exp(- 0.158 6.325 0.12) 3.5480.120.2 6.325 33.162 10

25、-2 ft/kipsP(N)(2)Sing tN) (3)Cos( 3N)(4)(5)M(6)(5)+A(7)(8)A(9)(10)(10)+B(11)(12)B(13)00100.787000000010.6880.7260.7263.5482.5760.6582.44140.9990.0530.2120.78732.3612.7883.99610.4338.2110.43790.751-0.649-5.0413.548-20.7246.84324.390.105-0.9919.9460.78736.25528.53327.3090.34534.40127.07433.45660.6080.

26、794-4.7643.548-16.902-3.648-12.94300.9870.1500.787-45.436014.13(5) (2) (4)(8) (6) (5)(10) (2) (3)(12) (11) (10)(14) (9) (3)- (13) (4)(15) F (14) v(t)第七章7-1?由題意可知：h=0.12s 等效剛度： ？(t)=K(t)+3?+6?T=101.336?(16) =A P+?(+3?+C3 ?(?(?)=A P+11.2 ?(+0)624 ?A ?(吊)A v(t)-3 ?(?)?(t)25 A v-3 ?(?,06 ?加速度：？?醫(yī)P(t)-C

27、?(幽(t)1 _02P(t)-0.4?(砌t)A? ' ' ' ?)?(S?(?A t) + A ?(? t)又 v(0)= ?(=?(為0 v(t)=v(t- A t)+ A v(t- A t)則由以上公式并結(jié)合題意可得下表t(s)P(kips)V(in)?)A P(kips)A ?A v(in)A ?00000110.009870.2470.1210.009870.2474.11238.3320.08221.0670.2440.09211.31413.688528.2580.27892.2080.3690.37103.52223.116053.8710.53201

28、.3470.4890.90304.869-0.858-350.9970.5033-1.9730.661.40632.856-32.044-66.439-0.0636-5.1770.7201.4699-2.281-54.2347-2由題意知：當(dāng)|v|>1 in 時(shí)K=0其他公式同7-1則有:效t)=K(t)+3?+箸K(t)+93.33A?n=A P+箸?(+3?|+C3 ?(磅)?(?)=A P+11.2?(+0)624 ?A ?(=?) v(t)-3 ?(?)?(t)25 A v-3 ?(砌6 ?1_ 一加速度：？?(助P(t)-C ?(幽(t)1 _豆P(t)-0.4?(砌t)?)?

29、(S?(?A t) + A ?(? t)v(0)= ?(0?(=)0v(t)=v(t- A t)+ A v(t- A t)綜上可得下表:t(s)P(kips)V(in)?n/s)?n/ ?)f s=VSA PA ?K?000000118101.330.1210.0098690.2474.1120.078938.3328101.330.2440.092071.31413.6890.7366528.2598101.330.3690.37093.52323.1152.9678053.8818101.330.4890.90264.860-0.8247.2208-350.918093.330.6061.

30、44823.969-17.9388-627.259093.330.7201.74030.441-40.8828A V(in)A ?n/s)0.0098690.2470.08221.0670.27892.2090.53171.3370.5456-0.8910.2921-3.528接上表接上表7-3K=?鏟22?-1(2?3?=8-32 ?貝U ?t) =101.33- 32 2399其余方程如7-1有h=0.12sA?1=A P+?(+3?|+C3 ?(?)?(?)=A P+11.2 ?(+0)624 ?A ?(=?) v(t)-3 ?(?)?(t)25 A v-3 ?(砌6 ?加速度：？?%P

31、(t)-C ?(幽1 _02P(t)-0.4?(砌t)v(0)= ?(0)?(=)0v(t)=v(t- A t)+ A v(t- A t)?(=?(? t) + A ?(? t)t(s)P(kips)V(in)?/?)?n/ ?)A P(kips)f s?0000010101.330.1210.0098690.2474.11230.0789101.330.2440.09212.87610.56950.7359101.300.3690.52454.42516.02504.025100.350.4891.118050.26-1.497-37.28996.850.6061.65843.548-16.

32、403-67.86391.550.7201.91510.306-35.5920.996綜上公式如下表有:接上表A v(in)a ?n/s)0.0098690.2470.082231.0680.43241.5490.59350.6010.5404-1.4780.2567-3.242第八章廣義單自由度體系8-1EI21.720L2m解:* *T 2 m /k =20.228mL4ei-32L3帶入數(shù)據(jù)得：T=1.776 sec*/ 3m (24*k 324 )mLEIL3T 8L:(3 8)1.771secr把 m= 2 rt, Igtr3帶入得:T 16L(24、L2r)匚Eg8-2 解:2(x

33、) dxm 2(L)8-3bFromL0m(x)2_(x) dx=0.228mL;''(x)2dx=且32 L3W 20.228mL I2g0.228(110 1b sec2/ ft2) 200 ft400 1 03 1b222 17430 1 b sec / ft 32.22 ft / sec24_ 9_ 2165 10 1b ft32(200 ft)362780 1b/ ft8-3解：17430T62780(2rtL- g32tr3L33.311 sec T 3.31sec16L/3 4產(chǎn)(2 )L rWL2 rtEg-jp 7T(f l之"fTTf = 一 r-

34、"IT L5萬(wàn)士 不SINnet i ouer js - - k »（£,上）不.艮妥外)f wJ1H = TH i( 3dt/蕓. 2 ) = Eh£tt 7t85Z s v/ = o ：84二p（D（火片）二佳）|鬻行存工。侵)1貴。梟。(tl Diritl eU il itri uin :,管）切5 = j, ;一盤(pán)金，田心你嚇（“/2）= 士 乏3 （。）'"v J丸/W）= -寸苧丸工）（3£）弟F田-/卜工 三。3）7群田-丫鬻祖 當(dāng)黑）-“"（小幺。蟲(chóng)D-T翳開(kāi)/4）一也.十年我&"弩

35、£Wd）二專(zhuān)pW叼一 3上,）一號(hào)“晟”8號(hào)4(", + ) =&乏Sw » r Jl 6v(-34/2t1)-8% = -I* x * 一 6"5M =-YJl?2LW田 &W =-工區(qū) &“-飛空之U)二"84 工上.76 8 弋 E 3L/£。=隈-弄乏火 y葭田“挈巨陽(yáng)隈+，Yo譽(yù)迅網(wǎng)g F仕氏一k芟陽(yáng)火_"亡祖）注-了；：；%（+女J口J I w1 %3nceo ,怨，"衣+）+林田+/至陽(yáng)打陽(yáng)(t? r) 4d；】R-> nciJ?乃亡 amiHon £ 干中&#

36、163;口門(mén)尸】屯 Zeajs £如 乏代1 + C* <«) + k* fH)=pH firsJ % oj itc. R-4F a=/ Edi%)#十Z?成中：十Zj工篤伊尸E* = ( THS) %jK 十 Zffl叫 + Eft：)(呼'廣找，（3f L£C* = / cO 夕C) Jx 4- at總工3 #彳Mj兀+ Zj ”力”1L-k*三/1oc"rx * / £工（如匕工/44- £；&K*-，”（之）夕小乂*代:,曄七）%）聲+乙公 分情率三TH工/j二亭彳。)十辭不”=7r 4“yHS2Ej 工

37、.5(”之川八皿卻二黯t+挈1濘"e1皿Edy十八句C* 二匚產(chǎn)f£/N廣* = c （/=（?/?武=k'=4汽£）'=我（上/三產(chǎn)=“/*）-p（4）3（事"之）-pGJW“3震門(mén)，cQ/k、g ,=河” n.予u8-4解:*Upth t“J/i弓珊工mptHn備 見(jiàn)TnSislffis cabli丁應(yīng)訂 ERSm tri L/n'JpT m tyRriPEQ4ct m bflr rn.S = E"'"M 00kG）匚p（W）=三立打JL /芝£戶(hù)口Mil 3LM fsfs(-2)kz(t

38、) ( 2)12_ LMi mL&t) M fF(-)042,1fsi k-y(t)fs2k y(t) z(t)foc( 1)&t)Mp p(t)L .1M.ifsi(L)k y(t)Ls 1Ma0Mfs2fs2(2L)k y(t) z(t) (2L)(D一,1因此：p(t)L ky(t)L 2k y(t) z(t) L 0 2Mb 0由式(1)5-m, c 6Mfs2fDMio因此:fs2(2)k y(t) z(t) (-2)fD(:)誠(chéng)t)()-) 22IoamL-強(qiáng)立12 L/21 L c1ky(t) z(t) L-cz(t)-m黑t)L2 26(2)可得:5c,k 2p

39、(t)8-6解:L0 m(X)2dx2X . dx2L里前140* L2k EI '' dx0(x)2L2(3x23'(x)2L2(2x2''(x)12L2(6-x、3“6) (1LL29EILT9EI3L3(13EI*p (t)L0p3 - (x)dx g pL8-7解:一*k3EIL3'(x)dxdx2Ldx*kG3A3l23x2L3dx一* k*kGEIL2'(x) 2 dxN(1-冊(cè)(-)2x(；)31(與4 dx4 x*kG9NL2(L)2x2勺4勺/dx啜* *kkG3 EIL L8-8解:(a)=sinx_.sinax_. cossin a ax_ sin cosa a2 cos ax cos ar(x, y)2(x, y) dA2DaF2-)2y其中:A(2)2y(b)2aF)2dA=2(1dA= A()()(22dA=A x yxcoscos a a22dA=A x y2-sin a2-sinx . ysin a ax . y sin sin2 2dx2 ar)dA