结构动力学-习题解答

7-1（a)试求图示体系的自振频率与周期。解;485311EIl;098.33mlEIl/2mEIl/2l)(1tyl/2l/4;027.23EImlT7-1（b)试求图示体系的自振频率与周期。解:;153611311EIl;11153632mlEI;531.03EImlTl常数EI2/l2/lm32/l16/l64/9l32/5l)(a2/l)(b求柔度系数：用位移法或力矩分配法求单位力作用引起的弯矩图（图a);将其与图b图乘，得;817.113mlEI7-1（c)试求图示体系的自振频率与周期。解328mlEI;22.23EImlTlEI2/lm刚性杆m2lA2/A222Am2mA0xFAlEImAmA322122o222Am2/2mAAlEI3122mA由右面竖杆的平衡可求出铰处约束力。由水平杆的平衡：;828.23mlEI7-1（d)试求图示体系的自振频率与周期。解;626.33EImlT;732.13mlEImEIlEIlm1EI3116lEIk33112326mlEImlEImk7-1（e)试求图示体系的自振频率与周期。解mkEIlm)2148(113112mEIl/2kkl/2kEIl21481311mkEIlm)2148(11311mkEIlT)21481(237-3试求图示体系质点的位移幅值和最大弯矩值。已知解：EIlFyPst3PF)(1ty6.0mEI=常数2ltFPsin2llsty1112/llFP5625.1/1122位移幅值EIlFyAPst35625.1PFAm3375.022/lEIl31135lFMPd169.1maxPF3375.0PFlFP169.1解：7-4图示梁跨中有重量为20kN的电动机，荷载幅值P=2kN，机器转速400r/min，,梁长l=6m。试求梁中点处的最大动位移和最大动弯矩。24.1006.1mkNEImEI=常数l/2tPsinl/2923.1/1122mPyAst41110326.16NmEIl/10245.41006.148648177331105.0)/1(115410245.410208.91273112sm)/1(97.33s)/1(888.41604002smNPlMd.10769.543max(b)阻尼比8726.14)1(12222mPyAst41110898.15mNPlMd.106178.543max解：7-5习题7-4结构的质量上受到突加荷载P=30kN作用，若开始时体系静止，试求梁中最大动位移。11PyAst不计阻尼时，动力系数为2，利用上题数据，可得m02547.0210245.41030737-6某结构在自振10个周期后，振幅降为原来初始位移的10%（初位移为零），试求其阻尼比。解：0366.010ln10218-1试求图示梁的自振频率和振型。m2mEIaaa解EIa321124102mI0/1/122222111222111mmmm令21111m03/14/12/11024/53/42181.0153.121aa/2)(1ty)(2ty61.0/;277.3/22122111xxxx639.11;305.0121xX8-2.试求图示刚架的自振频率和振型解:令2111/1m1637.0336.1213231140.2;749.0mlEImlEImlEImEIl1y2y12Xm222Xm1X2X112112221221212112XXmXm2222212212XXmXm02)1(211121XX0)2(2112211121XXllEIl3211221EIl3223123.214/312111XX897.014/322212XX1897.0;123.221XX112X111X8-3.试求图示梁的自振频率和振型。MPaEcmINmgcml54102,82.68,1000,100731110662.0EIls/175.384按反对称振型振动m2/lEI2/l2/l2/lmm2/l2/l按对称振型振动=15l/323l/16=1l/2m2/l2/l=1l/45311100151.048EIls/145.254ss/175.384/145.25421112X111X8-4.试求图示刚架的自振频率和振型。EIl1923113/856.13mlEI按反对称振型振动按对称振型振动=1l/2=1l/8m2/lEI2/l2/l2/lmEI2/lEI2/lmEIml/8l/82/l2/lmm=13l/165l/32l/2=1EIl3113/mlEI31/mlEI32/856.13mlEI1y2y1y8-5.试求图示刚架的自振频率和振型。mEI1EI1EIl2mEI2EI2EI2l2y311/60lEIk32112/24lEIkk322/27lEIk0222221122111mkkkmk01044147224321/965.7mlEI322/53.65mlEI31/822.2mlEI336.4;4612.022122111XXXX8-6.试求图示刚架的自振频率和振型。设楼面质量分别为m1=120t和m2=100t,柱的质量已集中于楼面，柱的线刚度分别为i1=20MN.m和i2=14MN.m,横梁刚度为无限大。mNk/1051611mNkk/1021621120222221122111mkkkmk063062.7012.024221/1713.97s559.1;5347.022122111XXXX870.111X642.012X1ym11EI1EIm22i2y2i1i1i4m4mmNk/1021622222/1287.537ss/1885.91s/1179.232