动力学系统建模作业

动力学系统建模作业问题V：请分析两端带有弹簧阻尼器支撑的刚性梁的振动特性(固有频率、振型、幅频响应曲线、相频响应曲线)。Figure:由弹簧阻尼器支撑的刚性梁刚性梁的有限元建模和网格划分本题中刚性梁的材料参数为弹性模量e二2.0x101N/m，密度P二7850g/m3，泊松比卩二0.3;梁截面为方形，几何参数为lxBxh=2mx0.1mx0.1m。通过有限兀软件ANSYSWORKBENCH15.0进行几何建模，对刚性梁自动网格划分(精细)后节点数6275个，单元数1104个，最后在刚性梁的两端添加弹簧(GroundToSolid)和阻尼(GroundToSolid)，并设置弹簧的刚度k=1.0xl06N/m，阻尼C=0.2N•s/m，得到刚性梁的有限元模型如图1所示。图1刚性梁的有限元模型

刚性梁的模态分析通过WORKBENCH对刚性梁模态分析后，得到其前10阶的固有频率和振型描述如表1所示，前10阶的模态振型见图2。表1前10阶的固有频率和振型描述阶数固有频率振型描述10整体绕X轴转动20整体绕X轴扭摆32.34E-04整体绕X轴扭摆并沿X轴左右摆动41.02E-03刚性梁左端绕X轴扭摆并在Z方向摆动517.27整体在Y轴方向上下振动630.894两端在Y轴方向来回上下摆动7128.57两端在Z轴方向同向振动8133.5两端在Y轴方向同向振动9348.8整体在Z轴方向双阶摆动，两端振幅前后最大10350.59整体在Y轴方向双阶摆动，两端振幅上下最大0.118940.107690.073950.0627030.0964430.0851970.14143Max0.130180.0514560.040209MinFrequen<?,'■：0.Hz0.118940.107690.073950.0627030.0964430.0851970.14143Max0.130180.0514560.040209MinFrequen<?,'■：0.HzUnit:rn2015/11/915:03(a)第一阶振型Unit:rn2015/11/915:06社(b)第二阶振型Frequency:z'.ildS5e-U04HzFrequency'■:l.Oz'cle-OOdHz2015/11/915:102015/11/915:110.13208Max0.123430.1147H0.0974H5o.oyyy:-!?0.OHO190.0715420J054246Mn0.17173Max0.157270.147M10.17MH50.0994^!：-!0.0«49&10.070499Frequency:z'.ildS5e-U04HzFrequency'■:l.Oz'cle-OOdHz2015/11/915:102015/11/915:110.13208Max0.123430.1147H0.0974H5o.oyyy:-!?0.OHO190.0715420J054246Mn0.17173Max0.157270.147M10.17MH50.0994^!：-!0.0«49&10.0704990.0560：-：60.041574Mn(c)第三阶振型d)第四阶振型(e)第五阶振型0.12420.12620.108390.0533550.0549650.0356430.0371560.0179320.0887770.0710660.0905830.0727740.15962Max0.141910.16182Max0.14401Frequenc?/:17.27HzUnit:rn2015/11/915:14Frequenq/:30.894HzUnit:rn2015/11/915:15FrequenOf1•:133.5HzUnit:rn2015/11/915:23Frequerw/:128.57HzUnit:rn2015/11/915:200.106490.083163Max0.0821130.0810640.0800140.0789650.0779150.07&8G6(c)第三阶振型d)第四阶振型(e)第五阶振型0.12420.12620.108390.0533550.0549650.0356430.0371560.0179320.0887770.0710660.0905830.0727740.15962Max0.141910.16182Max0.14401Frequenc?/:17.27HzUnit:rn2015/11/915:14Frequenq/:30.894HzUnit:rn2015/11/915:15FrequenOf1•:133.5HzUnit:rn2015/11/915:23Frequerw/:128.57HzUnit:rn2015/11/915:200.106490.083163Max0.0821130.0810640.0800140.0789650.0779150.07&8G60.0758160.0747670.073717Min0.13661Max0.121430.106250.0910730.0758940.0607150.0455360.0303580.0151790.0193470.0015378Minf)第六阶振型(g)第七阶振型h)第八阶振型Frequen«?,■'：348.8HzUnit:rn2015/11/915:25Frequen(?,■'：350.59HzUnit:m2015/11/915:260.15964Max0.14190.124160.106420.0886870.0709490.0532120.0354750.0177371.1723e-llh0.1606Max0.142750.124910.107060.089220.0713760.0535320.0356880.017844(i)第九阶振型(j)第十阶振型图2刚性梁的前十阶模态振型刚性梁的谐响应分析通过模态叠加法来分析刚性梁的谐响应，在刚性梁的上表面施加沿Y轴方向竖直向下的激励力为1.0106N，频率范围为0—1000Hz，边界条件的施加如图3

所示，得到X轴方向的幅频和相频响应曲线如图4所示，Y轴方向的幅频和相频响应曲线如图5所示，Z轴方向的幅频和相频响应曲线如图6所示.ZC:HarmonicResponseForceZC:HarmonicResponseForceFrequenc?/:0.Hz2015/11/916:30■Force:l.e+005NComponents:0^-l.e+006,0.N图3刚性梁上的激励力%505088771。{角位相oool009008007OQOooo004003002ool50505050544332211)艮{值幅Qu?OQyQuoOU7QU6Qus004%505088771。{角位相oool009008007OQOooo004003002ool50505050544332211)艮{值幅Qu?OQyQuoOU7QU6Qus004QwdQHZQm（a）幅频响应曲线图（b）相频响应曲线图图4X轴的幅频和相频响应曲线图864208642){岛5432101。{角位相QUMYQW9QtioQUYQuoQuoQU4QW3QwzQm频率864208642){岛5432101。{角位相QUMYQW9QtioQUYQuoQuoQU4QW3QwzQm频率（Hz）频率（Hz）（a）幅频响应曲线图（b）相频响应曲线图图5Y轴的幅频和相频响应曲线图)m9085)°80(75位706560频率（Hz）)m9085)°80(75位706560频率（Hz）QY频率（Hz）OOY009008QU7O0Z（a）幅频响应曲线图（b）相频响应曲线图图6Z轴的幅频和相频响应曲线图从图4、图5和图6可知，频率在（OTOOOHz）范围内，在X、Y和Z轴方向上的幅频响应曲线均表现为随频率的增加而递减，在（0-350Hz）范围内骤减