動力學(xué)系統(tǒng)建模作業(yè)

動力學(xué)系統(tǒng)建模作業(yè)問題V：請分析兩端帶有彈簧阻尼器支撐的剛性梁的振動特性(固有頻率、振型、幅頻響應(yīng)曲線、相頻響應(yīng)曲線)。Figure:由彈簧阻尼器支撐的剛性梁剛性梁的有限元建模和網(wǎng)格劃分本題中剛性梁的材料參數(shù)為彈性模量e二2.0x101N/m，密度P二7850g/m3，泊松比卩二0.3;梁截面為方形，幾何參數(shù)為lxBxh=2mx0.1mx0.1m。通過有限兀軟件ANSYSWORKBENCH15.0進(jìn)行幾何建模，對剛性梁自動網(wǎng)格劃分(精細(xì))后節(jié)點(diǎn)數(shù)6275個，單元數(shù)1104個，最后在剛性梁的兩端添加彈簧(GroundToSolid)和阻尼(GroundToSolid)，并設(shè)置彈簧的剛度k=1.0xl06N/m，阻尼C=0.2N?s/m，得到剛性梁的有限元模型如圖1所示。圖1剛性梁的有限元模型

剛性梁的模態(tài)分析通過WORKBENCH對剛性梁模態(tài)分析后，得到其前10階的固有頻率和振型描述如表1所示，前10階的模態(tài)振型見圖2。表1前10階的固有頻率和振型描述階數(shù)固有頻率振型描述10整體繞X軸轉(zhuǎn)動20整體繞X軸扭擺32.34E-04整體繞X軸扭擺并沿X軸左右擺動41.02E-03剛性梁左端繞X軸扭擺并在Z方向擺動517.27整體在Y軸方向上下振動630.894兩端在Y軸方向來回上下擺動7128.57兩端在Z軸方向同向振動8133.5兩端在Y軸方向同向振動9348.8整體在Z軸方向雙階擺動，兩端振幅前后最大10350.59整體在Y軸方向雙階擺動，兩端振幅上下最大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)第一階振型Unit:rn2015/11/915:06社(b)第二階振型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)第三階振型d)第四階振型(e)第五階振型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)第三階振型d)第四階振型(e)第五階振型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)第六階振型(g)第七階振型h)第八階振型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)第九階振型(j)第十階振型圖2剛性梁的前十階模態(tài)振型剛性梁的諧響應(yīng)分析通過模態(tài)疊加法來分析剛性梁的諧響應(yīng)，在剛性梁的上表面施加沿Y軸方向豎直向下的激勵力為1.0106N，頻率范圍為0—1000Hz，邊界條件的施加如圖3

所示，得到X軸方向的幅頻和相頻響應(yīng)曲線如圖4所示，Y軸方向的幅頻和相頻響應(yīng)曲線如圖5所示，Z軸方向的幅頻和相頻響應(yīng)曲線如圖6所示.ZC:HarmonicResponseForceZC:HarmonicResponseForceFrequenc?/:0.Hz2015/11/916:30■Force:l.e+005NComponents:0^-l.e+006,0.N圖3剛性梁上的激勵力%505088771。{角位相oool009008007OQOooo004003002ool50505050544332211)艮{值幅Qu?OQyQuoOU7QU6Qus004%505088771。{角位相oool009008007OQOooo004003002ool50505050544332211)艮{值幅Qu?OQyQuoOU7QU6Qus004QwdQHZQm（a）幅頻響應(yīng)曲線圖（b）相頻響應(yīng)曲線圖圖4X軸的幅頻和相頻響應(yīng)曲線圖864208642){島5432101。{角位相QUMYQW9QtioQUYQuoQuoQU4QW3QwzQm頻率864208642){島5432101。{角位相QUMYQW9QtioQUYQuoQuoQU4QW3QwzQm頻率（Hz）頻率（Hz）（a）幅頻響應(yīng)曲線圖（b）相頻響應(yīng)曲線圖圖5Y軸的幅頻和相頻響應(yīng)曲線圖)m9085)°80(75位706560頻率（Hz）)m9085)°80(75位706560頻率（Hz）QY頻率（Hz）OOY009008QU7O0Z（a）幅頻響應(yīng)曲線圖（b）相頻響應(yīng)曲線圖圖6Z軸的幅頻和相頻響應(yīng)曲線圖從圖4、圖5和圖6可知，頻率在（OTOOOHz）范圍內(nèi)，在X、Y和Z軸方向上的幅頻響應(yīng)曲線均表現(xiàn)為隨頻率的增加而遞減，在（0-350Hz）范圍內(nèi)驟減