ABAQUS瑞利阻尼

1、關(guān)于ABAQUS中的質(zhì)量比例阻尼總結(jié)論：ABAQUS中的質(zhì)量比例阻尼是和絕對(duì)速度有關(guān)的，即質(zhì)量比例阻尼產(chǎn)生的阻尼力由絕對(duì)速度引起。以阻尼系數(shù)表達(dá)的阻尼，產(chǎn)生的阻尼力由相對(duì)速度引起。Abaqus Analysis User's ManualMass proportional damping： The factor introduces damping forces caused by the absolute velocities of the model and so simulates the idea of the model moving through a viscous “e

2、ther” (a permeating, still fluid, so that any motion of any point in the model causes damping).幫助手冊(cè)也說(shuō)明了質(zhì)量比例阻尼是和絕對(duì)速度有關(guān)。問(wèn)題：1、 應(yīng)用直接積分法進(jìn)行時(shí)程分析，地震波一般以邊界條件的形式加到支座處，結(jié)構(gòu)阻尼只能使用Rayleigh阻尼，而這時(shí)產(chǎn)生的阻尼力是絕對(duì)速度產(chǎn)生的，而運(yùn)動(dòng)方程中的阻尼項(xiàng)產(chǎn)生的阻尼力是與相對(duì)速度有關(guān)。2、 SAP2000中施加地震波，支座處相對(duì)位移為0，絕對(duì)位移不為0，其相對(duì)位移相對(duì)哪一點(diǎn)來(lái)說(shuō)的？算例：?jiǎn)巫杂啥润w系，如圖（1），質(zhì)量m=0.02533kg，k=

3、1N/m，阻尼比=0.05，對(duì)應(yīng)的阻尼系數(shù)c=0.0159，若應(yīng)用直接積分法進(jìn)行時(shí)程分析，結(jié)構(gòu)的阻尼需要轉(zhuǎn)換成Rayleigh阻尼，使用如下公式：如果只使用質(zhì)量比例阻尼（結(jié)構(gòu)只有一階振型），即，容易得出=0.6283。. 圖（1）情況（1）：在ABAQUS中用spring單元模擬豎向的直桿，水平剛度k=1N/m，采用Rayleigh阻尼，通過(guò)*mass,alpha=0.6283（質(zhì)量比例阻尼）施加，地震波需用Elcentrol波，以邊界條件的形式加在支座處(豎向桿下端)。為了作對(duì)比，在SAP2000中的結(jié)構(gòu)阻尼在分析工況中以質(zhì)量比例阻尼的形式施加。MATLAB中變成使用NewMark-beta

4、方法。三者質(zhì)量的相對(duì)位移時(shí)程對(duì)比如下： 圖（2）質(zhì)量點(diǎn)相對(duì)位移時(shí)程對(duì)比圖（3）質(zhì)量點(diǎn)絕對(duì)位移時(shí)程對(duì)比圖（4）支座位移時(shí)程對(duì)比結(jié)論：質(zhì)量點(diǎn)相對(duì)位移時(shí)程SAP2000與MATLAB重合很好，ABAQUS與兩者差別較大；SAP2000與ABAQUS在支座處得位移時(shí)程重合很好。情況（2）：在ABAQUS中用spring單元模擬豎向的直桿，水平剛度k=1N/m，采用Rayleigh阻尼，通過(guò)*mass,alpha=0.6283（質(zhì)量比例阻尼）施加，地震波需用Elcentrol波，以慣性力的形式加質(zhì)量點(diǎn)處。SAP2000的參數(shù)設(shè)置同情況（1）。三者質(zhì)量的相對(duì)位移時(shí)程對(duì)比如下： 圖（5）質(zhì)量點(diǎn)相對(duì)位移時(shí)程對(duì)

5、比圖（6）質(zhì)量點(diǎn)絕對(duì)位移時(shí)程對(duì)比圖（7）支座位移時(shí)程對(duì)比結(jié)論：質(zhì)量點(diǎn)相對(duì)位移時(shí)程SAP2000與MATLAB及ABAQUS重合很好，幾乎完全一致。情況（3）：在ABAQUS中用spring單元模擬豎向的直桿，水平剛度k=1N/m，采用阻尼器模擬結(jié)構(gòu)阻尼，通過(guò)*dashpot施加阻尼系數(shù)c=0.0159，地震波需用Elcentrol波，以邊界條件的形式加在支座處(豎向桿下端)。SAP2000的參數(shù)設(shè)置：結(jié)構(gòu)阻尼在連接單元的屬性中施加阻尼阻，尼系數(shù)c=0.0159。圖（8）質(zhì)量點(diǎn)相對(duì)位移時(shí)程對(duì)比圖（9）質(zhì)量點(diǎn)絕對(duì)位移時(shí)程對(duì)比圖（10）支座位移時(shí)程對(duì)比結(jié)論：位移時(shí)程SAP2000與MATLAB及AB

6、AQUS重合很好，幾乎完全一致。情況（4）：在ABAQUS中用spring單元模擬豎向的直桿，水平剛度k=1N/m，采用阻尼器模擬結(jié)構(gòu)阻尼，通過(guò)*dashpot施加阻尼系數(shù)c=0.0159，地震波需用Elcentrol波，以慣性力的形式加質(zhì)量點(diǎn)處。SAP2000的參數(shù)設(shè)置：結(jié)構(gòu)阻尼在連接單元的屬性中施加阻尼阻，尼系數(shù)c=0.0159。圖（11）質(zhì)量點(diǎn)相對(duì)位移時(shí)程對(duì)比圖（12）質(zhì)量點(diǎn)絕對(duì)位移時(shí)程對(duì)比圖（13）支座位移時(shí)程對(duì)比結(jié)論：質(zhì)量點(diǎn)相對(duì)位移時(shí)程SAP2000與MATLAB及ABAQUS重合很好，幾乎完全一致。情況（5）：含阻尼器結(jié)構(gòu)體系不變，結(jié)構(gòu)阻尼采用質(zhì)量比例阻尼，alpha=0.6283

7、。在質(zhì)量點(diǎn)水平方向加入阻尼器，采用Maxwell模型，在ABAQUS中用spring單元和dashpot單元模擬，如圖（14）。阻尼器參數(shù)為cd =0.06366，彈簧剛度kd =1。地震波需用Elcentrol波，以慣性力的形式加質(zhì)量點(diǎn)處。 圖（14）在SAP2000中的結(jié)構(gòu)阻尼在分析工況中以質(zhì)量比例阻尼的形式施加。圖（15）質(zhì)量點(diǎn)相對(duì)位移時(shí)程對(duì)比圖（16）阻尼力滯回曲線對(duì)比結(jié)論： SAP2000與ABAQUS重合很好，幾乎完全一致，MATLAB與前兩者略有差別。情況（6）：含阻尼器結(jié)構(gòu)體系不變，結(jié)構(gòu)阻尼采用質(zhì)量比例阻尼，alpha=0.6283。在質(zhì)量點(diǎn)水平方向加入阻尼器，采用Maxwel

8、l模型，在ABAQUS中用spring單元和dashpot單元模擬，如圖（14）。阻尼器參數(shù)為cd =0.06366，彈簧剛度kd =1。地震波需用Elcentrol波，以邊界條件的形式加在支座處(豎向桿下端)，另外，水平阻尼器右端的支座固定。圖（17）質(zhì)量點(diǎn)相對(duì)位移時(shí)程對(duì)比圖（18）阻尼力滯回曲線對(duì)比結(jié)論： ABAQUS與其他兩者差別較大。情況（7）：含阻尼器結(jié)構(gòu)體系不變，結(jié)構(gòu)阻尼采用質(zhì)量比例阻尼，alpha=0.6283。在質(zhì)量點(diǎn)水平方向加入阻尼器，采用Maxwell模型，在ABAQUS中用spring單元和dashpot單元模擬，如圖（14）。阻尼器參數(shù)為cd =0.06366，彈簧剛度

9、kd =1。地震波需用Elcentrol波，以邊界條件的形式加在支座處(豎向桿下端)，另外，水平阻尼器右端的支座也加地震波。結(jié)論： 三者有差別，沒(méi)有情況（5）吻合的好ABAQUS響應(yīng)的INPUT文件如下：情況（1）*Heading不含阻尼器，采用質(zhì)量比例阻尼，地震波以邊界條件施加*Node1,0,02,0,1*Nset,Nset=Nout1,2*Element,Type=Mass,Elset=PointMass1,2*Mass,Elset=PointMass,alpha=0.62830.02533*Element,Type=SPRING2,Elset=spring2,1,2*SPRING,EL

10、SET=spring1,11*Boundary1,1,6*Step1:Gravity*STEP,NAME=GravitySTEP1:Gravity*Static0.1,1,1e-5,1*Dload ,GRAV,0,-9.8*Output,FIELD, VARIABLE=PRESELECT*END STEP*Step2:Modal*Step,Name=ModalAnalysis,PERTURBATIONStep2:Modal anlysis *Frequency3*Output,Field,Variable=Preselect*End Step*Step3:Earthquake*Step,Nam

11、e=TimeHistory,Inc=2000,NLGEOMStep3:Earthquake*Dynamic,HAFTOL=10000000,ALPHA=00.02,30,0,0.02*Amplitude,Name=Earthquake,Input=ELCENTRO.inp*Boundary,op=Mod,Type=Acceleration,Amplitude=Earthquake1,1,1,1E-2*Output, field, variable=PRESELECT*Output, history,FREQUENCY=1*Node Output,Nset=NoutU1,U2,RF*Elemen

12、t Output,Elset=springS11,E11*End Step情況（2）*Heading不含阻尼器，采用質(zhì)量比例阻尼，地震波以慣性力形式施加*Node1,0,02,0,1*Nset,Nset=Nout1,2*Element,Type=Mass,Elset=PointMass1,2*Mass,Elset=PointMass,alpha=0.62830.02533*Element,Type=SPRING2,Elset=spring2,1,2*SPRING,ELSET=spring1,11*Boundary1,1,6*Step1:Gravity*STEP,NAME=GravitySTEP

13、1:Gravity*Static0.1,1,1e-5,1*Dload ,GRAV,0,-9.8*Output,FIELD, VARIABLE=PRESELECT*END STEP*Step2:Modal*Step,Name=ModalAnalysis,PERTURBATIONStep2:Modal anlysis *Frequency3*Output,Field,Variable=Preselect*End Step*Step3:Earthquake*Step,Name=TimeHistory,Inc=2000,NLGEOMStep3:Earthquake*Dynamic,HAFTOL=100

14、00000,ALPHA=00.02,30,0,0.02*Amplitude,Name=Earthquake,Input=ELCENTRO.inp*Cload,Amplitude=Earthquake2,1,0.02533E-2*Output, field, variable=PRESELECT*Output, history,FREQUENCY=1*Node Output,Nset=NoutU1,U2,RF*Element Output,Elset=springS11,E11*End Step情況（3）*Heading不含阻尼器，采用阻尼器模擬結(jié)構(gòu)阻尼，地震波以邊界條件形式施加*Node1,0

15、,02,0,1*Nset,Nset=Nout1,2*Element,Type=Mass,Elset=PointMass1,2*Mass,Elset=PointMass0.02533*Element,Type=SPRING2,Elset=spring2,1,2*SPRING,ELSET=spring1,11*Element,Type=DASHPOT2,Elset=dashpot3,1,2*DASHPOT, ELSET=dashpot1,10.0159*Boundary1,1,6*Step1:Gravity*STEP,NAME=GravitySTEP1:Gravity*Static0.1,1,1e

16、-5,1*Dload ,GRAV,0,-9.8*Output,FIELD, VARIABLE=PRESELECT*END STEP*Step2:Modal*Step,Name=ModalAnalysis,PERTURBATIONStep2:Modal anlysis *Frequency3*Output,Field,Variable=Preselect*End Step*Step3:Earthquake*Step,Name=TimeHistory,Inc=2000,NLGEOMStep3:Earthquake*Dynamic,HAFTOL=10000000,ALPHA=00.02,30,0,0

17、.02*Amplitude,Name=Earthquake,Input=ELCENTRO.inp*Boundary,op=Mod,Type=Acceleration,Amplitude=Earthquake1,1,1,1E-2*Output, field, variable=PRESELECT*Output, history,FREQUENCY=1*Node Output,Nset=NoutU1,U2,RF*Element Output,Elset=springS11,E11*End Step情況（4）*Heading不含阻尼器，采用阻尼器模擬結(jié)構(gòu)阻尼，地震波以慣性力形式施加*Node1,0,

18、02,0,1*Nset,Nset=Nout1,2*Element,Type=Mass,Elset=PointMass1,2*Mass,Elset=PointMass0.02533*Element,Type=SPRING2,Elset=spring2,1,2*SPRING,ELSET=spring1,11*Element,Type=DASHPOT2,Elset=dashpot3,1,2*DASHPOT, ELSET=dashpot1,10.0159*Boundary1,1,6*Step1:Gravity*STEP,NAME=GravitySTEP1:Gravity*Static0.1,1,1e-

19、5,1*Dload ,GRAV,0,-9.8*Output,FIELD, VARIABLE=PRESELECT*END STEP*Step2:Modal*Step,Name=ModalAnalysis,PERTURBATIONStep2:Modal anlysis *Frequency3*Output,Field,Variable=Preselect*End Step*Step3:Earthquake*Step,Name=TimeHistory,Inc=2000,NLGEOMStep3:Earthquake*Dynamic,HAFTOL=10000000,ALPHA=00.02,30,0,0.

20、02*Amplitude,Name=Earthquake,Input=ELCENTRO.inp*Cload,Amplitude=Earthquake2,1,0.02533E-2*Output, field, variable=PRESELECT*Output, history,FREQUENCY=1*Node Output,Nset=NoutU1,U2,RF*Element Output,Elset=springS11,E11*End Step情況（5）*HeadingMaxwell模型阻尼器模擬,地震力以慣性力形式施加,采用質(zhì)量比例阻尼*Node1,0,02,0,13,0.5,14,1,1*

21、Nset,Nset=Nout1,2,4*Element,Type=Mass,Elset=PointMass1,2*Mass,Elset=PointMass,alpha=0.628320.02533*Element,Type=SPRING2,Elset=spring_12,1,2*SPRING,ELSET=spring_11,11*定義阻尼器的屬性，用Spring和Dashpot單元*Element,Type=SPRINGA,Elset=spring_23,3,4*Spring,Elset=spring_21*Element,Type=DASHPOTA,Elset=dashpot4,2,3*DA

22、SHPOT, ELSET=dashpot0.06366*Boundary1,1,64,1,6*Step1:Gravity*STEP,NAME=GravitySTEP1:Gravity*Static0.1,1,1e-5,1*Dload ,GRAV,0,-9.8*Output,FIELD, VARIABLE=PRESELECT*END STEP*Step,Name=ModalAnalysis,PERTURBATIONStep2:Modal anlysis *Frequency3*Output,Field,Variable=Preselect*End Step*Step3:Earthquake*St

23、ep,Name=TimeHistory,Inc=2000,NLGEOMStep3:Earthquake*Dynamic,HAFTOL=10000000,ALPHA=00.02,30,0,0.02*Amplitude,Name=Earthquake,Input=ELCENTRO.inp*Cload,Amplitude=Earthquake2,1,0.02533E-2*Output, field, variable=PRESELECT*Output, history,FREQUENCY=1*Node Output,Nset=NoutU1,U2,RF*Element Output,Elset=spr

24、ing_1S11,E11*Element Output,Elset=spring_2S11,E11*Element Output,Elset=dashpotS11,E11,ER11*End Step情況（6）*HeadingMaxwell模型阻尼器模擬,地震力以邊界形式施加,采用質(zhì)量比例阻尼*Node1,0,02,0,13,0.5,14,1,1*Nset,Nset=Nout1,2,4*Element,Type=Mass,Elset=PointMass1,2*Mass,Elset=PointMass,alpha=0.628320.02533*Element,Type=SPRING2,Elset=

25、spring_12,1,2*SPRING,ELSET=spring_11,11*定義阻尼器的屬性，用Spring和Dashpot單元*Element,Type=SPRINGA,Elset=spring_23,3,4*Spring,Elset=spring_21*Element,Type=DASHPOTA,Elset=dashpot4,2,3*DASHPOT, ELSET=dashpot0.06366*Boundary1,1,64,1,6*Step1:Gravity*STEP,NAME=GravitySTEP1:Gravity*Static0.1,1,1e-5,1*Dload ,GRAV,0,-

26、9.8*Output,FIELD, VARIABLE=PRESELECT*END STEP*Step,Name=ModalAnalysis,PERTURBATIONStep2:Modal anlysis *Frequency3*Output,Field,Variable=Preselect*End Step*Step3:Earthquake*Step,Name=TimeHistory,Inc=2000,NLGEOMStep3:Earthquake*Dynamic,HAFTOL=10000000,ALPHA=00.02,30,0,0.02*Amplitude,Name=Earthquake,In

27、put=ELCENTRO.inp*Boundary,op=Mod,Type=Acceleration,Amplitude=Earthquake1,1,1,1E-2*Output, field, variable=PRESELECT*Output, history,FREQUENCY=1*Node Output,Nset=NoutU1,U2,RF*Element Output,Elset=spring_1S11,E11*Element Output,Elset=spring_2S11,E11*Element Output,Elset=dashpotS11,E11,ER11*End Step情況（7）*HeadingMaxwell模型阻尼器模擬,地震力以邊界形式施加,采用質(zhì)量比例阻尼,右支座也加地震波*Node1,0,02,0,13,0.5,14,1,1*Nset,Nset=Nout1,2,4*Element,Type=Mass,Elset=PointMass1,2*Mass,Elset=PointMass,alpha=0.628320.02533*Element,Type=