瞬态响应分析

1、第七章瞬态响应分析7.1 概述(1) 计算时变激励的响应(2) 激励在时间域中显式定义，所有作用的力在每时间点给定(3) 计算的响应通常包括节点位移、速度、加速度、单元力和应力(4) 计算瞬态响应有直接法(Direct)和模态法(modal)7.2 直接瞬态响应分析(1)过程动力学方程Ml lift) + B+K (!) =P(t»对固定时间段At求出离散点的响应，用中心差分法1(<Jn = 2AfUn+1 -财Wnl =pun+l _ 2un + Un-l使用 Newmark-Beta 方法转化为(可以选择Willson-Theta 法、Hughes-Alpha . Bath

2、e )At“Filters”整理得到= lA2|A3unl + |A4lun_l)其中，A = M + B/ 2At + K/3| Dynamic MatrixApplied ForceInitial Conditions, a from PreviousTime StepA2l =顼|A« = |2M/At2-K/3|A4I = I M/At2+B 2At- K 3|(2)瞬态响应分析中的阻尼B = B1 + B2 + G WK1 + 1/W4yGEKE其中，B1 =阻尼单元(VISC,DAMP) + B2GGB2 = B2PP直接输入矩阵+传递函数G =整体结构阻尼系数(PARA

3、M,G)W3 =感兴趣的整体结构阻尼转化为频率-弧度/秒(PARAM,W3)K1 =整体刚度矩阵Ge =单元结构阻尼系数(GE在MATi卡中定义)W4 =感兴趣的单元结构阻尼转化为频率-弧度渺(PARAM,W4)Ke =单元刚度矩阵瞬态响应分析中的不允许复系数，因此结构阻尼转化为等效粘性阻尼进行计算W3,W4的缺省为0,这时不计阻尼7.3 模态瞬态响应分析(1)过程物理坐标与模态坐标变化无阻尼的动力学方程M町+ K|u =变换得到0T|M|(MI + |qT|IK|qH5 gT|P其中，= modal mass matrix (diagonal)0TK. j = modal stiffness

4、 matrix (diagonal)矿P = modal force vector解耦得到单自由度系统方程+ k古=Pj(t)其中，m| = i-th modal mass kj = i-th modal stiffness Pj = i-th modal force当存在阻尼时巾T&o 车 diagonal其中,|HTKPn + CPn + pn-?Dynamic MatrixApplied ForceInitial Conditions,> from PreviousTime Step(2)模态瞬态响应分析中的阻尼使用模态阻尼，每阶模态都存在阻尼，方程变为解耦的方程rn&am

5、p; * 岫 + kj§ = Pj(t)或&"2力弓 w处= l/mjpiti其中,§ =modal damping ratio二 krrij = modal frequency (eigenvalue)利用Duhamel积分得到COO, No Initial CondAreAllowed in MSC/M ASTRA IM forModal Transient Responset>tX2-谷一' 乏, | q &h N m T)sin一(3) Nastran中模态瞬态响应分析阻尼的输入 TABDMP1 Bulk Data entry

6、 defines the modal damping ratios.TAHDMP1IDTYPE+ ABC+AHC<191f2 .92qr 93%+ DLF+ DLF9s 'enDii8 Type = G (default), CRIT, or Q£ = b/bcr = G/2 Q = 1/(2)=1/GExample; for 10% critical dampingCRIT = 0J0Q = 5.0G = 0.2a) TABDMP1卡用SDAMPING=ID 情况控制卡选择b) fi (Hz)和gi为频率和阻尼值，用线性内插值给定点间的频率，用线性外插值给定端点外的频

7、率；如EnteredComputedfgfg2.00.10100.023.00.182.50.144.0D.13360.156.00.13550J3c）定义非模态阻尼(PARAM, G; VISC; DAMP: GE on MATi（4）模态瞬态响应分析数据的提取a）物理响应为模态响应的叠加b）计算量一般不如直接法大c）不必输出每个时间步的值（5）模态截断原因：a）不需要所有模态，仅须很少的低阶模态就可以得到满意的响应b）用PARAM,LFREQ 给出保留模态的频率下界c）PARAM,HFREQ 给出保留模态的频率上界d）PARAM,LMODES 给出保留模态的最小数目e）截断高频模态即截断了

8、高频响应7.4 瞬态激励力定义为时间的函数Nastran中定义方法TLOAD1TLOAD2,+Brute force; ordored time, force pairsinputEfficient definition for analytical-type loadings LSEQ1）时变载荷Generates dynartiie loads from static loadsa） TLOAD1定义的载荷Ptt» =其中,A=DAREA (or LSEQ) entryt=DELAY entryF(tT)=TABLEDi entryb) TLOAD2定义的载荷10,t< 0

9、 or t> T2-T1AtBeCtcos(2rcFt+，。""七-、L2) TLOAD作片P(tj - AF(t - t其中，TLOAD1SIDATYPETIDXXXAspatial load distribution and scale factor (DAREA or LSEQ)=DELAY entryF(t-T) = TABLEDi entrya) DELAY定义自由度及时间延退量b) TABLEDi定义时间和力对C)由DLOAD情况控制卡选择d) TYPE定义为IntegerExcitation Function0 Or blankForce or Mome

10、nt1Enforced Displacement23Enforced VelocityEnforced Acceleration3) TLOAD 2 卡片t < 0 ortAT? Tq其中,12P(t) = JAtetcos(2irFt + P)TLOAD2SIDATYPEFlT2FpC3)5678910A Defined as a spatial load distribution and scale factor (DAREA or LSEQ)r Defined on a DELAY entry (can only be used wrth a DAREA entry)TYPE De

11、fined as TLOAD1T1,T2 Time constants (T2>T1)F Frequency (Hz)P Phmse angle (degrMS)C Exponential coefficientB Growth coefficient该卡片由情况控制卡 DLOAD选取4）载荷的组合其中,Sc = overall scale factorscale factor for k-th load setPK = SID of TLOADU.OAUSIDScS|Pis2P2*sto-fi 7IO注：a）TLOAD1 和 TLOAD2 标号唯一b）用 DLOAD 组合 TLOADs

12、c）由情况控制卡DLOAD选取5 ) DAREAf定义动态载荷作用的自由度，与其他卡片关系DLOADCase ControlBulk DataTLOADTemporal DistributionScaleFactorDOFISpatialDistributionDAREA例子LOAD = 35fl 73910TLOAD1SIDDAWEA匚匕_3TYPETlDTLOAD1352931340DAREASIDPOINTSCALEAREA"SO-1DELAYSIDPOINTCCMUNENTLAGDELAY3130T0.2TABLED1IDXAXISYAXISXIY1X2Y2X3Y3Y4TAB

13、LED140-3.04.02.056605.6endt Result is the load specified by the TLOAD1, scaled by 52 delayed by 0.2 seconds, and applied to grid point 30 component T1.6) SLEQ#片将静态载荷用为动态载荷由情况控制卡LOADSET选取 包括含一个DAREA卡片，与其他卡片关系Case CgntrplBulk DataLOADLOADSETDynamic DAREA StaticLoadLoadEntriesTemporalDistributionRefere

14、nceLinkSpatialDistributionLSEQ例子LOADSET = 27DLOAD = 25LSEQLSEQSID 27AREA28VLID 26TLOAD1SIDDAREATLOAD12528STATIC LOADSID、DAREAPLOAD126ReferenceFORCE26Link7）初始条件a）瞬态响应分析中，初始位移与初始速度由TIC数据卡定义，在模态响应分析中无效b）由IC情况控制卡片选择c）未被约束的自由度为0d）由一个 A-set DOFs.给定e）初始条件仅须在直接瞬态响应中给定，模态瞬态响应中为0f）初始条件用于计算（u 1 时需要的（u 0 , （u -

15、1 ,P 0 , （P -1 ,所有点的初始加速度设置为0 （t<0）= |K（u0 + |BHu0J建议对任何类型的动态激励至少取一个时间步为0Forceg） TIC卡定义初始条件Format:其中，FieldContentsSlDki&nlificabon number. 0)GGrid, scalar, w point iderMificatiod number. > )CConponnl nimt>ar$. zero or blank tot scalar or &tr& poirlEr any 白n白 al th inlgrA1 tnraog

16、h 6 (or a grid p<nl.)UOInitial displaoefinenl. RealVOInitial velocity. (Real)8） TSTE叶a）定义直接瞬态响应和模态瞬态响应分析中的积分时间步长b）积分误差随频率的增加而增加c）建议在响应的一个周期内至少取8个时间步d）TSTEP控制求解和输出，由情况控制卡 TSTEP选取e）积分的代价与步长成正比f）对低频（长周期）响应用自适应方法更有效g）计算中可以改变积分步长，这时2。=佥他¥也-"MQdalDirect*Small ModelXLarge ModelXFew Time StepsX

17、Many Time StepsXHigh Frequency ExcitationXNonlinearitiesXInitial ConditionsX7.u P = UN-At2 U0 务P - = Ku ” , |B| u 1、+M虬"/=|Ku iHBH% h) TSTEP 卡片UniformAccelerationAssumedFormat:12345678910TfiTEPSIDN1DT1NOiH?DT2NOS个一-TSTEP210.001590.011Example:Field Contents曰idefllihcaboc number (Integer > 0)N

18、 Numt>ef a< time steps d value DTi. (intag&r > 1Ti Tinr rKramfini. (Ral > 0.0)NOi Skip factor kx output. Ey NOHh step wM be s&rtd tor oulpul. (kvteaGr > 0; Default 1)5直接瞬态响应与模态瞬态响应比较例子 1 ) DIRECT TRANSIENT RESPONSE7. 6瞬态响应求解控制CorhtroiSOILMe t nodSolutiorlSOCIUCOCC：DirectModali

19、 1 2(for reciuiredl iinput s-ee-*Cnitrol SQetinnDLOAO l-OADSET METHOD S DAMPING VCTSTEP require eft) opfionfiNj(moclaV r<FCfwiir«ici> (modal oiptiori-all> (diireiict ot t ionuaiil> (botlh - re c| ui rod)-Bulk Data SectionASET, OMIT EIGRL or EIGR TSTEP TIC TLOADi LSEQ TABLEDi DAREA D

20、ELAY DLOAD TABDMP1(both - optional) (modal - required (both - required) (direct - optional) (both - required (both - optional) (both - optional) (both - required*) (both - optional) (both - optional) (modal - optional)CASE CONTROL OUTPUT* Grid outputACCELERATIONDISPLACEMENT (or VECTOR)GPSTRESSNLLOAD

21、 (nonlinear load output)Ol_OAD (output applied loadSACCELERATION (solution set output - A-set in direct SDISPLACEMENT solutions modal variables in ©VELOCITYJ modal solutions)SVECTOR (A-set eigenvector)SPCFORCESVELOCITYMPCFORCE- Element outputEL STRESS (or STRESS) ELFORCE (or FORCE) STRAINOTIME

22、(controls solution output times)1 psi over the total surfaceINPUT FILEID SEMINAR, PROB4SOL 109TIME 30CENDTITLE= TRANSIENT RESOPONSE WITH TIME DEPENDENT PRESSURE AND POINT LOADSSUBTITLE= USE THE DIRECT METHODECHO= PUNCHSPC= 1SET 1= 11, 33, 55DISPLACEMENT= 1SUBCASE 1DLOAD= 700 SELECT TEMPORAL COMPONEN

23、T OF TRANSIENT LOADING LOADSET= 1$0SELECT SPACIAL DISTRIBUTION OF TRANSIENT LOADING TSTEP= 10PSELECT INTERGRATION TIME STEPS$OUTPUT (XYPLOT)XGRID=YESYGRID=YESXTITLE = TIME (SEC)YTITLE- DISPLACEMENT RESPONSE AT CENTER TIPXYPLOT DISP RESONSE / 11(T3)YTITLE= DISPLACEMENT RESPONSE AT CENTER TIPXYPLOT DI

24、SP RESPONSE / 33 (T3)YTITLE= DISPLACEMENT RESPONSE AT OPPSITE CORNERXYPLOT DISP RESPONSE . 55 (T3)$BEGIN BULKPARAM, COUPMASS, 1PARAM, WTMASS, 0.0025 $INCLUED ' plate.bdf '$ SPECIFY STRUCTURAL DIAMPING$ 3 PERCENT AT 250 HZ. = 1571 RAD/SEC$PARAM, G, 0.06PARAM, W3, 1571$ APPLY UNTI PRESSURE LOA

25、D TO PLATE$LSEQ, 100, 300, 400$PLOAD2, 400, 4., 4, THRU, 40$ VARY PRESSURE LOAD (250HZ)$TLOAD2, 200, 300, , 0, 0., 8.E-3, 250., -90.$ APPLY POINT LOAD OUT OF PAHSE WITH PRESSURE LOAD$TLOAD2, 500, 600, , 0, 0., 8.E-3, 250., -90.$DAREA, 600, 11, 3, 1.$ COMBINE LOADS$DLOAD, 700, 1., 1., 200, 50., 500$

26、SPECIFY INTERGRATION TIME STEPS$TSTEP, 100, 100, 4.0E-4, 1$ENDDATA2) MODAL TRANSIENT RESPONSE1.0 psi over the total surface25.0INPUT FILEID SEMINAR, PROB4SOL 112TIME 30CENDTITLE = TRANSIENT RESPONSE WITH TIME DEPENDENT PRESSURE AND POINT LOADSSUBTITLE = USE THE MODAL METHODECHO = UNSORTEDSPC = 1SET 111 = 11, 33, 55DISPLACEMENT(SORT2) = 111SDAMPING = 100SUBCASE 1METHOD = 100DLOAD = 700LOADSET = 100TSTEP = 100$OUTPUT (XYPLOT)XGRID=YESYGRID=YESXTITLE= TIME (SEC)YTITL