1、第11章随机响应分析第11章随机响应分析11.1 动力学环境分类11.2 概述1)随机振动是统计意义下描述的振动,在任何瞬时大小未知,但其大小的概率超过一给定的值。2)常见的例子如地震引起的地基运动、海洋波浪高度和频率、航天器和高耸建筑物受到的风压力、由于火箭与喷气发动机噪音引起的声波等。3)MSC/NASTRAN 对随机响应分析是作为频率响应后处理进行的。输入包括频率响应的输出、用户给定的载荷条件(形式为自相关的谱密度)。输出为响应功率谱密度、自相关函数、响应的均方值。4)MSC/NASTRAN 随机分析假设历经性随机过程5)随机动态环境例子11.3 自相关与自谱1)自相关函数注:Rj(0)
2、为均方值2)自谱函数Fourier变换为3)均方响应值4)外观频率为N06)例子11.4 各态历经性随机激励下线性系统响应计算1) 线性系统单输入输出关系由频率响应分析得到其中,Hja()为频率响应或输入到输出的传递函数对多输入单输出其矩阵形式为输出自相关谱为其单个输入谱为2)线性系统的多输入输出关系多输入输出谱关系其中,输入互谱矩阵为其谱特性为3)常用特殊情况(1)单输入分析(完全相关输入)(2)不相关多输入11.5 MSC/NASTRAN中随机分析的实现1)如果由频率响应计算结果为Hja(),但并不直接计算2)如需要Hja(),令 Fa()=111.5.1RANDPS卡片1)定义随机分析中
3、使用的功率谱密度因子,频率相关形式为2)格式3)由情况控制卡RANDOM = SID选取4)自谱密度,J=K, X为大于0的整数,Y为05)TID=0, G(F)=011.5.2 TABRND1卡片1)用表格函数定义功率谱密度函数2)格式3)11.5.3 随机响应输入要求1)执行控制 2)情况控制3) 模型数据11.5.4 随机响应例子1) 例1:单输入随机响应分析(1)问题描述:(a)矩形板如图;(b)基座运动(z方向)功率谱(PSD)表中给出;(c)整个频率范围的常临界阻尼比为0.03;(d)用log-log输入PSD;(e)使用模态求解法 (2) 使用具有大质量的模态法(在边界处用REB
4、2单元)确定a)9999点处的位移和加速度功率谱(PSD)b)确定结点33和55的位移功率谱(PSD) (3)输入文件ID SEMINAR, PROB10SOL 111TIME 30CENDTITLE= RANDOM ANALYSIS - BASE EXCITATIONSUBTITLE= USING THE MODAL METHOD WITH LANCZOSECHO= UNSORTEDSPC= 101SET 111= 33, 55, 9999ACCELERATION(SORT2, PHASE)= 111METHOD= 100FREQUENCY= 100SDAMPING= 100RANDOM=
5、100DLOAD= 100$OUTPUT(XYPLOT)XTGRID= YESYTGRID= YESXBGRID= YESYBGRID= YESYTLOG= YESXTITLE= FREQUENCYYTTITLE= ACCEL RESPONSE BASE, MAGNITUDEYBTITLE= ACCEL RESPONSE AT BASE, PHASEXYPLOT ACCEL RESPONSE / 9999 (T3RM, T3IP)YTTITLE= ACCEL RESPONSE AT TIP CENTER, MAGNITUDEYBTITLE= ACCEL RESPONSE AT TIP CENT
6、ER, PHASEXYPLOT ACCEL RESPONSE / 33 (T3RM, T3IP)YTTITLE= ACCEL RESPONSE AT OPPOSITE CORNER, MAGNITUDEYBTITLE= ACCEL RESPONSE AT OPPOSETE CORNER, PHASEXYPLOT ACCEL RESPONSE / 55 (T3RM, T3IP)$ PLOT OUTPUT IS ONLY MEANS OF VIEWING PSD DATA$XGRID= YESYGRID= YESXLOG= YESYLOG= YESYTITLE= ACCEL P S D AT LO
7、ADED CORNERXYPLOT ACCEL PSDF / 9999(T3)YTITLE= ACCEL P S D AT TIP CENTERXYPLOT ACCEL PSDF / 33(T3)YTITLE= ACCEL P S D AT OPPOSITE CORNERXYPLOT ACCEL PSDF / 55(T3)$BEGIN BULKPARAM,COUPMASS,1PARAM,WTMASS,0.00259$INCLUDE plate.bdf$GRID, 9999, , 0., 0., 0.$RBE2, 101, 9999, 12345, 1, 12, 23, 34, 45$SPC1,
8、 101, 12456, 9999$CONM2, 6000, 9999, , 1.0E8$MAT1, 1, .1, , .1, .286$ EIGENVALUE EXTRACTION PARAMETERS$EIGRL, 100 , , 2000.$ SPECIFY MODAL DAMPING$TABDMP1, 100, CRIT,+, 0., .03, 10., .03, ENDT$ POINT LOADING AT TIP CENTER$RLOAD2, 100, 600, , , 310$TABLED1, 310,+, 10., 1., 1000., 1., ENDT$DAREA, 600,
9、 9999, 3, 1.E8$ SPECIFY FREQUENCY STEPS$FREQ,100,30.FREQ1,100,20.,20.,50FREQ4,100,20.,1000.,.03,5$ SPECIFY SPECTRAL DENSITY$RANDPS, 100, 1, 1, 1., 0., 111$TABRND1, 111,LOG,LOG+, 20., 0.1, 30., 1., 100., 1., 500., .1,+, 1000., .1, ENDT$ENDDATA(4)部分结果基座的加速度PSD(大小、相位)与频率关系结点55的加速度PSD(大小、相位)与频率关系结点33的加速
10、度PSD(大小、相位)与频率关系例2:多输入随机响应分析问题:输入文件ID SEMINAR, PROB11SOL 111TIME 30CENDTITLE= FREQUENCY RESPONSE WITH PRESSURE AND POINT LOADSSUBTITLE= USING THE MODAL METHOD WITH LANCZOSECHO= UNSORTEDSPC= 1SET 111= 11, 33, 55DISPLACEMENT(PLOT, PHASE)= 111METHOD= 100FREQUENCY= 100SDAMPING= 100RANDOM= 100SUBCASE 1LA
11、BEL= PRESSURE LOADDLOAD= 100LOADSET= 100SUBCASE 2LABEL CORNER LOADDLOAD= 200LOADSET= 100$OUTPUT (XYPLOT)$XTGRID= YESYTGRID= YESXBGRID= YESYBGRID= YESYTLOG= YESYBLOG= NOXTITLE= FREQUENCY (HZ)YTTITLE= DISPLACEMENT RESPONSE AT LOADED CORNER, MAGNITUDEYBTITLE= DISPLACEMENT RESPONSE AT LOADED CORNER, PHA
12、SEXYPLOT DISP RESPONSE / 11 (T3RM, T3IP)YTTITLE= DISPLACEMENT RESPONSE AT TIP CENTER, MAGNITUDEYBTITLE= DISPLACEMENT RESPONSE AT TIP CENTER, PHASEXYPLOT DISP RESPONSE / 33 (T3RM, T3IP)YTTITLE= DISPLACEMENT RESPONSE AT OPPOSITE CORNER, MAGNITUDEYBTITLE= DISPLACEMENT RESPONSE AT OPPOSITE CORNER, PHASE
13、XYPLOT DISP RESPONSE / 55 (T3RM, T3IP)$ PLOT OUTPUT IS ONLY MEANS OF VIEWING PSD DATA$XGRID= YESYGRID= YESXLOG= YESYLOG= YESYTITLE= DISP P S D AT LOADED CORNERXYPLOT DISP PSDF / 11(T3)YTITLE= DISP P S D AT TIP CENTERXYPLOT DISP PSDF / 33(T3)YTITLE= DISP P S D AT OPPOSITE CORNERXYPLOT DISP PSDF / 55(
14、T3)$BEGIN BULKPARAM,COUPMASS,1PARAM,WTMASS,0.00259$ MODEL DESCRIBED IN NORMAL MODES EXAMPLE$INCLUDE plate.bdf$ EIGENVALUE EXTRACTION PARAMETERS$EIGRL, 100, 10., 2000.$ SPECIFY MODAL DAMPING$TABDMP1, 100, CRIT,+, 0., .03, 10., .03, ENDT$ FIRST LOADING$RLOAD2, 100, 300, , , 310$TABLED1, 310,+, 10., 1.
15、, 1000., 1., ENDT$ UNIT PRESSURE LOAD TO PLATE$LSEQ, 100, 300, 400$PLOAD2, 400, 1., 1, THRU, 40$ SECOND LOADING$RLOAD2, 200, 600, , , 310$ POINT LOAD AT TIP CENTER$DAREA, 600, 11, 3, 1.$ SPECIFY FREQUENCY STEPS$FREQ1, 100, 20., 20., 49$ SPECIFY SPECTRAL DENSITY$RANDPS, 100, 1, 1, 1., 0., 100RANDPS,
16、100, 2, 2, 1., 0., 200RANDPS, 100, 1, 2, 1., 0., 300RANDPS, 100, 1, 2, 0., 1., 400$TABRND1, 100,+, 20., 0.1, 30., 1., 100., 1., 500., .1,+, 1000., .1, ENDT$TABRND1, 200,+, 20., 0.5, 30., 2.5, 500., 2.5, 1000., 0.,+, ENDT$TABRND1, 300,+, 20., -.099619, 100., -.498097, 500., .070711, 1000., 0.,+, ENDT$TABRND1, 400,+, 20., .0078158, 100., .0435791, 500., -.70711, 1000., 0.,+, ENDT$ENDDATA