第十章响应谱 10.1概述 (1)响应谱是将单自由度系统的最大响应描述为基础激励的共振频率的函数 esponse Resonant Frequency(Hz (2)响应一般形式 0.0 1.0 MAX lB(t) Point on larger, vibrating structure Response computed for transient analysis (3)每个单自由度振子的峰值响应由x(t)计算,振子的运动uB由力或作用到大结构上 的基础激励给出 Example: An earthquake time history is applied to a power plant. Response spectra are calculated at the locations of the floors to be used in the design of components (i.e, machinery and piping systems). (4)假设为振子的质量与振动质量相比非常小,因此两者间无动态干扰 (5)阻尼作用到每个振子上,而不是作用到振动结构上 1 damping=0% critical Response 2 damping 3% critical 3 damping 5% critical Resonant Frequency(Hz) (6)每个振子的最大位移响应由X(t)计算,在振子和其基座间(振动结构上的一个点)
第十章 响应谱 10.1 概述 (1) 响应谱是将单自由度系统的最大响应描述为基础激励的共振频率的函数 (2) 响应一般形式 (3) 每个单自由度振子的峰值响应由 x(t)计算，振子的运动 uB由力或作用到大结构上 的基础激励给出 (4) 假设为振子的质量与振动质量相比非常小，因此两者间无动态干扰。 (5) 阻尼作用到每个振子上，而不是作用到振动结构上 (6) 每个振子的最大位移响应由 X(t)计算，在振子和其基座间（振动结构上的一个点）
的相对位移也这样计算 X maximum intertial (absolute) displacement Xr= maximum relative displacement ZETA=. 05 SDOF RESPONSE TO 4 HZ SINE PULSE 995.1 SINE 2 HZ SY.327 4 HZ SY 1.000 moz0m 1145 2.726 1.518 10 HZ SYS 1.039 20 HZ SYS1.068 40 HZ SYS 0.0 1195 1.016 999.7吨 1490 SHOCK SPECTRUM OF 4 HZ PULSE FOR ZETA = 05 2.73 4.025 1.2092.731 1.5021.037 ozmm0卫 3? 10.00 7422 100200 (7)对低频振子(O→0) X→0
的相对位移也这样计算 (7) 对低频振子（ →0 ）
(8)对高频振子(O→∞) 10.2响应谱求解控制 (1)输入 a)执行控制 SoL command selecting a transient solution(e. g, SOL 109) b)情况控制 XYPLOT SPECTRAL Compute spectra XYPUNCH SPECTRAL Punch spectra 如 XYPUNCH ACCELERATION SPECTRAL 1/1(T1RM) 该命令根据卡片DT, SPSEL的记录1,在结点1处xT)方向产生一组绝对加速度谱 数据模型 PARAM, RSPECTRA,0 Requests calculation of spectra DTL. SPSEL Correlates frequency and damping requests FREQ Used to specify frequencies and damping values(one FREQ set each (2) Example Input Sample Input PARAM RSPECTRA O $ s Tells MSC/NASTRAN to perform spectra creation $ S RECNO DAMP FREQ G1 G2 G3 G4 DTI SPSEL 1121234+SPSEL +SPSEL1 ENDREC s Tells the program that if RECNo 1 is selected by the XYPLOT command, s then DAMPing set 1 and FREQuency set 2 are to be used for GRIDs 1, 2, 3, and 4 (if requested) FREQ10..01.02 s This is the FREQ entry used by sPsel rEcNo 1 to specify damping ratios s to be used In this case, spectral will be generated for damping
(8) 对高频振子 ( → ) 10.2 响应谱求解控制 （1） 输入 a) 执行控制 b) 情况控制 如： 该命令根据卡片 DT1，SPSEL 的记录 1, 在结点 1 处 x(T1)方向产生一组绝对加速度谱 c) 数据模型 （2） Example Input Sample Input PARAM RSPECTRA 0 $ $ Tells MSC/NASTRAN to perform spectra creation $ $ RECNO DAMP FREQ G1 G2 G3 G4 DTI SPSEL 1 1 2 1 2 3 4 +SPSEL1 +SPSEL1 ENDREC $ $ Tells the program that if RECNO 1 is selected by the XYPLOT command, $ then DAMPing set 1 and FREQuency set 2 are to be used for GRIDs 1, $ 2,3, and 4 (if requested) $ FREQ 1 0. .01 .02 $ $ This is the FREQ entry used by SPSEL RECNO 1 to specify damping ratios $ to be used. In this case, spectral will be generated for damping
s ratios of 0%, 1%, and 2% of critical FREQ12.5.5200 s This is the FREQ entry used by SPSEL RECNo 1 to specify the s frequencies at which data points on the spectra will be s generated. In this case, spectra points will be generated s for oscillators with natural frequencies of. 5Hz to 100. 5Hz s by increments of 5 Hz 10.3响应谱应用 1)应用于S0L103 (b)“ Poor mans' transient”用于确定每阶模态的峰值响应 (c)峰值模态响应组合得到系统响应 (d)组合模态响应有三中方法(ABS,SRSS,NRL) 2)过程 (a)在结构上找出输入点的 SUPORT DOF (b)附加大质量到该 SUPORT DOF (c)得到 SUPORT DOFS未约束系统模态(包括0.0Hz模态) (d)估计附加在激励结构上的自由模态 3)应用 (a)X-为单自由度振子由于基座运动引起的响应 x十90x+2x=i(t) 在物理点实际响应为 uk(t)=∑∑kvx,9t 对ABS方法 uk=∑∑9kWx(9P 其中 Xri(oj g)=max xri(o g; t) I代表模态,r代表方向 对SRSS方法
$ ratios of 0%, 1%, and 2% of critical $ FREQ1 2 .5 .5 200 $ $ This is the FREQ entry used by SPSEL RECNO 1 to specify the $ frequencies at which data points on the spectra will be $ generated. In this case, spectra points will be generated $ for oscillators with natural frequencies of .5Hz to 100.5Hz $ by increments of .5 Hz 10.3 响应谱应用 1）应用于 SOL 103 （b） “Poor mans’ transient.” 用于确定每阶模态的峰值响应 （c） 峰值模态响应组合得到系统响应 （d） 组合模态响应有三中方法(ABS,SRSS, NRL) 2) 过程 （a） 在结构上找出输入点的 SUPORT’ DOF （b） 附加大质量到该 SUPORT’ DOF. （c） 得到 SUPORT DOFs 未约束系统模态(包括 0.0 Hz 模态) （d） 估计附加在激励结构上的自由模态 3) 应用 (a) Xr为单自由度振子由于基座运动引起的响应 在物理点实际响应为 对 ABS 方法 其中， I 代表模态，r 代表方向 对 SRSS 方法
2 rik Si 其中, vrxr(1,91) 对NRL方法 k= jksj ik 其中 ikSj is the peak modal magnitude 10.4求解控制 (1)执行控制 SOL statement selecting SoL 103 (2)情况控制 SDAMP To select modal damping ratios DLOAD To select input spectra METHOD To select eigenvalue solver 例 METHOD=1 Selects eigenvalue solution method 1 from the Bulk Data(be sure that the range includes 0.0) SDAMP =1 Selects modal damping to be used for the calcu- lated modes. Refers to a TABDMP1 entry in the Bulk Data DLOAD 1 Selects DLOAD Bulk Data entry that describes which spectra are applied at which ' SUPORT (3)数据模型
其中， 对 NRL 方法 其中， 10.4 求解控制 （1） 执行控制 （2） 情况控制 例： （3） 数据模型
PARAM, SCRSPEC, o Requests application of response spectra DLOAD Selects spectra and‘ SUPORT’ DOF at which to apply them DTI, SPECSEL Selects spectra, states associated damping and type of spectrum TABLED1 Provides input spectra Selects spectrum input locations TABDMP1 Describes modal damping for the calculated PARAM OPTION Selects modal combination method 输入示范 SUPORT 13 s Define input dof for the spectra -in this case, dof 3 for GRID 1 is selected coNM21001301000000 s apply large masses in the directions of the spectra input $ TABDMP1 1 CRIT +DMP1 +DMP10.0.01100..01100.01.021000..02+DMP2 +DMP2 ENDT s Select damping ratios for the calculated modes-in this case, a ratio of 1% of ctrtical s is used for all modes from ohz to 100hz and 2% of critical is used for all modes above 10001h PARAM SCRSPEC 0 s Tells MSC/NASTRAN to perform shock spectrum analysis S DEFINE WHERE AND HOW TO APPLY SPECTRA S NOTE THAT SPECTRA ARE APPLIED USING INTERNAL SORT.NOT ASCENDING S ORDER S SID S S1 L1 S2 L2 DLOAD11.01.01 $ Define where spectra are to be applied -this entry is called from Case Control by a$DLOAD=1 command-for this entry, an overall scale factor of 1.0(s)is applied, s a factor of 1.0 (s1)is used to apply spectrum 1(L1)at'SUPORT'dof 1
输入示范 SUPORT 1 3 $ $ Define input dof for the spectra - in this case, dof 3 for GRID 1 is selected $ CONM2 1001 3 0 1000000. $ $ apply large masses in the directions of the spectra input $ TABDMP1 1 CRIT +DMP1 +DMP1 0.0 .01 100. .01 100.01 .02 1000. .02 +DMP2 +DMP2 ENDT $ $ Select damping ratios for the calculated modes - in this case, a ratio of 1% of ctrtical $ is used for all modes from 0hz to 100hz and 2% of critical is used for all modes above $ 100.01hz $ $ PARAM,SCRSPEC,0 $ Tells MSC/NASTRAN to perform shock spectrum analysis $ DEFINE WHERE AND HOW TO APPLY SPECTRA $ $ NOTE THAT SPECTRA ARE APPLIED USING INTERNAL SORT...NOT ASCENDING $ ORDER $ $ SID S S1 L1 S2 L2 .... DLOAD 1 1.0 1.0 1 $ $ Define where spectra are to be applied - this entry is called from Case Control by a $ ’DLOAD=1’ command - for this entry, an overall scale factor of 1.0 (S) is applied, $ a factor of 1.0 (S1) is used to apply spectrum 1 (L1) at ’SUPORT’ dof 1
$ $(It should be noted that the order of the 'SUP ORT dof used on this s entry is the MSC/NASTRAN internal sort. If only one GRid point is used s this is no problem, but if more than one GRId point is used s then PARAM, USETPRT, 1 should be used to obtain the internal order DTI SPECSEL O DTI SPECSEL 1A 20.03.01+SP1 +SP14.02 $ s This table defines the relationship between the input tables $(from the spectrum creation run)and the spectra sets. For example, s record 1 defines a spectra set representing acceleration spectra s containing spectrum 2 for 0% of critical damping, spectrum 3 for 1% of s critical damping and spectrum 4 for 2% of critical damping s The program will interpolate between the spectra if a mode has a s damping value other than those defined in the table $ S GRID Component(XYPLOT terminology) 0.000000E+00 TABLED1 2 53.15641.0.0012631.5.0028422..005056 2.5.0079053..0113933.5.0155244..020303 4.5.0257385..0318395.5.0386156..046073 6.5.0542197..0630527.5.0725698..082766 100.53.87229ENDT s Table representing the input spectra
$ $ (It should be noted that the order of the ’SUPORT’ dof used on this $ entry is the MSC/NASTRAN internal sort. If only one GRID point is used, $ this is no problem, but if more than one GRID point is used, $ then PARAM,USETPRT,1 should be used to obtain the internal order) $ DTI SPECSEL 0 DTI SPECSEL 1 A 2 0.0 3 .01 +SP1 +SP1 4 .02 $ $ This table defines the relationship between the input tables $ (from the spectrum creation run) and the spectra sets. For example, $ record 1 defines a spectra set representing acceleration spectra, $ containing spectrum 2 for 0% of critical damping, spectrum 3 for 1% of $ critical damping, and spectrum 4 for 2% of critical damping. $ The program will interpolate between the spectra if a mode has a $ damping value other than those defined in the table. $ $ GRID Component (XYPLOT terminology) $ACCE 0 1 3 1 $ 0.000000E+00 TABLED1 2 .5 3.156-4 1.0 .001263 1.5 .002842 2. .005056 2.5 .007905 3. .011393 3.5 .015524 4. .020303 4.5 .025738 5. .031839 5.5 .038615 6. .046073 6.5 .054219 7. .063052 7.5 .072569 8. .082766 . . . 100.5 3.87229 ENDT $ Table representing the input spectra