教程5.13g加密所屬

1、S4-1SECTION 4EFFECTIVE MASS NAS122, Section 4, January 2004Copyright 2004 MSC.Software CorporationTABLE OF CONTENTSPagePARTICIPATION FACTOR THEORY4-3NASTRAN CASE CONTROL ENTRY4-6CASE STUDY4-8APPLICATIONS IN INDUSTRY4-18WORKSHOP 19 EFFECTIVE MASS4-19It is now known that the Eigenvectors preciously ca

2、lculated in Normal Modes Analysis are independent of each other and are arbitrarily scaled.Until some kind of loading is applied either transient or frequency response, then it is very difficult to predict which modes will play a dominant part in a structure.One method to help predict what are the i

3、mportant modes is to use a technique called Modal Participation Factor.It is now known that linear combinations of Eigenvectors can be assembled to make arbitrary shapes. In this case the shape can be made into a Rigid Body Vector in the direction of the response we are interested in.The Rigid Body

4、Vector is DRAssume where e is a vector of scaling factors on the eigenvectors F, i.e. a set of Participation Factors.PARTICIPATION FACTOR THEORYPre Multiply by FTM:Where Mii is the diagonal matrix of generalized masses for each mode The term FTMDR is commonly known as the Participation Factor.The sc

5、aling factor ei is then a scaling on the generalized mass Mii to achieve the Participation Factor.It can also be defined as a rigid body mass Mr, it can be generalized as massButSoPARTICIPATION FACTOR THEORY (Cont.)So the contribution which each mode provides to the rigid body mass Mr is as Mii is a

6、 diagonal matrixThis is known as the modal effective mass.Mass Normalize the so participation Factor is e, Modal Effective Mass is e2The modal effective weight is modal effective mass factored by g in the appropriate units.PARTICIPATION FACTOR THEORY (Cont.)The command has the following form:Example

7、s:MEFFMASSMEFFMASS(GRID=12, SUMMARY,PARTFAC)DescribersMeaningPRINTWrite output to the print file. (Default)NOPRINTDo not write output to the print file.PUNCHWrite output to the punch file.NOPUNCHDo not write output to the punch file. (Default)gidReference grid point for the calculation of the Rigid

8、Body Mass Matrix.SUMMARYRequests calculation of the Total Effective Mass Fraction, Modal Effective Mass Matrix, and the A-Set Rigid Body Mass Matrix. (Default)NASTRAN CASE CONTROL ENTRYDescribersMeaningPARTFACRequests calculation of Modal Participation Factors.MEFFMRequests calculation of Modal Effe

9、ctive Mass in unit of mass.MEFFWRequests calculation of the Modal Effective Mass in units of weight.FRACSUMRequests calculation of the Modal Effective Mass Fraction.NASTRAN CASE CONTROL ENTRY (Cont.)Mode Shape and Frequencies for the 10 Normal Modes analyzed.Revisit the Satellite Structure to assess

10、 the Participation Factors and Modal Effective MassCASE STUDYSetup a Normal Modes analysis similar to the run in Case Study 1.CASE STUDYUsing Direct Text Input, include the following case control entry into the .bdf file: MEFFMASS(ALL)=YESThis will tell MSC.Nastran to calculate the effective mass pa

11、rticipation for each of the normal modes calculated.CASE STUDYOnce MSC.Nastran has finished the analysis, open the .f06 file to examine the tables generated by the insertion of MEFFMASS entry.The first pair of tables show the Modal Effective Mass Fraction for the Translational and Rotational Rigid B

12、ody Vectors respectively.CASE STUDYWhat do these tables mean ?The Modal Effective Mass Fraction is the amount each mode contributes to the total Rigid-Body Mass.This is shown both as a fraction for each mode and a running total or sum for all the modes. Looking just at the translational terms:In our

13、 case the contribution in the T1 or x direction from Mode 1 and Mode 2 dominates at 0.3574 and .1194. The running total is .4768 after these two modes and .4942 for all ten modes.The contribution in the T2 or y direction is similar with Mode 1 and Mode 2 swapping contributions and a total of .4951 f

14、or all ten modes. This is because of the near orthogonality of the modes.The contribution in T3 or z is negligible.CASE STUDYIt turns out that this is a special case because there is a pair of near orthogonal or repeated roots. Mode 1 and 2 are virtually identical, due to the symmetry of the structu

15、re. Both orthogonal modes contribute towards the total. Many of the higher modes are also orthogonal, as a result it is obvious that the contribution in the x AND y direction are summing to an approximate 1.0, i.e. 100% CASE STUDYThe third table shows the Modal Participation Factors for the Translat

16、ional and Rotational Rigid Body Vectors.The totals are summed in each directionCASE STUDYWhat do these tables mean ?The Modal Participation Factor is the factor as defined on 4as as eigenvectors are mass normalized, then PF = e.CASE STUDYWhat do these tables on the next slide mean ?The Modal Effecti

17、ve Mass is the equivalent mass contribution to each mode. The total should sum to the system mass. In order to have a identical Modal Effective Weight a factor of g needs to be multiplied.So in the case over page the total mass is 1.15 in x and 1.15 in y.Total weight is 430.6 lbs in x direction and

18、431.4 lbs in y direction.The actual weight is 872 lbs, and as noted previously two orthogonal modes, 1 and 2 exist, so total effective weight is around 862 lbs.CASE STUDYCASE STUDYThe values calculated are used by different industries in different ways: For example, in Civil Engineering seismic anal

19、ysis: The contribution from each mode is assessed as a percentage and the total is summed.Any shortfall from 100% is classified as missing mass.If the missing mass is significant then it may indicate errors in the analysis, typically insufficient modes being used in a modal method.Missing mass is often cha