S4-1 SECTION 4 EFFECTIVE MASS NAS122, Section 4, August 2005 Copyright 2005 MSC.Software Corporation

S4-2 NAS122, Section 4, August 2005 Copyright 2005 MSC.Software Corporation

S4-3 NAS122, Section 4, August 2005 Copyright 2005 MSC.Software Corporation n n Until some kind of loading is applied, either transient or frequency response, it is very difficult to predict which modes will play a dominant role in the response of a structure. n n One method to help predict what the important modes are is to calculate what is called modal participation factors. These factors are used for enforced (base) motion. n n Linear combinations of eigenvectors can be used to define any vector. This is because eigenvectors calculated in a normal modes analysis are linearly independent of each other and span the vector space used to define the model response. n n A rigid body vector can be constructed from a set of flexible body eigenvectors, with it having motion in a desired direction. n n A rigid body vector {D} R Use, where { is a vector of scaling factors for the eigenvectors in. PARTICIPATION FACTOR THEORY

S4-4 NAS122, Section 4, August 2005 Copyright 2005 MSC.Software Corporation Pre-multiply the expression for {D} R by [ T [M] u u where [m] is the diagonal matrix of generalized masses for the normal modes. The term [ T [M]{D} R is commonly known as the participation factor, { }. The scaling factor i multiplies the generalized mass m ii to define the participation factor i. n n The relationship between the rigid body vector {D} R and the corresponding rigid body mass, M R, is PARTICIPATION FACTOR THEORY (Cont.)

S4-5 NAS122, Section 4, August 2005 Copyright 2005 MSC.Software Corporation n n Using n n Then So the contribution which the i-th mode provides to the rigid body mass M R is i 2 m ii n n This is known as the modal effective mass. Mass Normalize the eigenvectors, [ ] T [M][,so the participation factors are i = i, and the modal effective mass is i n n The modal effective weight is modal effective mass factored by g with the appropriate units. PARTICIPATION FACTOR THEORY (Cont.)

S4-6 NAS122, Section 4, August 2005 Copyright 2005 MSC.Software Corporation The command has the following form: Examples: MEFFMASS MEFFMASS(GRID=12, SUMMARY,PARTFAC) DescribersMeaning PRINTWrite 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 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 ENTRY

S4-7 NAS122, Section 4, August 2005 Copyright 2005 MSC.Software Corporation DescribersMeaning PARTFACRequests calculation of Modal Participation Factors. MEFFMRequests calculation of Modal Effective 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.)

S4-8 NAS122, Section 4, August 2005 Copyright 2005 MSC.Software Corporation Mode Shape and Frequencies for the 10 Normal Modes analyzed. n n Revisit the Satellite Structure to assess the Participation Factors and Modal Effective Mass CASE STUDY

S4-9 NAS122, Section 4, August 2005 Copyright 2005 MSC.Software Corporation Setup a Normal Modes analysis similar to the run in Case Study 2. CASE STUDY

S4-10 NAS122, Section 4, August 2005 Copyright 2005 MSC.Software Corporation Using Direct Text Input, include the following case control entry into the.bdf file: MEFFMASS(ALL)=YES This will tell MSC.Nastran to calculate the effective mass participation for each of the normal modes calculated. CASE STUDY

S4-11 NAS122, Section 4, August 2005 Copyright 2005 MSC.Software Corporation Once 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 Body Vectors respectively. CASE STUDY

S4-12 NAS122, Section 4, August 2005 Copyright 2005 MSC.Software Corporation n n What do these tables mean ? n n The Modal Effective Mass Fraction is the amount each mode contributes to the total Rigid-Body Mass. n n 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: n n In our case the contribution in the T1 or x direction from Mode 1 and Mode 2 dominates at and The running total is.4768 after these two modes and.4942 for all ten modes. n n The contribution in the T2 or y direction is similar with Mode 1 and Mode 2 swapping contributions and a total of.4951 for all ten modes. This is because of the near orthogonality of the modes. n n The contribution in T3 or z is negligible. CASE STUDY

S4-13 NAS122, Section 4, August 2005 Copyright 2005 MSC.Software Corporation n n It 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 structure. 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 STUDY

S4-14 NAS122, Section 4, August 2005 Copyright 2005 MSC.Software Corporation The third table shows the Modal Participation Factors for the Translational and Rotational Rigid Body Vectors. The totals are summed in each direction CASE STUDY

S4-15 NAS122, Section 4, August 2005 Copyright 2005 MSC.Software Corporation n n What do these tables mean ? n n The modal participation factor is defined on Page 4-4 Eigenvectors are mass normalized, so CASE STUDY

S4-16 NAS122, Section 4, August 2005 Copyright 2005 MSC.Software Corporation n n What do these tables mean ? (continued) n n Eigenvectors are mass normalized, so (continued) MSC.Nastran calculates all the value of the participation factors with respect to the normal modes, which results in m ii =1 regardless of the method chosen to normalize the modes, in order to get always comparable values. The sign of the participation factors will be the only difference between different normalization methods. CASE STUDY

S4-17 NAS122, Section 4, August 2005 Copyright 2005 MSC.Software Corporation n n What do these tables on the next slide mean ? n n The Modal Effective 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. n n So in the case over page the total mass is 1.15 in x and 1.15 in y. n n Total weight is lbs in x direction and lbs in y direction. n n 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 STUDY

S4-18 NAS122, Section 4, August 2005 Copyright 2005 MSC.Software Corporation CASE STUDY = PF i 2 = (1.0/WTMASS) * PF i 2

S4-19 NAS122, Section 4, August 2005 Copyright 2005 MSC.Software Corporation n n The values calculated are used by different industries in different ways: u u For example, in Civil Engineering seismic analysis: l l The contribution from each mode is assessed as a percentage and the total is summed. l l Any shortfall from 100% is classified as missing mass. l l If the missing mass is significant then it may indicate errors in the analysis, typically insufficient modes being used in a modal method. l l Missing mass is often characterized as higher frequency body type loading and can be simulated by applying a 1g inertia load in the appropriate direction, factored by the % missing mass, added as a static load. This is done outside Nastran. APPLICATIONS IN INDUSTRY

S4-20 NAS122, Section 4, August 2005 Copyright 2005 MSC.Software Corporation WORKSHOP 19 EFFECTIVE MASS n Please carry out Workshop 19, which assesses the normal modes of a cantilever beam as described in Section 2, but also includes the effective Mass parameter. n Attempt to asses the meaning of the tables output in the.f06 file. n Note: There are no repeated roots in that case so the assessment is easier, but note carefully the values and meaning of the X direction results.