1. Comparison of Test and Analysis Modal Analysis and Testing S. Ziaei-Rad

2. Objectives Objectives of this lecture: to review some of the different types of structural models which are derived from modal tests; to discuss some of the applications to which the model obtained from a modal test can be put; to prepare the way for some of the more advanced applications of test-derived models.

3. S. Ziaei-Rad Applications Of Test-derived Models comparison with theoretical model correlation with theoretical model correction of theoretical model structural modification analysis structural assembly analysis structural optimisation operating response predictions excitation force determination

4. S. Ziaei-Rad Strategy For Model Validation

5. S. Ziaei-Rad Types Of Mathematical Model Spatial modelModal model Response model

6. S. Ziaei-Rad Derivation Of Model From Modal Test Step 1 - measure Step2 - modal analysis  Step 3 - model

7. S. Ziaei-Rad Theory/Experiment Comparison Comparisons possible: (a) FRFs b) Modal Properties Modal Properties -Natural Frequencies -Mode Shapes

8. S. Ziaei-Rad Comparison of Modal Properties 1- Comparison of Natural Frequencies Natural Frequencies Standard Comparison

9. S. Ziaei-Rad Comparison of Modal Properties Mode shapes 2- Mode Shapes (Graphical)

10. S. Ziaei-Rad Comparison of Modal Properties Modes 1,2 & 3 (systematic error) Modes 1,2 & 3 (remeasured) 2- Mode Shapes (Graphical)

11. S. Ziaei-Rad Correlation Of Modal Properties 2- Mode Shapes (numerical correlation) Modal scale factor (MSF) - slope of best-fit line from {  } 1 vs {  } 2 plot Or if we take the experimental mode as reference If

12. S. Ziaei-Rad Correlation Of Modal Properties 2- Mode Shapes (numerical correlation) Mode Shape Correlation Coefficient, or Modal Assurance Criterion (MAC) -scatter of points about best fit line: Or If

13. S. Ziaei-Rad MAC Correlation Between Two Sets Of Modes Experimental Mode Number

14. S. Ziaei-Rad Natural Frequency Plot For Correlated Models.. paired by frequencies.. paired by CMPs

15. S. Ziaei-Rad Data for Correlated Modes

16. S. Ziaei-Rad Effectiveness Of The Correlation Process Some features of the MAC (which affect its effectiveness): lack of scaling (so not a true orthogonality measure) inadequate selection of DOFs inappropriate selection of DOFs Modified versions of the MAC: the AutoMAC the Mass-Normalised MAC the Selected-DOF MAC

17. S. Ziaei-Rad Inadequate Selection of Dofs in Mac MAC using all DOFsMAC using subset of DOFs

18. S. Ziaei-Rad Use of Automac to Check Adequacy of DOFs AUTOMAC is the MAC computed from the correlation of a set of vectors with themselves AIUTOMAC using all DOFsAIUTOMAC using subset of DOFs

19. S. Ziaei-Rad Use of Automac to Check Adequacy of DOFs a- Automac(A) for full set of 102 DOFs b- Automac(A) for reduced set of 72 DOFs c- Automac(A) for reduced set of 30 selected DOFs d- Automac(X) for reduced set of 30 selected DOFs e- MAC for reduced set of 30 DOFs

20. S. Ziaei-Rad Normalised Version Of The Mac Mass-normalised MAC can be computed using the analytical mass matrix from: -Weighting matrix W, can be provided either by mass or stiffness matrices of the system. -The difficulty is the reduction of the mass or stiffness matrices to the size of the measured DOF -A Guyan type or a SEREP-based reduction can be used. If SEREP used then a pseudo-mass matrix of the correct size can be calculated as

21. S. Ziaei-Rad Normalised Version Of The Mac Approximate mass-normalised MAC (SCO) can be computed using the active modal properties only: SCO = SEREP-Cross-Orthogonality

22. S. Ziaei-Rad Normalised Mac - Features AUTOMAC for test caseAUTOSCO for test case

23. S. Ziaei-Rad Error Location - The COMAC -COMAC is a means of identifying which DOFs display the best or the worse correlation across the structure. -COMAC uses the same data as is used to compute the MAC but it performs the summation of all contributions (one from each DOF for each mode pair) across all the mode pairs instead of across all the DOFs (as is done in the MAC) -COMAC is defined as:

24. S. Ziaei-Rad COMAC - Example 1

25. S. Ziaei-Rad COMAC - Example 2

26. S. Ziaei-Rad Correlation Of Other Parameters: Frequency Response Functions The Assurance Criterion concept can be applied to any pairs of corresponding vectors (not only mode shape vectors) including FRFs - to give the FRAC - and also to vectors of Operating Deflection Shapes, in situations where modal properties are difficult to obtain

27. S. Ziaei-Rad Correlation Of Other Parameters: Frequency Response Functions Frequency Response Assurance Criterion:

28. S. Ziaei-Rad Example Of FRAC Plot