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Comparison of Test and Analysis

Comparison of Test and Analysis. Modal Analysis and Testing S. Ziaei-Rad. Objectives. Objectives of this lecture:

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Comparison of Test and Analysis

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  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. S. Ziaei-Rad

  3. 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 S. Ziaei-Rad

  4. Strategy For Model Validation S. Ziaei-Rad

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

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

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

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

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

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

  11. Correlation Of Modal Properties2- Mode Shapes (numerical correlation) Modal scale factor (MSF) - slope of best-fit line from {f}1 vs {f}2 plot Or if we take the experimental mode as reference If If S. Ziaei-Rad

  12. Correlation Of Modal Properties2- Mode Shapes (numerical correlation) • Mode Shape Correlation • Coefficient, or Modal • Assurance Criterion (MAC) • scatter of points about best fit line: • Or • If • If S. Ziaei-Rad

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

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

  15. Data for Correlated Modes S. Ziaei-Rad

  16. 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 S. Ziaei-Rad

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

  18. 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 DOFs AIUTOMAC using subset of DOFs S. Ziaei-Rad

  19. 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 S. Ziaei-Rad

  20. 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 S. Ziaei-Rad

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

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

  23. 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: S. Ziaei-Rad

  24. COMAC - Example 1 S. Ziaei-Rad

  25. COMAC - Example 2 S. Ziaei-Rad

  26. 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 S. Ziaei-Rad

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

  28. Example Of FRAC Plot S. Ziaei-Rad

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