1. Modal Analysis Advanced Topics Module 8

2. Training Manual January 30, 2001 Inventory #001447 8-2 Module 8 Modal Analysis - Advanced Topics A. Learn how to do a prestressed modal analysis B. Learn how to take advantage of cyclic symmetry in a modal analysis C. Learn how to perform a modal analysis following a large deflection static analysis

3. Training Manual January 30, 2001 Inventory #001447 8-3 A. Prestressed Modal Analysis What is prestressed modal analysis and why? Modal analysis of a prestressed structure. Some structures show different dynamic behavior depending on their stress state. –A guitar string or a drum head, for example, will vibrate at higher frequencies as its tension is increased. –When a turbine blade spins, its natural frequencies tend to be higher because of the prestress caused by centrifugal forces. To properly design such structures, both stress-free and prestressed modal analyses may be required.

4. Training Manual January 30, 2001 Inventory #001447 8-4 Three main steps: Build the model Prestress the model with a static analysis Do the modal analysis with prestress Build the Model: Same considerations as a normal modal analysis. Remember to specify density with proper units. Prestressed Modal Analysis Procedure

5. Training Manual January 30, 2001 Inventory #001447 8-5 3Build the model Prestress the model with a static analysis Choose analysis type & options: Be sure to activate prestress effects. Loading: Apply the loads causing the prestress. Postprocessing: Review the results to make sure that the proper loads have been applied. Solution > Unabridged Menu > Analysis Options … Prestressed Modal Analysis … Procedure

6. Training Manual January 30, 2001 Inventory #001447 8-6 Prestressed Modal Analysis … Procedure Element Plot - Static Analysis of Prestressed Modal Stress Plot - Static Analysis of Prestressed Modal

7. Training Manual January 30, 2001 Inventory #001447 8-7 3Build the model 3Pre-stress the model with a static analysis Do the modal analysis with prestress Same procedure as a normal modal analysis except that prestress effects must be included when specifying analysis options. Prestressed Modal Analysis … Procedure

8. Training Manual January 30, 2001 Inventory #001447 8-8 Prestressed plateWithout prestress Compare: Prestressed Modal Analysis … Procedure

9. Training Manual January 30, 2001 Inventory #001447 8-9 3Build the model 3Prestress the model with a static analysis 3Do the modal analysis with Pre-stress Prestressed Modal Analysis … Procedure

10. Training Manual January 30, 2001 Inventory #001447 8-10 B. Workshop In this workshop, you will Pre-stress the disc shown below and then determine its natural frequencies. If time permits, determine the natural frequencies and mode shapes of the disc without any Pre- stress and compare the results. See your Dynamics Workshop supplement for details (Pre-stressed Modal Analysis Workshop - Pre-Stressed Disc, Page W-49.).Pre-stressed Modal Analysis Workshop - Pre-Stressed Disc, Page W-49.

11. Training Manual January 30, 2001 Inventory #001447 8-11 C. Modal Cyclic Symmetry What is modal cyclic symmetry? A modal analysis that takes advantage of cyclic symmetry. You can model only one sector, then view mode shapes of the entire structure! –Saves modeling time - no need to model all 360 degrees. –Saves computer time and disk space - fewer elements and DOF. Applications Any structure that is cyclically symmetric: turbines, impellers, rotors, fans, etc.

12. Training Manual January 30, 2001 Inventory #001447 8-12 Modal Cyclic Symmetry Procedure Seven main steps: Model the basic sector Identify cyclic symmetry planes Generate a copy of the basic sector Apply BC’s on both sectors Specify modal analysis type and options Solve using CYCSOL Review results by expanding to 360 degrees

13. Training Manual January 30, 2001 Inventory #001447 8-13 Modal Cyclic Symmetry Model the Basic Sector Basic sector Must be in the global cylindrical system: X radial, Y along , Z axial. Cyclic symmetry planes (or edges): –Must have matching node patterns. You can ensure this by specifying line divisions. –Can be curved. The sector angle modeled, , can be any number as long as the total number of sectors (360/  ) is an integer.

14. Training Manual January 30, 2001 Inventory #001447 8-14 Modal Cyclic Symmetry Identify Cyclic Symmetry Planes 3Model the basic sector Identify cyclic symmetry planes Select nodes along the lowest  angle. Create a component of nodes: Utility Menu > Select > Comp/Assembly > Create Component… No need to create a component for the opposite edge, but it might be useful. Be sure to select everything when done! Components ND0 and ND36

15. Training Manual January 30, 2001 Inventory #001447 8-15 Modal Cyclic Symmetry Generate Copy of Basic Sector 3Model the basic sector 3Identify cyclic symmetry planes Generate copy of basic sector Modal cyclic symmetry requires two copies of the basic sector. First make sure that all nodes and elements in the basic sector are selected. Then use the CYCGEN command (macro). Preprocessor > Cyclic Sector… Only F.E. entities are copied, not solid model entities.

16. Training Manual January 30, 2001 Inventory #001447 8-16 Model the basic sector Identify cyclic symmetry planes Generate copy of basic sector Apply BC’s on both sectors Mainly displacement constraints. Apply on nodes only, not on solid model entities (since the second sector contains only nodes and elements). Select nodes by location, not by numbers. No need to specify symmetry BC (unless you are doing a static analysis for prestress). Modal Cyclic Symmetry Apply BC’s on Both Sectors

17. Training Manual January 30, 2001 Inventory #001447 8-17 Modal Cyclic Symmetry Specify Analysis Type & Options 3Model the basic sector 3Identify cyclic symmetry planes 3Generate copy of basic sector 3Apply BC’s on both sectors Specify analysis type Analysis Type - Modal Main Menu > Solution > New Analysis...

18. Training Manual January 30, 2001 Inventory #001447 8-18 Options: –Block Lanczos method is recommended. –Number of modes extracted (NMODE) is per nodal diameter (explained later). –Constraint equation processing - discussed next. –Expand as many modes as the number extracted. Modal Cyclic Symmetry … Specify Analysis Type & Options

19. Training Manual January 30, 2001 Inventory #001447 8-19 Modal Cyclic Symmetry … Specify Analysis Type & Options Constraint equation processing: Hundreds, even thousands, of constraint equations may be automatically generated between the two cyclic symmetry planes. Processing constraint equations using direct elimination is not efficient. The Lagrange multiplier method is recommended (it is the default). There are two choices: –Quick method is fast but may not give accurate eigenvalues for the higher modes. –Accurate method (default option) is exact but somewhat slower.

20. Training Manual January 30, 2001 Inventory #001447 8-20 Modal Cyclic Symmetry Solve using CYCSOL 3Model the basic sector 3Identify cyclic symmetry planes 3Generate copy of basic sector 3Apply BC’s on both sectors 3Specify analysis type & options Solve using CYCSOL CYCSOL is a macro to generate the necessary constraint equations and obtain the modal solution. Menu path is Solution > Modal Cyclic Sym… NMODE modes are extracted for each nodal diameter. Explained next.

21. Training Manual January 30, 2001 Inventory #001447 8-21 Modal Cyclic Symmetry … Solve using CYCSOL Nodal diameter A diametric line of zero displacement during vibration for a circular membrane (like a COSINE wave). Provides relationship to compute mode shape of entire model from the basic sector results. One nodal diameter typically causes one “wave” around the circumference, two nodal diameters cause two waves, and so on. Each nodal diameter has multiple modes of vibration.

22. Training Manual January 30, 2001 Inventory #001447 8-22 Modal Cyclic Symmetry … Solve using CYCSOL One nodal diameter Notice one diametric line of zero displacement in the UZ contour plot below. An end view of the mode shape is shown on the right.

23. Training Manual January 30, 2001 Inventory #001447 8-23 Modal Cyclic Symmetry … Solve using CYCSOL Two nodal diameters

24. Training Manual January 30, 2001 Inventory #001447 8-24 Modal Cyclic Symmetry … Solve using CYCSOL Three nodal diameters

25. Training Manual January 30, 2001 Inventory #001447 8-25 Modal Cyclic Symmetry … Solve using CYCSOL Four nodal diameters

26. Training Manual January 30, 2001 Inventory #001447 8-26 Modal Cyclic Symmetry … Solve using CYCSOL Zero nodal diameters (axisymmetric mode)

27. Training Manual January 30, 2001 Inventory #001447 8-27 Modal Cyclic Symmetry … Solve using CYCSOL Why is the nodal diameter range important? For each nodal diameter ANSYS will extract a specified number of modes. The user controls the range of nodal diameters for each of which modes are extracted. Minimum nodal diameter number is 0 ( “breathing mode”). Maximum nodal diameter value is (NSECTOR/2) for even number of sectors or ( NSECTOR-1)/2 for odd number number of sectors. Usually, the first few modes are extracted for the whole range of nodal diameters to cover all the low frequency modes.

28. Training Manual January 30, 2001 Inventory #001447 8-28 Modal Cyclic Symmetry Review Results over 360º 3Model the basic sector 3Identify cyclic symmetry planes 3Generate copy of basic sector 3Apply BC’s on both sectors 3Specify analysis type & options 3Solve using CYCSOL Review results over 360º Use the General Postprocessor (POST1). Four main steps: –List frequencies. –Specify number of sectors needed for expansion to 360º. –Read in results for the desired mode. –Animate the mode shape.

29. Training Manual January 30, 2001 Inventory #001447 8-29 Modal Cyclic Symmetry … Review Results List frequencies: General Postproc > Results Summary… Each nodal diameter is stored as a separate load step. Nodal diameter 0, modes 1-5 Nodal diameter 1, modes 1-5 Nodal diameter 2, modes 1-5 Nodal diameter 3, modes 1-5 Nodal diameter 4, modes 1-5 …scroll down to see more

30. Training Manual January 30, 2001 Inventory #001447 8-30 Modal Cyclic Symmetry … Review Results Specify number of sectors needed for 360º: Type the command EXPAND,n where n is the number of sectors. Actual expansion is done upon reading in the results. Read in results for the desired mode, using the SET command or “By Load Step…” Nodal diameter. LSTEP=1 means nodal diameter 0 in this case. Mode number

31. Training Manual January 30, 2001 Inventory #001447 8-31 Animate the mode shape PlotCtrls > Animate > Mode Shape... Modal Cyclic Symmetry … Review Results

32. Training Manual January 30, 2001 Inventory #001447 8-32 Modal Cyclic Symmetry … Review Results

33. Training Manual January 30, 2001 Inventory #001447 8-33 Modal Cyclic Symmetry … Review Results

34. Training Manual January 30, 2001 Inventory #001447 8-34 Modal Cyclic Symmetry … Review Results

35. Training Manual January 30, 2001 Inventory #001447 8-35 Modal Cyclic Symmetry … Review Results

36. Training Manual January 30, 2001 Inventory #001447 8-36 Modal Cyclic Symmetry … Review Results Compare cyclic symmetry and full solutions: –Frequencies match well. –Notice that the lower modes are the first few modes for each nodal diameter. –560 elements and 1960 active DOF vs. 2800 elements and 18560 active DOF. –The symmetry model requires less than half the CP time for solution. –Results file size: 1.3 MB vs. 4.2 MB. 36  Symmetry ModelFull 360  Model

37. Training Manual January 30, 2001 Inventory #001447 8-37 Modal Cyclic Symmetry D. Workshop In this workshop, you will model one tooth of the spiral bevel gear shown to determine its natural frequencies. See your Dynamics Workshop supplement for details ( Modal Cyclic Symmetry Workshop - Spiral Bevel Gear, Page W-54. ). Modal Cyclic Symmetry Workshop - Spiral Bevel Gear, Page W-54.

38. Training Manual January 30, 2001 Inventory #001447 8-38 E. Large Deflection Modal Analysis What is large deflection modal analysis? Modal analysis of a structure that has undergone significant geometry change due to loads. Some applications include –When pressure or spin load is applied to a relatively thin turbine blade, it tends to untwist the airfoil affecting natural frequency. –Undersea pipeline installations where contact with seabed causes change in frequencies. –Membranes under pressure load.

39. Training Manual January 30, 2001 Inventory #001447 8-39 What is the difference between large deflection modal analysis and prestressed modal analysis? Prestressed modal assumes that stresses will affect the natural frequencies but deflections are small; that is the geometry has not changed. Large deflection modal assumes that the geometry is changing significantly due to deformation and that this updated geometry (in addition to the stress) will change the natural frequencies and mode shapes. … Large Deflection Modal Analysis Contact and large deflection

40. Training Manual January 30, 2001 Inventory #001447 8-40 Large Deflection Modal Analysis Procedure Five main steps: Build the model Run static analysis with large deflection effects turned on Update geometry to the deformed geometry Perform modal analysis using partial solve procedures Review results Build the Model: Same considerations as a normal modal analysis. Remember to specify density with proper units.

41. Training Manual January 30, 2001 Inventory #001447 8-41 Large Deflection Modal Analysis Run Static Analysis 3Build the model Run Static analysis Choose analysis type & options: Be sure to activate both prestress and large deflection effects. Loading: Apply the static loads. Follow guidelines from Chapter 8, Structural Analysis Guide Solve Solution > Unabridged Menu > Analysis Options …

42. Training Manual January 30, 2001 Inventory #001447 8-42 Large Deflection Modal Analysis Update Geometry to deformed shape 3Build the model 3Run static analysis with large deflection effects Update geometry Add displacements from static analysis to the original geometry. This creates the new geometry on which modal analysis will be carried out.

43. Training Manual January 30, 2001 Inventory #001447 8-43 3Build the model 3Run static analysis with large deflection effects 3Update geometry to the deformed geometry Perform modal analysis using partial solve procedures Step 1. Analysis type and options Step 2. Triangularize the matrix ( PSOLVE,TRIANG) Step 3. Compute eigenvalues ( PSOLVE,EIGLANB) Step 4. Expand mode shapes ( PSOLVE,EIGEXP) Large Deflection Modal Analysis Perform modal analysis

44. Training Manual January 30, 2001 Inventory #001447 8-44 Large Deflection Modal Analysis … Perform Modal Analysis Step 1. Analysis type and options –Set analysis type to Modal –Select mode extraction method ( Block Lanczos recommended) –Select the number of modes to extract

45. Training Manual January 30, 2001 Inventory #001447 8-45 Large Deflection Modal Analysis … Perform Modal Analysis Step 2. Triangularize the matrix (PSOLVE,TRIANG) Solution > -Solve- Partial Solu …

46. Training Manual January 30, 2001 Inventory #001447 8-46 Large Deflection Modal Analysis … Perform Modal Analysis Step 3. Compute eigenvalues (PSOLVE,EIGLANB)

47. Training Manual January 30, 2001 Inventory #001447 8-47 Step 4. Expand mode shapes This is done as a separate pass (issue FINISH and get back into Solution) Turn expansion key ON Large Deflection Modal Analysis … Perform Modal Analysis

48. Training Manual January 30, 2001 Inventory #001447 8-48 Large Deflection Modal Analysis … Perform modal analysis Step 4. Expand mode shapes (…continued) Select how many modes to expand

49. Training Manual January 30, 2001 Inventory #001447 8-49 Large Deflection Modal Analysis … Perform modal analysis At this point the user will have a standard modal analysis results file. Step 4. Expand mode shapes (…continued) Perform partial solution to expand modes

50. Training Manual January 30, 2001 Inventory #001447 8-50 Mode 4, Frequency= 585.631 Hz Mode 2, Frequency = 151.584 Hz Mode 6, Frequency=881.08 Hz Large Deflection Modal Analysis Review results

51. Training Manual January 30, 2001 Inventory #001447 8-51 Large deflection modal analysis –The mode shapes are based on deformed geometry. –You should remember that nonlinearities are ignored and contact elements retain their initial status at the start of the modal analysis. – For instance, only modes where the beams are in contact with each other will be extracted in the example used in this chapter. –With contact elements sliding motion may be allowed depending on the value of coefficient of friction used. –Use “Rough Contact” (keyopt(12)=1) to prevent sliding motion. Large Deflection Modal Analysis … Review results