Applies To Product(s): AutoPIPE, Version(s): 2004, XM, & V8i Environment: N/A Area: Frequency Results Subarea: Original Author: Bentley Technical Support Group Comments, Questions, and Answers with AutoPIPE's Output "Mode Shape" Sub Report: Item #1: Notes #1: Natural frequency and mode shapes are property of the structure and depend on the mass and elasticity. They describe the tendency of the structure to vibrate when subjected to dynamic loading. Number of frequencies and mode shapes with which a structure can vibrate depends on the number of mass degrees of freedom in the structure. Mode shapes describe relative displacement of the structure (mass normalized). Number of mode shapes and frequencies required depends on the frequency of the applied load. #2: Mode shape #1 occurs at a frequency, that is the fundamental frequency or the 1st natural frequency. Each mode shape after that frequency up to the cut-off frequency are additional natural frequencies of the system. #3: The participation factors are the mass participation factors which are used directly in a dynamic analysis to calculate the dynamic response. The sum of the participation factors times the mode shape at each natural frequency should equal 1. The mass participation factors indicate an amount of the lump mass in the system which contributes to the mode shape. Typically the higher values of mass participation factors appear in the first modes. These Participation Factors are normalized by the equation: However, not to be confused with mass normalized which means that the modal displacements are divided by the the following transformation: Participation Factors are not so much as an indication of percentage of mass associated with each mode, but more the actual lumped mass in the system associated with each mode. One reference book is "dynamics of structures" by Klough and Penzien #4: When looking at the frequency output report, the last column on the far right (Percent Average) provides the user with how much of the mode shape is contributing to the total captured mass of the system. As an iterative approach the modal analysis settings "cut-of frequency" in the model can be incrementally increased to achieve a suggested total of between 75% - 100% participation. As higher cut-off frequencies are entered there will be a point where the higher modes do not contribute as much to the total vs the lower modes. Therefore, no need to analyze with any higher modes as they are not contributing to the results. Item #2: What options are available to increase the participation factors in a model with multiple disconnected systems? Answer: The participation factors can be increased by increasing number of mass points so that missing mass at the supports is minimized. However, that may not be effective for all models. Another way to have more mass is to add more modes up to the limit of 999. Change the Modal analysis setting for number of modes to 999, before analyzing the model In large models with multiple disconnected systems (segments that represent other systems of piping not all connected in one group, check groups of segments by pressing Select> Connected Segment> provides a list of segment groups or disconnected segments) another more effective way is to reduce the model size, so that more modes can be analyzed in a smaller model. If needed, create a new model for each disconnect found in the original model. If some of these disconnected piping has a much larger frequency, then you will not get a single mode for that subsystem and the analysis may not be correct even if there model achieves 95% modal participation. For ZPA option, this options will essentially impose a static force just like static earthquake analysis and would apply to subsystems with no frequencies. Subdividing the model is more important for shock or water hammer type of loading since the loading have a higher frequency. Item #3: Why a simple cantilever system doesn't match hand calculations I have built a very simple cantilever model for verification of the calculation of natural frequency of a piping system. To verify the accuracy of AutoPIPE v8i frequency calculations, I used the following model: The pipe section chosen was 4" STD (sch 40) pipe with OD 4.5", ID 4.026", with no corrosion allowance and a density of 0 for the contents. The material chosen was API5L?B at a room temperature of 70 deg F. The model was built using a single element, with one end rigidly fixed in all directions and the other end free. The modal run resulted in a natural frequency of 32.6473 Hz. Please see attached output from AutoPIPE. Hand Calculation This simple model can be hand calculated using standard published formulas in closed form. The hand calculated natural frequency is 47.12 Hz as follows: C is a constant that is 3.52 for the 1st mode. E = 29.5x106 psi. I = 7.23259 in4, w = 10.78 lb/ft = 0.898 lb/in. g = 386 in/sec2. L = 60". ANSYS FEA Comparison I built a model of the same system with ANSYS 11.0. With this model, I get 47.22 Hz using a single element model as well that is identical as far as I can tell to the AutoPIPE model. Discussion I would expect the AutoPIPE natural frequencies to be lower than using an ANSYS beam model for common systems due to the flexibility of elbows since I don't believe that ANSYS models the elbow flexibility well. However, I would see no reason why the simple cantilever system doesn't match hand calculations Answer: The natural frequency formula assume a uniformly distributed weight. In AutoPIPE the weight is lumped at the nodes. So ½ the weight is placed on each end. In order to simulate the natural frequency, additional mass points can be added. Either actual or automatic points can be added. When the automatic mass point option is used (Tools> Model Options> Edit) with cut-off frequency set at 200 Hz, the first mode frequency will be 44.5. When the cut-off frequency is higher at 2000 Hz, the frequency becomes 46.4 Hz. Item #4: Why does AutoPIPE state that the frequency for all the pipe runs are the same? I am modeling large runs of overland piping and I have tried to perform a modal analysis to find out the frequency of the piping. Result: The frequency for the whole pipeline is said to be the same! Question: Practically the pipe runs between different anchors and different segments should have a different frequency due to the different stiffness and weight plus the pipelines should not interact with each other across anchors and for completely different segments? Answer: AutoPIPE solves the whole system and so mode shape 1, if spans are the same, would be a common frequency. The development team suggested that you have one or more intermediate nodes between anchors to see the different modes. AutoPIPE does have an option to add automatic mass points in Tools> Model Options> Edit. You can set the automatic mass points option to "A" for auto and enter the cut off frequency on the next line. Having actual physical points will help you visualize the mode shapes better as AutoPIPE does not show the intermediate mass points on the plot or in the animation. Item #5: Can you please provide some more information about the meaning of "total modal mass"? Is a level of 90% always recommended for a dynamic analysis and is it possible to increase this further? How accurate are the results expected to be for a total modal mass of 90%? Because of the difficulties we have had in setting up the AutoPipe model for this type of analysis, we also constructed a beam model using FEA in ABAQUS. This takes more effort to set up but we can get more detailed output such in the attached plot which shows the time history of the lateral reaction forces on one of the guides. As can be seen in the summary below, the reaction forces from a static analysis are very similar. However, the maximum reaction force from the dynamic analysis in AutoPipe is about 90% of the value predicted by the FEA. At this stage I would guess that the FEA is more accurate but do you have any comments? Answer: Please see the following AutoPIPE help section: Help > Contents> Search Tab> enter " Missing Mass and ZPA Correction " (include the quotes), press List Topics button, double click on the selected topic from the list provided to see more information. For information on how modal mass is calculated. The modal mass in the frequency report does not apply to time history loading unless it is earthquake load. The analysis summary report will include the missing and added modal mass. AutoPIPE does not have missing mass option for time history. The ZPA option should be used instead. The total modal mass is a measure of how good are the results, but that does not give a direct measure of accuracy. That is 90% does not mean you have 10% error in the results. In some cases the load frequency is 300 Hz and analyzing with 200 Hz cut-off frequency (with 95% modal mass) can still give very large errors. In order to capture more modal mass, automatic mass points needs to be added in Tools> Model Options> Edit up to cut off frequency. Cut-off frequency should be increased and analysis performed up to cut-off frequency to have more modal contributions. AutoPIPE applies half the mass of attached pipe to anchor point. I am not sure if ABAQUS does that as this may cause some differences. When adding more mass points, anchor or support mass is reduced. Item #6: After running the modal analysis multiple times I get different Participation Factors and Captured Modal Mass but the totals are the same. Answer: This model appears symmetric. without looking at the model, see the frequencies are repeated. This happens for example for a vertical pipe supported on the ground. The first mode vibration can be in any horizontal direction, with same frequency. It will have one X and one Z mode with same frequency. But since X and Z are arbitrary for the structure, any two modes that are orthogonal will be fine and that is the reason the participation factors are changing and that should be fine. If so concerned, AutoPIPE can force the modes to be in X and Z instead of skewed in XZ plane. That can be done if the model is updated with a slightly different support or anchor stiffness in X or Z. e.g instead of RIGID. Recommend using a value close to rigid value. The rigid value is in the Tools>Model Options> edit>. Notice the participation factors are flipped from X to Z to make it orthogonal. See Also Bentley AutoPIPE External Links Bentley Technical Support KnowledgeBase Bentley LEARN Server Comments or Corrections? Bentley's Technical Support Group requests that you please submit any comments you have on this Wiki article to the "Comments" area below. THANK YOU!
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