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Output report, subsection - Frequency found the Participation Factor-X =-0, Captured Modal Mass-X = 0 and Cumulative Modal Mass-X = 0, for all calculated natural frequencies, but in anchors there are existing forces greater than 0, FX(Point 10) = 350.87 N and FX(Point 100) = 360.91 N. How can this situation be explained?
The model was found to be a single segment, 100m long on the Global X axis. The pipe has no bends, expansion loops, or is modeled on any other axis except Global X.
As a result the participation factors were reported in the output report as 0.00 for the same pipe axis (Global X), however the actual value may not be 0.00. AutoPIPE is only able to report a number with 2 significant digits. use the following procedure to validate the actual value calculated:
1. Open the model
2. Analyze the model
3. Select Results> Grids
4. Select Frequency Tab in the grid
5. Select any cell in the Participation Factor X column, note that the value is not 0.00 but a very small number, ex: -5.2860372e-011. Some AutoPIPE output reports / grids are not able to show such small values.
Suggestion, confirm actual value calculated using the results grid.
Given a model with a single pipe, modeled between 2 anchors on the Global X axis, the calculated inertial forces and moments in the TEST1 model are FX, FY, FZ (where, FZ=2258.35 N), MX, MY (where, MY=5588.1 N-m) & MZ, for both anchor points 10 and 100, are significantly lower than the inertial forces and moments FX, FY (where, FY=3030.55) FZ, MX, MY (where, MY=8585.51N-m) & MZ calculated in TEST2 model, accordingly.
The only difference between these 2 models is that modal analysis cut of freq = 66 hz for TEST1 & 120 hz to TEST2. Thus, even if more frequencies and their associated modal masses are obtained in the analysis TEST2 model (Fr eq = 120 Hz and 12 modes obtained), the lesser inertial forces and moments values are obtained in anchor points 10 and 100, com paring with TEST1 (Freq = 60.2 Hz and 6 modes obtained), respectively. So, how can this situation be explained?
One issue was that more than a different value for modal analysis was found between the 2 original models. To be absolutely sure that the models are identical, open the 1st model, saved as 2nd model name, and make the changes as required, ex: change modal cut-off frequency from 33hz to 120 hz.
To answer the question, might find that the anchor reaction is more for the model with higher cut-off frequency as it has higher level of discretization and thus able to capture higher modes better.
Analyzing the 2 models TEST1 and TEST2, we observe that for the first 6 vibration modes (Mode No 1 to Mode No 6) each calculation model gives different values for the first 6 calculated frequencies, as well as for the first 6 Participation Factors (in t he X, Y and Z directions) and for the first 6 Captured Modal Mass (in the X, Y and Z directions) respectively. Obviously, the first 6 Cumulated Modal Masses (in the X, Y and Z directions) are also different in the 2 models (TEST1 and TEST2). Furthermore, the first 6 Shape Modes from each model are different. How is this possible, given the identical conditions in the calculation models - except for the different Cutoff Frequencies (66Hz and 120 Hz, respectively)?
One issue was that more than a different value for modal analysis was found between the 2 original models. To be absolutely sure that the models are identical, open the 1st model, saved as 2nd model name, and make the changes as required, ex: change modal cut-off frequency from 33hz to 120 hz. Knowing the files are now identical with exception to changes made, performed a model analysis and Static analysis on both models.
Changing the cut-off frequency when you have Tools> Model Options> Edit> Mass points per span = A option enabled will lead to different level of discretization in the model. That should explain the differences in the frequencies.
Another words, do not expect the first 7 frequencies to be same between the two models as they are no longer "equivalent" - because the level of discretization is not same. The higher the cutoff frequency, the higher the level of discretization.
Cutoff Frequency and Maximum Number of modes
It seems the Cutoff Frequency under the Model Options is always superseded by the values declared under the Dynamic Analysis? When/Where does the Cutoff Frequency under the Model Options control?
Edit Model options .. this cut off frequency is used to calculate the optimal mass span length only when Mass Points per span = A (Auto).
From Online help:
This optimal length is important.
a. If the distance between consecutive node points was less than this calculated optimal length, then NO mass points are added to the span.
b. If the distance between consecutive node points was more than this calculated optimal length, then mass points are added to the span as needed.
If Mass points per span was set to 0 - 9, than that number of mass points are added to each span regardless.
In order to capture the spatial distribution of the inertial loads, the system must be properly discretized. This can be achieved by assuring that mass points in the system are properly spaced. If this criteria is not satisfied, additional points should be added to refine the model. These points will not serve any function other than to provide better mass distribution of the model for dynamic loads.
Are there any (practical ) maximum cut-off frequency values, I tried 100,000 and the following occurred:?
See the following for suggestions to this error message: click here
Estimate the cutoff frequency for my dynamic water hammer analysis?
The maximum frequency cutoff can be estimated from:
E is the modulus of elasticity of the pipe material,
p is the density of the pipe material
L is the length of a single pipe element in the primary run that is to have accurate stresses computed due to the passing of the water hammer originated acoustic stress wave.
Calculation of the maximum cutoff frequency for between 2 elbows (node point 45 & 75) with 20-foot pipe lengths is given as follows:
When performing a modal analysis on the piping system, impulse loading such as water hammer may have high excitation frequencies even as high as 200-300 Hz. For small piping systems, the extraction of high frequency modes is relatively fast and will more accurately predict local dynamic responses than the static correction methods.
What is considered to be low / high frequency values?
There may be no such clear cut separation between high and low frequency phenomenon. Some may suggest:
Low frequency (<300hz)
From Modal Analysis Theory, that modal analysis is performed as a linear analysis but nothing is mentioned about if Buoyancy is considered during the frequency calculations. We did consider added mass in our calculations but it looks like AutoPIPE is using 'weight in air+added mass' instead of 'submerged weight + added mass. Could you please confirm?
For submerged pipe, the buoyancy "Added mass coeff" increases the mass of the pipe by Coeff x Mass of displaced water during vibration. So you should expect the frequencies to be lower. Again, the mass of the pipe is not affected by buoyancy.
What are the advantage of 'discretizing' the model with mass points. Why to discretized?
It improves accuracy for the analysis. Please see the following AutoPIPE help section:
Help > Contents> Contents Tab> Bentley AutoPIPE> Frequently Asked questions, scroll down #77.
What we wanted to do was to apply anchor displacement and pre-stress the pipe before performing modal analysis i.e. check the vibrations in its deformed operating condition?
The modal displacements and rotations describe the set of natural "shapes" or "patterns" of the system when vibrating (no external load). The model shapes depend on how the system's mass and stiffness are distributed.
Therefore, at this time, AutoPIPE CONNECT 11.01.xx.xx and lower cannot consider anchor or support displacement in conjunction with modal analysis.
Why are there no modes of vibration in my modal analysis?
Logged Feb 2015, AutoPIPE V8i 09.06.01.11
If the model is very stiff then increase then your 1st mode of vibration will be very high. Suggest increasing one or both the following modal values:
a. Number of mode
b. Cut-Off frequency
When a modal analysis has been run for a model that has several spans between pipe supports (e.g. guides), how to to extract the natural frequency of EACH span.
Logged April 2018, AutoPIPE CONNECT 11.02.00.10
The Frequency report provides the user information about the contributions of each natural frequency has on the entire system. While the Modal report provides the user how the system responded per each frequency at each node point.
Guides cannot be seen as breaking a system in to two distinct systems. If interested in the natural frequency of piping between guide supports, consider creating individual models of each span and perform a modal analysis on just that span of piping. Only problem with this approach would be how the connected piping affects cannot be accounted for fairly easily.