Question:
If a model has 4 disconnected segment groups, why does the results change when one or more disconnected groups are removed from the model?
Answer:
In short, the results of dynamic analysis can change with the number and distribution of mass points because the mass matrix is directly based on these points. Thus, removing disconnected segment groups, changes the mass matrix which directly affects the calculation of results.
Longer explanation, AutoPIPE's Dynamic analysis in always starts from a linear condition (no load sequence, no gaps, no friction, no soil properties), but the results can still change depending on how the mass matrix is constructed, which is directly influenced by the total number of mass points and distribution of mass points in the system. Why?
In dynamic analysis, the mass matrix is basically how the system “tracks” where all the weight is in your piping model. AutoPIPE handles this using a lumped mass approach, meaning the weight of the pipe, contents, and components is placed at the model’s physical node points.
Because of this, where you place those nodes—and how many you use—has a direct impact on results. If the mass isn’t distributed well, the calculated loads can be off, which can change your dynamic results even if everything else in the model stays the same.
To improve accuracy, you can add more nodes (mass points) in areas where the dynamic behavior matters most. This helps spread the mass more realistically across the model. This process is called mass discretization, and it simply means making sure your model represents the real system’s mass distribution as closely as possible, so the results are more reliable. If the spacing between points is too large, additional mass points are automatically generated during the solution process. These points are used solely for mass distribution and are not accessible for other analysis/modeling purposes. The optimum spacing for mass points can be calculated based on the free vibration characteristics of an equivalent simply supported beam (for more information see AutoPIPE help> Mass Discretization)
AutoPIPE has the following settings to help control mass point distribution:
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- Adding / removing physical node points
- Mass points per span (A-Auto, 0-none)
- Cutoff frequency
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Mass Matrix
Once more, AutoPIPE lumps the mass of the pipe, components, and contents at the associated node points. Analysis requires this information to take the form of a diagonal matrix referred to as the Mass Matrix, meaning there are no mass coupling terms between different degrees of freedom at different nodes. Each node typically has three translational mass degrees of freedom (X, Y, Z). Rotational mass is generally ignored, except at points with eccentric weights, where up to three additional rotational mass degrees of freedom may be included.
The nature of the mass matrix simplifies the dynamic equations, as each mass point acts independently in terms of inertia. The general form of the eigenvalue problem for modal analysis is:
For more information see AutoPIPE help Modal analysis Theory:
Impact of Mass Points:
The total number of mass points (nodes) determines the size of the mass matrix and the number of modes that can be extracted in the analysis. More mass points lead to a finer mass matrix, which can capture higher-frequency dynamic effects and provide more accurate results. Conversely, fewer mass points may miss important dynamic behavior, especially in regions with significant mass or stiffness changes.
See Also