| Applies To | |
| Product(s): | AutoPIPE |
| Version(s): | ALL; |
| Area: | Results |
| Original Author: | Bentley Technical Support Group |
| Date Logged & Current Version | Feb. 2017 10.01.00.09 |
Problem:
Why a simple cantilever system doesn't match hand calculations for Modal Analysis in AutoPIPE?
Example:
A very simple cantilever model for verification of the calculation of natural frequency of a piping system. To verify the accuracy of AutoPIPE frequency calculations, see 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:
A model of the same system was made with ANSYS 11.0. the results were, 47.22 Hz using a single element model as well that is identical to the AutoPIPE model.
Discussion:
One should expect the AutoPIPE natural frequencies to be lower than using an ANSYS beam model for common systems due to the flexibility of elbows in ANSYS models the elbow flexibility as well. However, should be no reason why the simple cantilever system doesn't match hand calculations
Solution:
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.