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solids4foam for natural frequency of a cantilever beam |
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July 29, 2020, 11:10 |
solids4foam for natural frequency of a cantilever beam
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#1 |
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Hi (Structural) Foamers,
Thought this post might help some of you to understand the importance of time step in a structural solver using solids4foam toolbox. The frequency of cantilever beam was validated using the finite volume method by the authors Slone et al https://www.sciencedirect.com/scienc...07904X02000604. Please see fig 3 in this paper. The natural frequency is approx 20 s. The same case was run using linearGeometryTotalDisplacement model from solids4foam toolbox. The left part of the attached image shows the displacement variation with time for the force inputs as shown in right for different time steps. As given in the paper, the force was linearly ramped upto 10 s and then released. However, the displacement from simulation does not capture the natural frequency when time step, dt = 1 s. There is too much damping arising from first order Euler scheme. With finer time steps, this numerical damping disappeared to a large extent and the natural frequency is as expected. Unlike the Slone et al's article, the peak displacement is greater than 0.1 m and it gradually reduced with increasing time. Thanks to Philip Cardiff (aka bigphil) for suggesting to perform time step checks. |
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July 29, 2020, 11:24 |
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#2 |
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I forgot to mention in the above message. At time step = 0.1 s, the results for backward scheme and Euler scheme are same though. As backward scheme is second order and Euler is first order, why is displacement response not sensitive to the type of time scheme?
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July 29, 2020, 11:33 |
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#3 | |
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Philip Cardiff
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Quote:
Also, for a given time-step size, second-order methods are often more accurate in absolute terms than first-order methods, but this does not have to be the case. In your case, I suggest you perform the same time-step analysis using both Euler and backward and compare them, and you should see that backward approaches the final solution at a higher rate. Philip EDIT: by the way, first order Euler is generally known to require very small toe-steps to be accurate in comparison to Newmark or trapezoidal second order schemes, which can produce the same accuracy with much larger time-step sizes. Last edited by bigphil; July 29, 2020 at 11:35. Reason: Add comment about Euler |
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December 12, 2022, 21:49 |
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#4 | |
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Chao Li
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December 13, 2022, 17:45 |
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#5 | |
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Philip Cardiff
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Quote:
Last edited by bigphil; December 14, 2022 at 09:51. Reason: Fix URL |
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December 13, 2022, 21:29 |
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#6 | |
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Chao Li
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December 14, 2022, 10:04 |
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#7 | |
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Philip Cardiff
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In reply to your questions
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December 14, 2022, 20:15 |
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#8 | |
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Chao Li
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