# Structural Dynamics Analysis - Modal method or time integration?

1. Jun 27, 2014

### Hassan2

Hi all,

I need help with numerical solution of motion equation.

From the numerical point of view and in the real of the finite element method, which method is recommended for the solution of damped ( proportional damping) linear motion equation?

I have been trying three common methods; Modal decomposition, time integration ( Newark method), and frequency domain method ( for steady state solution). I faced a problem with the accuracy of modal decomposition method as I don't and can not use all the modes. In addition , if the displacements of all nodes are desired, the method turns out to be more time consuming than the time integration method. The frequency domain method is another choice when steady-state solution is sought but, in my code , it may need too much memory. So, I found the time integration to be the best and it is fast if we use an iterative matrix solver and use the solution of the previous time-step as the initial value of the current step. But isn't this contrary to claims that the modal decomposition method is the method of choice for linear motion equation?

Your help would be highly appreciated.
Thanks.

2. Jun 27, 2014

### AlephZero

The "best" method is the one that is accurate enough and fast enough to give you what you want. In dynamics, "best" is usually problem dependent.

Modal decomposition with a limited number of modes can give problems if there are stiff load paths in your structure, which are only represented by high frequency modes. That can be a serious problem if you don't realize it exists, because the results may look plausible even if they are completely wrong.

One way to fix it is the "mode acceleration method," which adds the static response of the structure to the modal response. http://rotorlab.tamu.edu/me617/HD 8 Mode Accel addendum 2008.pdf (or use Google).

A more general version of this is the Craig Bampton method, sometimes called component mode synthesis. There are several variations on the basic idea. Google will find lots of references.

3. Jun 27, 2014

### Hassan2

Thank you very much AlephZero. You have always been a good source of help to me.

Yes my problem is stiff. I have spent days and weeks to spot the cause of the error in the results obtained from the modal decomposition method. I Even used 200 modes but the error which was in fact in low frequencies persisted. As can be seen in the attached figure, the method follows the Newmark method very well in high harmonics but there is a significant error associated with low frequencies. I wrongly thought that since the error was at low frequencies, it was not due to neglecting higher modes ( higher than 200) but now I realize that even static response can be calculated from the method and high enough number of modes are required for that to be accurate enough.

The attachment shows the results.

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• ###### modal.png
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