## Transient Analysis with enforced acceleration

One way to excite a model in transient analysis is through an enforced acceleration. This can be done with an SPCD of type “acce” and a tabular function that expresses the acceleration profile over time, applied at a certain point of the model. People sometimes are interested into evaluating the structural response to impulsive loads like the acceleration profile of Figure 1. Figure 1: generic acceleration profile

Bringing the acceleration back to 0 could be thought sufficient to stop the motion of the structure, but this is not correct. We know that acceleration is the 2nd derivative of displacement. This means that if we just remove the acceleration, velocity will remain constant, and displacement will still increase over time. This behavior is shown in the example below where a simple model is excited with an imposed 1G acceleration at node #1 and the response is measured at node #21. Figure 2: one-point acceleration profile

If we plot acceleration, velocity and displacement over time the behavior of the model is clear. In the image below, red curves are vertical responses at node #1 and blue curves represent responses at node #21. Applied acceleration is removed at 0.2s, damping effect is seen in blue curve response that slowly goes down to 0, but looking at velocity plot it is evident that velocity remains constant, with damping effect still visible and displacement is still increasing. Figure 3: acceleration, velocity and displacement plots

This means that eventually Node #21 will be dragged by adjacent structure (that is dragged by Node #1) and flying away together.

To overcome the issue of the rigid body motion of the structure a different type of acceleration must be used. For example, a global acceleration load can be used or the sign of the one-point acceleration load has to be reverted.  Figure 5: local acceleration with reverted sign

Comparison of results with different acceleration methods is visible in Figure 6. Figure 6: Response plots with different acceleration methods

In conclusion, be careful when defininig loading condition for enforced acceleration applied to transient analysis, results can be not so obvious.