Dear Wai-Kwok Chen

This is an issue of integration of sine functions, where the first integration (velocity) will include a constant C, and the second integration (displacement) will include a linear term and a new constant (C * t + D). See the attached figure of integration of a sine function.

• The top graph is the acceleration (sine function),
• the second graph is its integrated velocity (a cosine function + a constant) and
• the third graph is its integrated displacement (a sine function + constant * time + constant)

If you want to minimize this effect, then you need to use a windowing function that increase the amplitude initially and reduce the amplitude towards the end. This can be achieved by for instance a tapered hann window. See the second figure attached.

You could also integrate the acceleration to velocity and remove the constant (i.e. ensure that the mean of the velocity is zero). Thereafter, apply the velocity (or stress input, where tau = v * rho *cs)

I have attached a matlab script that shows you how to use an example of a hann window-function.

Then specify the windowed acceleration (boundary condition), the velocity (boundary condition) or the load (force = tau / area) in Abaqus with the calculated amplitude function and run your dynamic implicit analysis.

Best regards

Richard Malm

https://www.jvejournals.com/article/16965/pdf

http://www.strc.ch/2006/Arraigada_Pratl_STRC_2006.pdf