Time varying displacement can be defined only in a step. So once you've defined a dynamic step, go to Load Module in Abaqus. Then create boundary -> from drop down menu, select the step you would like to define time varying displacement -> Enter Components -> at the bottom, amplitude (default ramp for dynamic) -> create amplitude...select the type that suits your purpose.
Alternatively, you can define amplitude variation through Load Module -> Tools Menu (on Top Menu) -> Amplitude -> Amplitude Manager -> Create Amplitude
Details about different amplitude types can be found in Abaqus Analysis Manual (Prescribed Conditions -> Overview
Note: If you would send me an email (through imechanica) or post me your email id, I can send you both papers. However, first one (Int J. Comput. Methods Eng. Sci. Mech.) is the more detailed one, so it has everything you need. Just don't use the simplified equivalent system matrices, since they misprinted the equations.
Let me know if you need any help. I will send you a sample input file.
------
The world started with 0, is progressing with 0, but doesn't want 0.