Abstract
The discontinuity at the end of an impulse will lead to an extra impulse and thus an extra displacement. Consequently, an amplitude distortion is introduced in the numerical solution. The difficulty arising from the discontinuity at the end of an impulse can be overcome by using a very small time step to perform the step-by-step integration since it reduces the extra impulse and thus extra displacement. However, computational efforts might be significantly increased since the small time step is performed for a complete step-by-step integration procedure. A remedy is devised to computationally efficiently overcome this difficulty by using a very small time step immediately upon termination of the applied impulse. This is because that the extra impulse caused by the discontinuity is almost proportional to the discontinuity value at the end of the impulse and the step size. The feasibility of this proposed remedy is analytically and numerically confirmed herein.
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