Shock Response from Pseudodynamic Test Using Momentum Equations of Motion

Abstract

The feasibility of using pseudodynamic techniques to yield shock responses from impulses is studied herein. A direct integration method is often used to solve the force equation of motion in performing a conventional pseudodynamic test. However, this technique might not be applicable to obtain an accurate shock response from an impulse as a load discontinuity occurs at the end of the impulse. This is because this discontinuity will lead to an extra amplitude distortion and the amount of this amplitude distortion is increased with the increase of time step. Hence, a small time step is needed to reduce the extra amplitude distortion and thus the displacement increment for each time step might be smaller than or as small as the resolution of the displacement transducer. As a result, the displacement increment cannot be accurately imposed upon the specimen and the responses will be contaminated by the noise. In addition, the test duration is drastically increased. Alternatively, this difficulty might be overcome if the momentum equation of motion instead of the force equation of motion is solved pseudodynamically. Hence, an external momentum is used in the solution of the momentum equation of motion. Since the external momentum is a resultant of the time integration of the external force the discontinuity problem will automatically disappear. Consequently, reliable shock responses can be obtained from pseudodynamic tests.