| Summary: | 碩士 === 國立臺北科技大學 === 土木與防災技術研究所 === 92 === It was found that numerical accuracy might be significantly different for various shapes of impulses during the step-by-step integration procedure although the same time step and loading duration are used. This mainly originates from the discontinuity in the external force at the end of an impulse. To overcome this difficulty, a small time step is additionally performed right after the end of the impulse so that the numerical error caused by the discontinuity can be reduced. In this study, the response to a linear loading for a single degree of freedom system is achieved by two different ways. One is using the fundamental theory of structural dynamics to obtain a theoretical solution and the other is using a spectral decomposition technique to analytically obtain the response computed from the Newmark explicit method and the constant average acceleration method. Comparing the analytically obtained numerical solution to the theoretical solution, it is found that the numerical error caused by the discontinuity of the impulse can be effectively reduced by conducting an extra small time step right after the end of the impulse. Furthermore, the smaller the extra time step, the less the numerical error. All these analytical results are thoroughly confirmed by numerical examples.
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