Analysis of dynamic systems is more time-consuming than static ones due tot he presence of inertia force which vary in time. Equations of a dynamic system excited by arbitrary loads, result in partial differential equations. The spatial part is discretized by finite element method and temporal part by implicit or explicit integration scheme. The time integration methods have already proved their effectiveness. However, in order to improve resolution computing-time and quality of results, we present in this paper, a semi-analytical method based on asymptotic method which allows to obtain continuous solution for all time. Advantage of this method is that displacement is expressed in power series. From this series, velocity and acceleration are easily computed. The load must be pressed also in series in the same manner as displacement. We use Fourier integral to obtain analytical function of an arbitrary load and then, we develop this function in power series using Taylor series. The dynamic asymptotic method (DAM) belongs to onditionally stable-explicit methods. We apply this method in modal space in order to eliminate high-frequencies which influence critical time (time segment length). Trough numerical examples, we show better effectiveness of asymptotic method compared to Newmark method when both are projected in modal space.
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