CAJ | 학술논문

为了建立精度更高、稳定性更好的显式积分算法，在双步长线性加速度假设的条件下，通过积分推导，提出了双步长显式法和修正双步长显式法。对这两种新方法进行了稳定性、精度和截断误差分析，并通过算例对两种新方法、中心差分法和解析解进行比较。结果表明，无阻尼情况下，双步长显式法是不稳定的，而修正双步长显式法与中心差分法具有相同的稳定条件；大步长情况下修正双步长显式法和中心差分法的幅值误差小于双步长显式法；小步长情况下修正双步长显式法的阻尼比误差和周期误差都比中心差分法小，具有良好的综合性能。
위료건립정도경고、은정성경호적현식적분산법，재쌍보장선성가속도가설적조건하，통과적분추도，제출료쌍보장현식법화수정쌍보장현식법。대저량충신방법진행료은정성、정도화절단오차분석，병통과산례대량충신방법、중심차분법화해석해진행비교。결과표명，무조니정황하，쌍보장현식법시불은정적，이수정쌍보장현식법여중심차분법구유상동적은정조건；대보장정황하수정쌍보장현식법화중심차분법적폭치오차소우쌍보장현식법；소보장정황하수정쌍보장현식법적조니비오차화주기오차도비중심차분법소，구유량호적종합성능。
In order to establish a dynamical explicit method with higher accuracy and better stability,an explicit algorithm of double time steps and a corrected explicit algorithm of double time steps were proposed through integration under the assumption of linear acceleration in two time steps.The stability,accuracy and truncation error analyses were performed for the two new algorithms.A numerical example was utilized for the comparison of the two new algorithms,the central difference method and the analytical solution.The results show that the explicit algorithm of double time steps is unstable under undamped condition,however,the corrected explicit algorithm of double time steps has the same stability condition as the central difference method.The amplitude error of the explicit algorithm of double time steps is bigger than the corrected explicit algorithm of double time steps and the central difference method when the time step is long.The corrected explicit algorithm of double time steps possesses excellent comprehensive properties with less damping ratio error and periodic error than the central difference method in the case of short time step.