中文摘要 本文主要利用2N數值法處理結構動力問題,探討結構自然頻率接近載荷頻率時,所產生的共振現象及時間積分法因假設所造成的假共振問題。 計算的過程中乃利用解析處理方法建立數學模型進行分析,採用的是精細時間積分及狀態空間數值計算。其中為了使2N數值法的線性化誤差達到最小,在此引入動量平衡方程式的觀念。 由於2N數值法為解析計算法,所以沒有高頻消散能力,因此模擬物理問題為了降低物體因空間半離散所產生的不正確高頻反應,在模擬前先分析模型基本振態,再根據模型自然振動頻率的分佈並配合雷利阻尼的選取,使得2N-精細時間積分法亦具有高頻消散能力。 關鍵字:2N數值法、精細時間積分、狀態空間數值空間、動量平衡方程式、假共振。
Abstract In this study 2N algorithm deals with the problems of linear elastic structures and discuss the spurious resonance from the assumption of time integration when natural frequency approach of load frequency. The process of algorithm is analyzed by mathematical model building on algorithmic method which is like high precision direct integration method(HPD) or state space method(SS). At the same time, 2N algorithm is using momentum equilibrium for the minimum of linear error. Because 2N algorithm is algorithmic method, it has not any frequency dissipation. In order to reduce the high frequency effects in the space discretization the frequency of model is first analyzed and Rayleigh damping is chosen later. After this process 2N algorithm can reduce the high frequency effects gradually. Keywords:2N algorithm、HPD、SS、momentum equilibrium、spurious resonance