本文選題：結(jié)構(gòu)動力學(xué)顯式算法 + 離散控制理論��； 參考：《力學(xué)學(xué)報》2015年02期

【摘要】：利用離散控制理論,針對結(jié)構(gòu)動力學(xué)方程時間積分提出了一種新的無條件穩(wěn)定的顯式算法.新算法采用CR算法的速度和位移遞推格式,同時利用Z變換獲得算法對應(yīng)的傳遞函數(shù),進(jìn)而根據(jù)極點條件推導(dǎo)了遞推格式系數(shù)的具體表達(dá)式.然后,在其系數(shù)中引入了一個控制周期延長率的變量s,從而調(diào)節(jié)新算法的精度.理論分析表明無條件穩(wěn)定顯式新算法具有二階精度、零振幅衰減率、無超調(diào)和自起步特性,且周期延長率可以用變量s控制,而CR算法只是本文新算法的特例.最后,確定了非線性剛度硬化系統(tǒng)的穩(wěn)定性界限,并給出了使新算法精度達(dá)到較高的變量s的區(qū)間.算例分析表明,在此變量區(qū)間內(nèi)取值時,新算法的精度要優(yōu)于紐馬克常平均加速度算法和CR算法.
[Abstract]:Based on the discrete control theory, a new unconditionally stable explicit algorithm is proposed for the time integral of structural dynamic equations. The new algorithm uses the CR algorithm's velocity and displacement recursion scheme and the Z transform to obtain the corresponding transfer function, and then derives the concrete expression of the recursive format coefficient according to the pole condition. In its coefficient, a variable s that controls the extension rate of the control period is introduced to adjust the accuracy of the new algorithm. The theoretical analysis shows that the unconditional stable explicit algorithm has two order precision, zero amplitude attenuation rate, no super harmonic self starting characteristic, and the period extension rate can be controlled by variable s, and the CR algorithm is only a special case of the new algorithm in this paper. Finally, the new algorithm is a special case of the new algorithm. The stability limit of the nonlinear stiffness hardening system is determined and the interval of the new algorithm with a high variable s is given. An example analysis shows that the precision of the new algorithm is better than the Newmark constant average acceleration algorithm and the CR algorithm when the value of the variable is taken in the interval.
【作者單位】： 大連理工大學(xué)工程力學(xué)系工業(yè)裝備結(jié)構(gòu)分析國家重點實驗室;
【基金】：國家自然科學(xué)基金(51478086,11332004) 陜西省科技統(tǒng)籌創(chuàng)新工程重點實驗室基金(2013SZS02-K02)資助項目~~
【分類號】：TU311.3
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本文編號：2091071