【摘要】：彈簧-阻尼-作動器(spring-damper-actuator,SDA)是多體系統(tǒng)中常見的力元,在工程領(lǐng)域中有著廣泛的應(yīng)用.采用絕對坐標(biāo)方法建立的多體系統(tǒng)動力學(xué)控制方程通常是復(fù)雜的非線性微分-代數(shù)方程組.為了保證數(shù)值解的精度和穩(wěn)定性,通常需要采用隱式算法求解動力學(xué)方程,而雅可比矩陣的計算在隱式數(shù)值求解過程中至關(guān)重要.對于含有SDA的多體系統(tǒng),SDA造成的附加雅可比矩陣是與廣義坐標(biāo)和廣義速度相關(guān)的高度非線性函數(shù).目前的很多研究工作專注于廣義力向量的計算,然而對附加雅克比矩陣的計算則少有關(guān)注.針對含SDA的多剛體系統(tǒng)進(jìn)行動力學(xué)分析,首先基于Newmark算法研究其在動力學(xué)方程求解中的雅可比矩陣的構(gòu)成形式;然后推導(dǎo)SDA的廣義力向量對應(yīng)的附加雅可比矩陣,其中包括廣義力向量對廣義坐標(biāo)和對廣義速度的偏導(dǎo)數(shù)矩陣.最后通過兩個數(shù)值算例研究附加雅可比矩陣對動力學(xué)分析收斂性的影響;數(shù)值分析表明:當(dāng)SDA的剛度、阻尼和作動力數(shù)值較大時,SDA導(dǎo)致的附加雅可比矩陣對數(shù)值解的收斂性有重要影響;當(dāng)考慮SDA對應(yīng)的附加雅可比矩陣時,動力學(xué)分析可以以較少的迭代步實現(xiàn)收斂,從而減少分析時間.
[Abstract]:Spring-damping-actuator (spring-damper-actuator,SDA) is a common force element in multi-body systems and has been widely used in engineering fields. The dynamic control equations of multibody systems established by the absolute coordinate method are usually complex nonlinear differential-algebraic equations. In order to ensure the accuracy and stability of the numerical solution, implicit algorithm is usually used to solve the dynamic equation, and the Jacobian matrix is very important in the implicit numerical solution. For multibody systems with SDA, the additional Jacobian matrix is a highly nonlinear function related to generalized coordinates and generalized velocities. Many researches have focused on the computation of generalized force vectors, but little attention has been paid to the computation of additional Jacobian matrices. The dynamic analysis of multi-rigid body system with SDA is carried out. Firstly, the form of Jacobian matrix in solving dynamic equation is studied based on Newmark algorithm, and then the additional Jacobian matrix corresponding to generalized force vector of SDA is derived. It includes generalized force vector to generalized coordinate and partial derivative matrix to generalized velocity. Finally, two numerical examples are used to study the effect of the additional Jacobian matrix on the convergence of the dynamic analysis. The additional Jacobian matrix caused by damping and dynamic values has an important effect on the convergence of the numerical solution, and when the additional Jacobian matrix corresponding to SDA is considered, the dynamic analysis can achieve convergence with fewer iterative steps. As a result, the analysis time is reduced.
【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(diǎn)實驗室;
【基金】：國家自然科學(xué)基金(11472069,11772074,91648204) 國家重點(diǎn)研發(fā)計劃(2016YFB0200702)資助項目
【分類號】：O313.7
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本文編號：2225481