一个新的显式算法及其在转子动力学中的应用

A NEW EXPLICIT TIME INTEGRATION ALGORITHM FOR THE ROTOR DINAMICS PROBLEM

通过引入5个自由参数进行算法设计,提出了一个新的用于线性、非线性动力响应数值计算的显式算法。基于有限差分分析理论对算法进行了设计和分析,结果表明算法的显式特性不需要阻尼矩阵对角化的假设,还具有一定的算法阻尼,这优于传统的中心有限差分方法。对单自由度的线性、非线性算例从数值上分析、比较了新算法的性能。最后给出了新算法在基础松动与碰摩耦合的转子系统的非线性动力学响应计算问题中的应用,表明该算法可以推广到更广泛的转子动力学问题。

A new explicit single step time integration method is presented for linear and nonlinear dynamic system. Five free parameters are introduced into the equilibrium equation of motion after the finite element discretization in space, then a finite difference analysis of the algorithm is performed. Accuracy, stability and dissipation performance are analyzed for the linear damped case. The presented scheme is second-order accurate and explicit inherently with diagonal mass matrix, even when the damping matrix not diagonal or the internal force vector is a non-linear function of velocities, and possess good high-frequency dissipation performance. The advantage of the proposed algorithm compared with the center difference method is verified numerically by the some linear and nonlinear examples. Finally, nonlinear dynamic behaviors of the rotor system with local rubbing and pedestal looseness faults are studied by the proposed method and explicit Runge-Kutta method used.