利用状态空间法对一类非线性振动系统的数值方法研究

Numerical Method Research for a Class of Nonlinear Oscillation Systems Using the State-Space Approach

提出了一类非线性振动系统的隐式解 ,导出了相应的数值计算方法 ,并对该数值方法的收敛性、误差和稳定性进行了研究。与传统的非线性振动系统的数值求解方法如 :Houbolt法、Wilson- θ法、Newm ark- β法以及考虑高阶余项的连续线性化模型及其 Taylor变换法相比 ,该方法具有更高的求解精度和效率。将该数值方法应用到结晶器四偏心式振动机构这样复杂的弹性机构非线性振动系统的研究中 ,取得了良好的效果 。

A state space model for a class of non-linear oscillation systems is put forward. The model is an improvement on the traditional non-linear oscillation equations in state space. An implicit analytical solution for the systems is derived; also a numerical method is presented based on the analysis of the structure property of the model and the implicit analytical solution. Calculation precision is greatly improved using iterative method, the convergency, error and stability of the numerical method are studied. Compared with the traditional numerical methods such as Houbolt method, wilson-θ method, Newmark-β method and the continuous linearization model and its numerical calculation method by using Taylor transformation, the presented numerical method has higher calculation precision and efficiency. Finally as a multi-degrees of freedom system example, the dynamic equation of an oscillation mechanism with 4-eccentric axes for continuous casting machine is analyzed.