一种新型高精度半显式基于模型的积分算法

A New Semi-explicit Model-based Integration Algorithm with High Accuracy

摘要:

提出了一种新型高精度基于模型的积分算法，该算法采用了半显式Chang算法的速度、位移表达式，但是具有不同的积分参数。采用离散控制理论中“零极点匹配”和二阶Pade近似推导出新算法的积分参数。对算法的精度、稳定性、周期延长和振幅衰减等数值特性进行分析。与Newmark族积分算法和两种典型的基于模型的积分算法相比，新算法具备四阶精度，并且有非常小的周期误差。最后，通过三个数值算例验证了新算法的高精度特性。

Abstract:

A new model-based integration algorithm with high accuracy is proposed. The proposed algorithm adopts the formulations of velocity and displacement of the semi-explicit Chang algorithm but uses different integration parameters. The integration parameters of the new algorithm are derived by using the zero-pole matching in discrete control theory and second-order Pade approximation. The numerical properties including accuracy， stability， period elongation and amplitude decay are analyzed. Compared with the Newmark family algorithms and two typical model-based integration algorithms， the proposed algorithm is fourth-order accurate and possess extremely small period error. Finally， the high accuracy of the algorithm is demonstrated by three numerical examples.