This paper proposes an implicit and unconditionally stable two-sub-step composite time integration method with controllable numerical dissipation for general dynamics called the two-sub-step generalized central difference (TGCD) method. The proposed method is established by performing the generalized central difference scheme in two sub-steps as the nondissipative and dissipative parts to ensure amplitude accuracy and controllable damping, respectively. It is accurate to the second order, with the amount of numerical dissipation controlled exactly by the spectral radius [Formula: see text]. In addition, the related parameters of the proposed method are determined by optimizing the amplitude and phase accuracy of the free vibration of a single degree-of-freedom system. Several representative linear and nonlinear numerical examples are analyzed to demonstrate the advantages of the proposed method in terms of accuracy, stability and efficiency, especially its stability in solving nonlinear problems.

中文翻译：

---

一般动力学的两子步广义中心差分法

本文提出了一种用于一般动力学的具有可控数值耗散的隐式无条件稳定的两子步复合时间积分方法，称为两子步广义中心差分（TGCD）方法。所提出的方法是通过在两个子步骤中作为非耗散部分和耗散部分执行广义中心差分方案来建立的，以分别确保幅度精度和可控阻尼。它精确到二阶，数值耗散量由光谱半径精确控制[公式：见正文]。此外，该方法的相关参数是通过优化单自由度系统的自由振动的幅度和相位精度来确定的。