非连续变形分析方法中的阻尼问题研究

定量研究了非连续变形分析(DDA)方法中的黏性阻尼与数值阻尼。首先，基于Newmark直接积分法，推导了块体系统的运动方程。其次，通过动力学中的黏性阻尼理论建立了DDA中动力系数、时间步长与黏性阻尼比的关系式，探讨了DDA中的常加速度积分方案的数值阻尼分区及阻尼比计算方法，进而得到两种阻尼共同作用时的阻尼比表达式，并分析了频域内阻尼比的分布情况。最后，以谐振激励下的块体振动为例，通过对比不同阻尼作用下块体位移的DDA计算值与理论解，验证了本文提出的阻尼比计算公式的正确性。研究表明：黏性阻尼对低频的衰减作用明显，数值阻尼则可以很快地消除高频干扰，而二者共同作用下可降低阻尼的频率相关性。该研究成果为DDA的振动、波动等动力计算的阻尼取值提供了理论依据。

Damping problem in discontinuous deformation analysis method

This paper quantitatively investigates the viscous damping and numerical damping in the discontinuous deformation analysis (DDA) method. The motion equations of the block system are first developed based on the Newmark method; and the relationship among the viscous damping ratio, the dynamic coefficient and the time interval of each step in DDA is developed based on the kinetic theory of viscous damping. The constant acceleration integration scheme in DDA, the partitions and the damping ratio of the numerical damping are discussed; and the calculating formulations of the damping ratio for the combined damping are obtained. An example of the block vibration is analyzed under simple harmonic motions; and the proposed formulations are validated by comparing the DDA calculations to the theoretical solutions. The simulation results show that the viscous damping significantly affects the low frequencies; and the numerical damping can quickly eliminate the interference of the high frequencies. If the two dampings are combined, the frequency-dependence can be reduced. The study results provide a theoretical basis for the vibration and wave calculation using the DDA method.