离散网格中的弹性波动(Ⅲ)——时域离散化对波传播规律的影响

ELASTIC WAVE MOTION IN DISCRETE GRIDS (Ⅲ)——The effect of discietizalion in time domain on wave motior

本文采用一维模型分析了时域离散化后有限元离散网格中波动的基本特征。文中讨论了时域离散化对波动的频散、截止频率及寄生振荡的影响,分析了由时域离散化引起的在频率域及由空间离散化引起的在波数域波动解的多重分支现象,并指出在研究中应取其基本分支。文中也给出了考虑时间步长影响的有限元离散化准则。研究结果表明,从模拟连续模型的精度上看,时域离散化使集中质最有限元法优于一致质量法,前者可取较大时间步长。从计算精度、容易程度及经济性各方面衡量,集中质量法均比一致质量法可取。本文的工作不但对波动有限元模拟的参数选取有指导意义,同时也是分析时域人工边界稳定性的基础工作之一。

Fundamental characteristics of elastic wave propagation are analyzed for one dimension finite element models after time discretization. The effect of discretization in time domain on dispersion, cut-off frequency and parasitic oscillation are discussed, the phenomena of multiple branches of solution of wave motion equation are studied both in frequency domain caused by time discretization and in wave number domain caused by space discretization, and the fundamental blanch must be considered in the theoretical analysis. The discretization criterion of finite elements is then given based on consideration of all discretization effects. This paper shows that the time discretization makes the lumped-mass method much better than the consistent-mass one as accuracy is concerned for simulating wave motion in the continuous model. Therefore, the lumped-mass method is the best choice because of not only easy implementation, economics but also the higher accuracy in the simulation. This work provides a guideline for selection of the discjete parameters of finite elements in wave motion simulation and also a foundation to analyze the stability of the artificial boundary.