一种新的高阶弹簧-阻尼-质量边界——无限域圆柱对称波动问题

A NOVEL HIGH-ORDER SPRING-DASHPOT-MASS BOUNDARY FOR CYLINDRICAL-SYMMETRY WAVE MOTIONS IN INFINITE DOMAIN

提出一种描述力-位移时间卷积关系的高阶弹簧-阻尼-质量模型,并将其作为人工边界条件直接应用于弹性动力学无限域圆柱对称运动问题的时域数值求解.该人工边界条件不存在旁轴近似、多次透射等位移型外推人工边界条件普遍存在的高、低频失稳问题;与黏性、黏弹性边界等应力型人工边界条件相比,它具有高阶精度,且是严格高、低频双渐近的,也可以退化到黏性、黏弹性边界;该边界可以像黏性、黏弹性边界一样利用商用有限元软件中内置的并联弹簧-阻尼器、质量单元和时间积分求解器在商用软件中方便地实现,便于研究人员和工程师应用.分析的几个简单数值算例也验证了该边界条件的上述优点.

A novel high-order spring-dashpot-mass model （SDMM） for convolution integral of force-displacement relationship in time domain is proposed and applied into the cylindrical-symmetry wave motions in infinite do- main as an artificial boundary condition （ABC）. First, the high-order SDMM is dynamically and numerically stable, while lowand high-frequency instabilities occur under the displacement-type ABCs in term of spacetime extrapolation, such as multi-transmitting formula （MTF） and Pad6 boundary. Second, SDMM has higher numerical accuracy than the stress-type ABCs, such as viscous boundary （VB） and viscous-spring boundary （VSB）. Third, SDMM is strictly doubly asymptotic at low- and high-frequency limits, and can be degenerated to VB or VSB. Fourth, SDMM can be incorporated simply and easily into commercial FE software by using the internal spring-dashpot and mass elements and time-integration solvers. Several numerical cases were carried out to validate the particular features of SDMM.