半无限弹性空间中移动荷载动力响应的频域-波数域比例边界有限元法分析

发布时间：2018-01-15 13:16

本文关键词：半无限弹性空间中移动荷载动力响应的频域-波数域比例边界有限元法分析　出处：《振动工程学报》2017年05期 　论文类型：期刊论文

【摘要】：基于Fourier积分变换和虚功原理,形成了频域-波数域比例边界有限元法,分析了移动荷载作用下半空间域弹性空间动力响应。首先对半无限域弹性体的动力控制方程进行时间到频域,荷载移动方向的空间域到波数的Fourier积分变换,然后选择比例中心,利用虚功原理,在地铁隧道孔洞横截面环向上采用有限元法意义离散,建立了频域-波数域比例边界有限元方程,进而形成了一阶微分矩阵方程形式的半无限空间动力刚度。文中理论推导表明:利用文中方法分析半无限域中沿地铁隧道结构纵轴向的移动荷载动力响应问题,不仅可避免无穷边界计算处理误差,而且可极大减小计算分析量。计算结果表明:半无限弹性地基的振动响应随移动荷载速度增大而增大,尤其是当荷载速度增大到土体剪切波速后,振动波传播到土体表面引起土体振动显著增大,土体振动性增大,将会对土体及表面结构的安全性形成一定影响,另一方面土体的振动在沿地铁隧道纵轴向的衰减比竖向慢。
[Abstract]:Fourier integral transform and based on the principle of virtual work, the formation of the frequency wavenumber domain scaled boundary finite element method, analysis of the response of half space elastic dynamic space under moving loads. The first semi infinite elastic body dynamic equations of time to frequency domain Fourier transform load moving direction of the spatial domain to the wavenumber, then the proportion of the center, using the principle of virtual work, the finite element method is adopted to discrete significance of subway tunnel cross section ring hole, established frequency wavenumber domain scaled boundary finite element equations, and the formation of the semi infinite space form a dynamic differential matrix equation of stiffness. Theoretical deduction in this paper shows that the use of this method analysis of moving loads along the longitudinal axis to the subway tunnel structure dynamic response of semi infinite domain, not only can avoid the infinite boundary calculation error, and can greatly reduce calculation amount. The calculation results show that with increasing the velocity of the moving load increases the vibration response of semi infinite elastic foundation, especially when the load speed increases to shear wave velocity, vibration wave propagation to the soil surface increased significantly by soil vibration, vibration of the soil increased, the security will be on the soil and surface structure of the formation of a certain influence, another vibration in the aspect of soil along the subway tunnel longitudinal attenuation ratio of vertical slow.

【作者单位】：华东交通大学教育部振动与噪声工程中心;南昌工程学院土木与建筑工程学院;
【基金】：国家自然科学基金资助项目(51269021,51478184,51569016) 江西省自然科学基金重点资助项目(20133ACB20006) 江西省教育厅科技资助项目(GJJ14755,GJJ151096) 江西省优势科技创新团队建设计划项目(2017BCB19001)
【分类号】：TU435;U231;U451
【正文快照】： 引言对于半无限地基土体动力响应,采用有限元法,不可避免需建立有效的人工边界与合理离散网格。尽管目前国内外学者已建立了具有各自优点的人工边界模型动力有限元法[1-3],分析无限域地基土体动力问题,但仍不具有有限元意义上的精确性,即低阶边界精度不足、高阶边界稳定性差,

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