Decoupling coefficients of dilatational wave for Biot's dynamic equation and its Green's functions in frequency domain

doi:10.1007/s10483-016-2015-9

Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (1): 121-136.doi: https://doi.org/10.1007/s10483-016-2015-9

• 论文 • 上一篇

Decoupling coefficients of dilatational wave for Biot's dynamic equation and its Green's functions in frequency domain

Boyang DING^1,2, A. H. D. CHENG³, Zhanglong CHEN²

1. Zhejiang University City College, Hangzhou 310012, China;
2. Department of Civil Engineering, Zhejiang University of Technology, Hangzhou 310014, China;
3. College of Civil Engineering and Architecture, University of Mississippi, Mississippi 38677-1848, U. S. A.

收稿日期:2015-03-16 修回日期:2015-06-06 出版日期:2016-01-01 发布日期:2016-01-01
通讯作者: Boyang DING E-mail:dingboyang@zjut.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 51478435, 11402150, and 11172268)

Decoupling coefficients of dilatational wave for Biot's dynamic equation and its Green's functions in frequency domain

Boyang DING^1,2, A. H. D. CHENG³, Zhanglong CHEN²

1. Zhejiang University City College, Hangzhou 310012, China;
2. Department of Civil Engineering, Zhejiang University of Technology, Hangzhou 310014, China;
3. College of Civil Engineering and Architecture, University of Mississippi, Mississippi 38677-1848, U. S. A.

Received:2015-03-16 Revised:2015-06-06 Online:2016-01-01 Published:2016-01-01
Contact: Boyang DING E-mail:dingboyang@zjut.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 51478435, 11402150, and 11172268)

摘要/Abstract

摘要：

Green's functions for Biot's dynamic equation in the frequency domain can be a highly useful tool for the investigation of dynamic responses of a saturated porous medium. Its applications are found in soil dynamics, seismology, earthquake engineering, rock mechanics, geophysics, and acoustics. However, the mathematical work for deriving it can be daunting. Green's functions have been presented utilizing an analogy between the dynamic thermoelasticity and the dynamic poroelasticity in the frequency domain using the u-p formulation. In this work, a special term "decoupling coefficient" for the decomposition of the fast and slow dilatational waves is proposed and expressed to present a new methodology for deriving the poroelastodynamic Green's functions. The correctness of the solution is demonstrated by numerically comparing the current solution with Cheng's previous solution. The separation of the two waves in the present methodology allows the more accurate evaluation of Green's functions, particularly the solution of the slow dilatational wave. This can be advantageous for the numerical implementation of the boundary element method (BEM) and other applications.

关键词: dilatational wave, frequency domain, decoupling coefficient, poroelastodynamic Green's function, Biot's equation

Abstract:

Key words: decoupling coefficient, poroelastodynamic Green's function, frequency domain, dilatational wave, Biot's equation

中图分类号:

00A71

Boyang DING, A. H. D. CHENG, Zhanglong CHEN. Decoupling coefficients of dilatational wave for Biot's dynamic equation and its Green's functions in frequency domain[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(1): 121-136.

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Decoupling coefficients of dilatational wave for Biot's dynamic equation and its Green's functions in frequency domain

Decoupling coefficients of dilatational wave for Biot's dynamic equation and its Green's functions in frequency domain

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