基于偶应力弹性梯度理论的饱和孔隙介质中Rayleigh波的传播特性

李国强; 郑佩; 张克明

doi:10.21656/1000-0887.450259

基于偶应力弹性梯度理论的饱和孔隙介质中Rayleigh波的传播特性

doi: 10.21656/1000-0887.450259

上海理工大学机械工程学院, 上海 200093

详细信息

作者简介:
李国强（1997—），男，硕士生(E-mail: 1767445763@qq.com);郑佩（1980—），男，副教授，硕士生导师(通讯作者. E-mail: aliaspei@usst.edu.cn);张克明（1983—），男，副教授，硕士生导师(E-mail: zhangkeming@usst.edu.cn).

通讯作者:
郑佩（1980—），男，副教授，硕士生导师(通讯作者. E-mail: aliaspei@usst.edu.cn)

中图分类号: O347.4⁺¹
计量
- 文章访问数: 25
- HTML全文浏览量: 8
- PDF下载量: 1
- 被引次数: 0
出版历程
- 收稿日期: 2024-09-25
- 修回日期: 2024-10-25
- 网络出版日期: 2025-11-13

Propagation Characteristics of Rayleigh Waves in Saturated Porous Media Based on the Couple-Stress Elastic Gradient Theory

School of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai 200093, P.R.China

摘要

摘要: 基于偶应力弹性梯度理论，研究了饱和孔隙介质中Rayleigh波的传播特性.首先，基于偶应力理论建立了包含材料内禀长度的波动方程，并在频域内通过位移场的势函数分解，将两组耦合的波动方程解耦为4个标量的Helmholtz方程，分别控制P-1波、P-2波、SV波和SH波的传播.进一步，针对Rayleigh波，通过求解Helmholtz方程的特征值问题，确定了势函数的具体形式.然后，通过引入边界条件，求解了Rayleigh波的传播特性.最后，通过数值算例，研究了材料内禀长度对Rayleigh波的传播特性的影响规律.
- 孔隙介质 /
- Rayleigh波 /
- 偶应力 /
- 弹性梯度理论 /
- 归一化位移
Abstract: The propagation characteristics of Rayleigh waves in saturated pore media were investigated based on the couplestress poroelastic gradient theory. Firstly, the fluctuation equations containing material intrinsic lengths were established based on the couplestress theory, and the 2 sets of coupled fluctuation equations were decoupled into 4 scalar Helmholtz equations through the potential function decomposition of the displacement field to control the propagation of the P-1,P-2, SV and SH waves, respectively. Further, for Rayleigh waves, the specific form of the potential function was determined through solution of the eigenvalue problem of the Helmholtz equation. Then, the propagation characteristics of Rayleigh waves were solved under introduced boundary conditions. Finally, the influence rule of the material intrinsic length on the propagation characteristics of Rayleigh waves was investigated by numerical examples.
- porous material /
- Rayleigh wave /
- couple stress /
- elastic gradient theory /
- normalized displacement

HTML全文

参考文献(24)

RAYLEIGH L. On waves propagated along the plane surface of an elastic solid[J].Proceedings of the London Mathematical Society,1885,1(1): 4-11.

[2]KIM G, IN C W, KIM J Y, et al. Air-coupled detection of nonlinear Rayleigh surface waves in concrete: application to microcracking detection[J].NDT & E International,2014,67: 64-70.

[3]VOIGT W. Theoritical studies on the elasticity relationships of cristals[J].R Soc Sci,1887,34: 3-51.

[4]COSSERAT E, COSSERAT F.Theory of Deformable Bodies[M]. Paris: Scientific Library A. Hermann and Sons, 1909.

[5]TOUPIN R A. Elastic materials with couple-stresses[J].Archive for Rational Mechanics and Analysis,1962,11(1): 385-414.

[6]TOUPIN R A. Theory of elasticity with couple-stress[J].Arch Rat Mech Anal,1964,17: 85-11.

[7]KOITER W T. Couple stresses in the theory of elasticity Ⅰ & Ⅱ[J].Proceedings of the Koninklijke Nederlandse Akademie Van Wetenschappen,1964,67: 17-44.

[8]MINDLIN R D, TIERSTEN H F. Effects of couple-stresses in linear elasticity[J].Archive for Rational Mechanics and Analysis,1962,11(1): 415-448.

[9]YANG F, CHONG A C M, LAM D C C, et al. Couple stress based strain gradient theory for elasticity[J].International Journal of Solids and Structures,2002,39(10): 2731-2743.

[10]ZHENG P, LI G, SUN P, et al. Couple-stress-based gradient theory of poroelasticity[J].Mathematics and Mechanics of Solids,2024,29(1): 173-190.

[11]BIOT M A. Theory of propagation of elastic waves in a fluid-saturated porous solid, Ⅰ: low-frequency range[J].The Journal of the Acoustical Society of America,1956,28(2): 168-178.

[12]BIOT M A. Theory of propagation of elastic waves in a fluid-saturated porous solid, Ⅱ: higher frequency range[J].The Journal of the Acoustical Society of America,1956,28(2): 179-191.

[13]DING H, TONG L H, XU C, et al. On propagation characteristics of Rayleigh wave in saturated porous media based on the strain gradient nonlocal Biot theory[J].Computers and Geotechnics, 2022,141: 104522.

[14]HIRAI H. Analysis of Rayleigh waves in saturated porous elastic media by finite element method[J].Soil Dynamics and Earthquake Engineering,1992,11(6): 311-326.

[15]LIU H, ZHOU F, WANG L, et al. Propagation of Rayleigh waves in unsaturated porothermoelastic media[J].International Journal for Numerical and Analytical Methods in Geomechanics,2020,44(12): 1656-1675.

[16]TONG L H, LAI S K, ZENG L L, et al. Nonlocal scale effect on Rayleigh wave propagation in porous fluid-saturated materials[J].International Journal of Mechanical Sciences,2018,148: 459-466.

[17]SU C, GUAN W, YIN Y, et al. Elastic waves in fluid-saturated porous materials with a couple-stress solid phase[J].Journal of Sound and Vibration,2024,569: 117993.

[18]MNCH I, NEFF P, MADEO A, et al. The modified indeterminate couple stress model: why Yang et al.’s arguments motivating a symmetric couple stress tensor contain a gap and why the couple stress tensor may be chosen symmetric nevertheless[J].ZAMM-Journal of Applied Mathematics and Mechanics,2017,97(12): 1524-1554.

[19]HADJESFANDIARI A R, DARGUSH G F. Couple stress theory for solids[J].International Journal of Solids and Structures,2011,48(18): 2496-2510.

[20]HADJESFANDIARI A R. On the skew-symmetric character of the couple-stress tensor[J/OL].ArXiv: General Physics, 2013[2024-10-25］.https://api.semanticscholar.org/CorpusID:116973411.

[21]AKI K, RICHARDS P G.Quantitative Seismology[M]. 2nd ed. University Science Books,2002.

[22]ZHENG P, DING B. Potential method for 3D wave propagation in a poroelastic medium and its applications to Lamb’s problem for a poroelastic half-space[J].International Journal of Geomechanics,2016,16(2): 04015048.

[23]CHENG A H D.Poroelasticity[M]. Switzerland: Springer International Publishing, 2016.

[24]MAVKO G, MUKERJI T, DVORKIN J.The Rock Physics Handbook[M]. 2nd ed. Cambridge: Cambridge University Press, 2009.

施引文献

资源附件(0)

访问统计

计量

文章访问数: 25
HTML全文浏览量: 8
PDF下载量: 1
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

留言板

基于偶应力弹性梯度理论的饱和孔隙介质中Rayleigh波的传播特性

doi: 10.21656/1000-0887.450259

作者简介:
李国强（1997—），男，硕士生(E-mail: 1767445763@qq.com);郑佩（1980—），男，副教授，硕士生导师(通讯作者. E-mail: aliaspei@usst.edu.cn);张克明（1983—），男，副教授，硕士生导师(E-mail: zhangkeming@usst.edu.cn).

通讯作者:
郑佩（1980—），男，副教授，硕士生导师(通讯作者. E-mail: aliaspei@usst.edu.cn)

计量

Propagation Characteristics of Rayleigh Waves in Saturated Porous Media Based on the Couple-Stress Elastic Gradient Theory

计量

目录

留言板

基于偶应力弹性梯度理论的饱和孔隙介质中Rayleigh波的传播特性

doi: 10.21656/1000-0887.450259

作者简介: 李国强（1997—），男，硕士生(E-mail: 1767445763@qq.com);郑佩（1980—），男，副教授，硕士生导师(通讯作者. E-mail: aliaspei@usst.edu.cn);张克明（1983—），男，副教授，硕士生导师(E-mail: zhangkeming@usst.edu.cn).

通讯作者: 郑佩（1980—），男，副教授，硕士生导师(通讯作者. E-mail: aliaspei@usst.edu.cn)

计量

出版历程

Propagation Characteristics of Rayleigh Waves in Saturated Porous Media Based on the Couple-Stress Elastic Gradient Theory

计量

出版历程

目录

作者简介:
李国强（1997—），男，硕士生(E-mail: 1767445763@qq.com);郑佩（1980—），男，副教授，硕士生导师(通讯作者. E-mail: aliaspei@usst.edu.cn);张克明（1983—），男，副教授，硕士生导师(E-mail: zhangkeming@usst.edu.cn).

通讯作者:
郑佩（1980—），男，副教授，硕士生导师(通讯作者. E-mail: aliaspei@usst.edu.cn)