Dynamic analysis of pre-stressed elastic plates resting on layered soils

LIU Chun-lin; AI Zhi-yong; TANG Meng-xiong; HU He-song

doi:10.11779/CJGE202101020

Volume 43 Issue 1

Turn off MathJax

Article Contents

Abstract

References

Chinese Journal of Geotechnical Engineering > 2021 > 43(1): 174-180. > DOI: 10.11779/CJGE202101020

LIU Chun-lin, AI Zhi-yong, TANG Meng-xiong, HU He-song. Dynamic analysis of pre-stressed elastic plates resting on layered soils[J]. Chinese Journal of Geotechnical Engineering, 2021, 43(1): 174-180. DOI: 10.11779/CJGE202101020

Citation:

PDF (1117 KB)

Dynamic analysis of pre-stressed elastic plates resting on layered soils

1.
Guangzhou Institute of Building Science Co., Ltd., Guangzhou510440, China
2.
Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China
3.
School of Civil Engineering and Transportation, South China University of Technology, Guangzhou510641, China

More Information

Received Date: December 30, 2019
Available Online: December 04, 2022

Graphical Abstract

Abstract

Abstract

Based on the analytical layer-element method and classical the elastic thin plate theory, a method for solving the vertical dynamic interaction between the layered soils and the pre-stressed elastic plates is proposed. Starting from the fundamental solution of soils and the dynamic equation of elastic plates, a dynamic coupling equation for the soils and elastic plates in the transformation domain is obtained by means of the Hankel integral transformation and the compatibility condition at the soil-elastic plate interface. The displacement solution for the pre-stressed elastic plates in frequency domain is further obtained by solving the coupling equation and the numerical inverse transformation. By comparing with the results in the existing literatures, the accuracy of the proposed method and the program is verified. Finally, the influences of the stiffness ratio of the plates to the soils and the radial pre-stress of plate on the vertical dynamic displacement of pre-stressed elastic plates are discussed.
- pre-stressed elastic plate,
- layered soil,
- analytical layer-element method,
- vertical vibration,
- classical elastic thin plate theory

FullText(HTML)

References (21)

References

[1]	RAJAPAKSE R K N D. Dynamic response of elastic plates on viscoelastic half space[J]. Journal of Engineering Mechanics, 1989, 115(9): 1867-1881. doi: 10.1061/(ASCE)0733-9399(1989)115:9(1867)
[2]	GUCUNSKI N, PEEK R. Vertical vibrations of circular flexible foundations on layered media[J]. Soil Dynamics and Earthquake Engineering, 1993, 12(3): 183-192. doi: 10.1016/0267-7261(93)90045-S
[3]	金波. 用第二类Fredholm积分方程求解弹性半空间上弹性板的垂直振动[J]. 应用数学和力学, 1998, 19(2): 145-150. https://www.cnki.com.cn/Article/CJFDTOTAL-YYSX802.006.htm JIN Bo. Using Fredholm integral equation of the second kind to solve the vertical vibration of elastic plate on an elastic half-space[J]. Applied Mathematics and Mechanics, 1998, 19(2): 145-150. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YYSX802.006.htm
[4]	YU L, SHEN H S, HUO X P. Dynamic responses of Reissner-Mindlin plates with free edges resting on tensionless elastic foundations[J]. Journal of Sound and Vibration, 2007, 299(1/2): 212-228.
[5]	CHEN S S, HOU J G. Modal analysis of circular flexible foundations under vertical vibration[J]. Soil Dynamics and Earthquake Engineering, 2009, 29(5): 898-908. doi: 10.1016/j.soildyn.2008.10.004
[6]	张建辉. 双参数地基板的无单元法[J]. 岩土工程学报, 2005, 27(7): 776-779. doi: 10.3321/j.issn:1000-4548.2005.07.011 ZHANG Jian-hui. Element-free method for two-parameter subgrade plates[J]. Chinese Journal of Geotechnical Engineering, 2005, 27(7): 776-779. (in Chinese) doi: 10.3321/j.issn:1000-4548.2005.07.011
[7]	王春玲, 赵鲁珂, 李东波. 非饱和地基上多层矩形板稳态响应解析研究[J]. 岩土工程学报, 2019, 41(12): 2182-2190. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201912005.htm WANG Chun-Lin, ZHAO Lu-ke, LI Dong-bo. Analytical study on dynamic response of multi-layered plate in unsaturated half-space[J]. Chinese Journal of Geotechnical Engineering, 2019, 41(12): 2182-2190. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201912005.htm
[8]	孙璐, 邓学钧. 弹性基础无限大板对移动荷载的响应[J]. 力学学报, 1996, 28(6): 756-760. doi: 10.3321/j.issn:0459-1879.1996.06.016 SUN Lu, DENG Xue-jun. General theory for stead dynamic problem of infinite plate on an elastic foundation[J]. Acta Mechanica Sinica, 1996, 28(6): 756-760. (in Chinese) doi: 10.3321/j.issn:0459-1879.1996.06.016
[9]	KIM S M, ROESSET J M. Moving loads on a plate on elastic foundation[J]. Journal of Engineering Mechanics, 1998, 124(9): 1010-1017. doi: 10.1061/(ASCE)0733-9399(1998)124:9(1010)
[10]	卢正, 姚海林, 杨洋. 上覆弹性板双层地基在移动荷载作用下的动力响应[J]. 岩石力学与工程学报, 2008, 27(增刊2): 3312-3320. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX2008S2006.htm LU Zheng, YAO Hai-lin, YANG Yang. Dynamic response of an elastic slab resting on double-layered subgrade subjected to moving load[J]. Chinese Journal of Rock Mechanics and Engineering, 2008, 27(S2): 3312-3320. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX2008S2006.htm
[11]	蔡袁强, 孙宏磊, 徐长节. 移动荷载下上覆弹性板饱和地基的动力响应[J]. 计算力学学报, 2008, 25(2): 156-161. https://www.cnki.com.cn/Article/CJFDTOTAL-JSJG200802003.htm CAI Yuan-qiang, SUN Hong-lei, XU Chang-jie. Response of beams on poroelastic half-space soil medium to moving load[J]. Chinese Journal of Computational Mechanics, 2008, 25(2): 156-161. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JSJG200802003.htm
[12]	CAI Y, CAO Z, SUN H, et al. Dynamic response of pavements on poroelastic half-space soil medium to a moving traffic load[J]. Computers and Geotechnics, 2009, 36(1/2): 52-60.
[13]	曹彩芹, 李诚诚, 李华. 移动荷载作用下路面板与饱和弹性地基的动力响应[J]. 西安建筑科技大学学报(自然科学版), 2014, 46(2): 204-209. https://www.cnki.com.cn/Article/CJFDTOTAL-XAJZ201402010.htm CAO Cai-qin, LI Cheng-cheng, LI Hua. Dynamic response of pavement plate-saturated elastic foundation under moving loads[J]. Journal of Xi'an Univerdity of Architecture & Technology (Natural Science Edition), 2014, 46(2): 204-209. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-XAJZ201402010.htm
[14]	张春丽, 王博, 祝彦知. 移动荷载下正交各向异性地基无限大板的动力响应[J]. 岩土工程学报, 2017, 39(2): 352-358. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201702024.htm ZHANG Chun-li, WANG Bo, ZHU Yan-zhi. Dynamic response of infinite elastic plate on orthotropic half-space medium under moving loads[J]. Chinese Journal of Geotechnical Engineering, 2017, 39(2): 352-358. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201702024.htm
[15]	KIM S M, CHUNG W. Vibration of simplified presstressed pavement model under moving two-axle harmonic loads[J]. KSCE Journal of Civil Engineering, 2009, 13(6): 409-421.
[16]	艾智勇, 杨轲舒. 横观各向同性层状地基上弹性矩形板的参数研究[J]. 岩土工程学报, 2016, 38(8): 1442-1446. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201608011.htm AI Zhi-yong, YANG Ke-shu. Parametric study on an elastic rectangle plate on transversely isotropic multi-layered soils[J]. Chinese Journal of Geotechnical Engineering, 2016, 38(8): 1442-1446. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201608011.htm
[17]	AI Z Y, XU C J, REN G P. Vibration of a pre-stressed plate on a transversely isotropic multilayered half-plane due to a moving load[J]. Applied Mathematical Modelling, 2018, 59: 728-738.
[18]	AI Z Y, LI Z X, CANG N R. Analytical layer-element solution to axisymmetric dynamic response of transversely isotropic multilayered half-space[J]. Soil Dynamics and Earthquake Engineering, 2014, 60: 22-30.
[19]	CHONAN S. Moving load on a pre-stressed plate resting on a fluid half-space[J]. Ingenieur-Archiv, 1976, 45(3): 171-178.
[20]	SNEDDON I N. The Use of Integral Transforms[M]. New York: McGraw-Hill, 1972.
[21]	艾智勇, 成怡冲. 轴对称受荷弹性圆板下横观各向同性多层地基分析[J]. 建筑结构学报, 2012, 33(4): 154-157. https://www.cnki.com.cn/Article/CJFDTOTAL-JZJB201204022.htm AI Zhi-yong, CHENG Yi-chong. Analysis of transversely isotropic layered soils beneath axisymmetrically loaded elastic circular plate[J]. Journal of Building Structures, 2012, 33(4): 154-157. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JZJB201204022.htm