弹性半空间地基梁的水平动力等效刚度

兰州理工大学学报 ›› 2020, Vol. 46 ›› Issue (5): 113-117.

弹性半空间地基梁的水平动力等效刚度

王雪¹, 周凤玺^1,2

1.兰州理工大学土木工程学院, 甘肃兰州 730050;
2.兰州理工大学西部土木工程防灾减灾教育部工程研究中心, 甘肃兰州 730050

收稿日期:2019-11-01 出版日期:2020-10-28 发布日期:2020-11-06
通讯作者: 周凤玺(1979-),男,甘肃会宁人,博士,教授.
作者简介:王雪(1994-),女,黑龙江大兴安岭人,硕士.
基金资助:
国家自然科学基金(51368038),甘肃省陇原青年创新创业人才资助项目

Horizontal dynamic equivalent rigidity of foundation beam on elastic half space

WANG Xue¹, ZHOU Feng-xi^1,2

1. College of Civil Engineering, Lanzhou Univ. of Tech., Lanzhou 730050, China;
2. Engineering Research Center of Disaster Mitigation in Civil Engineering of Ministry of Education, Lanzhou Univ. of Tech., Lanzhou 730050, China

Received:2019-11-01 Online:2020-10-28 Published:2020-11-06

摘要/Abstract

摘要： 基于弹性动力学的基本方程、考虑弹性梁和弹性半空间的动力相互作用,建立力学分析模型,并利用Fourier积分变换,得到弹性半空间地基梁的水平动力等效刚度的解析表达式.通过数值算例分析地基梁的水平动力等效刚度及其阻尼的变化情况.结果表明:地基梁的水平动力刚度和阻尼系数不为常数,而是与弹性梁中传播的相速度有关,当相速为Rayleigh波的速度时,水平动力等效刚度达到峰值,此时弹性梁的纵向振动向弹性半空间传递的能量最大.水平动力等效刚度与弹性地基梁的频率和波数密切相关,随着波数增大,水平动力等效刚度的实部和虚部均相应增大.

关键词: 弹性半空间, 欧拉-伯努利梁, Fourier积分变换, 水平动力等效刚度

Abstract: Based on the basic equation of elastodynamics and taking into account the dynamic interaction between elastic beam and elastic half-space, a mechanical analysis model is established. An analytical expression of horizontal dynamic equivalent stiffness of an elastic half-space foundation beam is obtained by using Fourier integral transformation. The variation of horizontal dynamic equivalent stiffness and damping of the elastic foundation beam is analyzed respectively by numerical examples. The results show that the horizontal dynamic stiffness and damping coefficient of the elastic foundation beam are not constant, but are related to phase velocity of the elastic foundation beam. When the phase velocity is equal to velocity of Rayleigh wave, the horizontal dynamic equivalent stiffness reaches the peak, and the longitudinal vibration of the elastic foundation beam transfers the maximum energy to the elastic half-space. The horizontal dynamic equivalent stiffness of the elastic foundation beam is closely related to the frequency and number of waves in the beam. With increase of wave number, the real and imaginary parts of the horizontal dynamic equivalent stiffness increase accordingly.

Key words: elastic half space, Euler-Bernoulli beam, Fourier integral transformation, horizontal dynamic equivalent stiffness

中图分类号:

TU311
TU470

王雪, 周凤玺. 弹性半空间地基梁的水平动力等效刚度[J]. 兰州理工大学学报, 2020, 46(5): 113-117.

WANG Xue, ZHOU Feng-xi. Horizontal dynamic equivalent rigidity of foundation beam on elastic half space[J]. Journal of Lanzhou University of Technology, 2020, 46(5): 113-117.

参考文献

[1] 杨光.求解地基动力刚度系数的频域有限元:局部透射边界方法 [J].世界地震工程,1994(1):21-24.
[2] 杨先健.天然地基各向动力刚度的相互关系[J].建筑结构,1996(12):15-19.
[3] 王四根.刚性动力荷载作用下地基动力反应的若干问题[J].岩土力学,2003,24(2):000202-208.
[4] 王军.垫层地基与复合地基土动力参数的试验研究[D].西安:西安建筑科技大学,2006.
[5] 蔡袁强,胡秀青.饱和地基中埋置刚性圆柱基础的等效竖向动力刚度[J].岩石力学与工程学报,2008,27(2):361-367.
[6] 胡秀青,蔡袁强.下卧基岩饱和地基中埋置刚性基础的竖向振动问题研究[J].岩土力学,2009,30(12):003739-003746.
[7] 余文正,陶忠,杨瑞欣,等.土-相邻基础相互作用的地基刚度计算分析[J].岩土力学,2016,37(6):1633-1641.
[8] 巴振宁,梁建文,胡黎明.层状横观各向同性地基中埋置刚性基础的平面外动力刚度系数[J].岩土工程学报,2017,39(2):343-351.
[9] 巴振宁,胡黎明,梁建文.层状横观各向同性地基上刚性条形基础动力刚度系数[J].土木工程学报,2017(9):67-81.
[10] DIETERMAN H A.The equivalent stiffness of a half-space interacting with a beam,critical velocities of a moving load along the beam[J].European Journal of Mechanics-A/Solids,1996,15(1):67-90.
[11] METRIKINE A V,DIETERMAN H A.The equivalent vertical stiffness of an elastic half-space interacting with a beam,including the shear stresses at the beam-half-space interface[J].European Journal of Mechanics A Solids,1997,16(3):408-14.
[12] ANAM I,ROSET J M.Dynamic stiffnesses of surface foundations:an explicit solution[J].International Journal of Geomechanics,2004,4(3):216-223.
[13] SENJUNTICHAI T,MANI S,RAJAPAKSE R K N D.Vertical vibration of an embedded rigid foundation in a poroelastic soil[J].Soil Dynamics & Earthquake Engineering,2006,26(6):626-636.
[14] RAJAPAKSE R K N D,SHAH A H.Impedances of embedded rigid strip foundations[J].Earthquake Engineering & Structural Dynamics,2010,16(2):255-273.
[15] HAN Z,LIN G,LI J.Dynamic impedance functions for arbitrary-shaped rigid foundation embedded in anisotropic multilayered soil[J].Journal of Engineering Mechanics,2015,141(11):04015045.
[16] GUHA I,RANDOLPH M F,WHITE D J.Evaluation of elastic stiffness parameters for pipeline-soil interaction[J].Journal of Geotechnical & Geoenvironmental Engineering,2016,142(6):04016009.
[17] LIANG J,FU J,TODOROVSKA M I,et al.In-plane soil-structure interaction in layered,fluid-saturated,poroelastic half-space I:structural response[J].Soil Dynamics & Earthquake Engineering,2016,81:84-111.
[18] LAMB H.On the propagation of tremors over the surface of an elastic solid[J].Philosophical Transactions of the Royal Society of London,1904,203(359-371):1-4.