三参数Pasternak粘弹性地基中锥形桩的横向自由振动特性研究

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摘要研究了初始轴向压力作用下三参数Pasternak粘弹性地基中圆截面锥形桩的横向自由振动特性。将桩体简化为竖向线弹性Timoshenko锥形梁-柱, 考虑桩-土界面摩擦力及桩周土地基参数沿桩身纵向变化, 建立锥形桩-土体系动力学模型的控制方程；通过分离变量、无量纲化与微分求积法的数值模拟, 将该方程的求解转化为变系数的一般线性代数方程组的一次特征值问题, 进而采用QR法求解获得各阶特征值及其特征向量。探讨了相应边界条件下桩身锥角、桩顶轴向荷载、桩长径比、桩侧摩阻力与桩周土地基参数及其沿桩身线性变化情况等对桩横向自由振动基频及其衰减系数的影响。结果表明, 锥形桩的固有频率及其衰减系数随锥角的增加而降低, 且锥角越大, 临界阻尼越小, 锥角与地基阻尼的有明显的耦合效应; 桩侧摩阻力与桩周土地基参数沿桩身纵向的不均匀分布对其基频的影响不可忽略。

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	张金轮
	张阿祥
	葛仁余
	孙俊伟

关键词 ：粘弹性地基, 锥形桩, 横向自由振动, 微分求积法

Abstract：Based on a three-parameter Pasternak viscoelastic foundation model, the transverse free vibration characteristics of tapered pile of circular section subjected to initial axial pressure were investigated. The pile was simplified into a vertical linear elastic Timoshenko tapered beam-column, and the effects of pile-soil interface friction and the longitudinal variation of foundation parameters around the pile were considered, and then the dynamic governing equations for the tapered pile-soil system were derived. The solution of the equations was transformed into the first order eigenvalue problem of general linear algebraic equations with variable coefficients by means of variable separation, dimensionless and numerical simulation of the differential quadrature method. Then, the eigenvalues and eigenvectors of each order were solved by QR method. The effects of cone angle of pile, axial load on pile head, length-diameter ratio, lateral friction, soil foundation parameters around pile and their linear variation on the fundamental frequencies and attenuation coefficients of the tapered pile were discussed under corresponding boundary conditions. The results show that the natural frequencies and corresponding attenuation coefficients of tapered pile decrease with the increase of cone angle, and the critical damping decreases with the increase of cone angle, and then the coupling effect between cone angle and foundation damping is obvious. The influence of the lateral friction and the non-uniform distribution of foundation parameters along the longitudinal direction of the pile on the fundamental frequency cannot be ignored.

Key words： viscoelastic foundation tapered pile transverse free vibration differential quadrature method

收稿日期: 2021-07-29 出版日期: 2022-03-28

引用本文:

张金轮，张阿祥，葛仁余，孙俊伟. 三参数Pasternak粘弹性地基中锥形桩的横向自由振动特性研究[J]. 振动与冲击, 2022, 41(6): 183-196.
ZHANG Jinlun,ZHANG Axiang,GE Renyu,SUN Junwei. Transverse free vibration characteristics of a tapered pile in the three-parameter Pasternak viscoelastic foundation. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(6): 183-196.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2022/V41/I6/183

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