地震激励下深水桥墩的随机振动分析  

Stochastic vibration analysis of a deep-water pier under seismic excitation

作　　者：黄湘凤 陈林聪[1,2] 赵珧冰 HUANG XiangFeng;CHEN LinCong;ZHAO YaoBing(College of Civil Engineering,Huaqiao University,Xiamen 361021,China;Key Laboratory for Intelligent Infrastructure and Monitoring of Fujian Province,Xiamen 361021,China)

机构地区：[1]华侨大学土木工程学院,厦门361021 [2]福建省智慧基础设施与监测重点实验室,厦门361021

出　　处：《中国科学：技术科学》2023年第4期622-630,共9页Scientia Sinica(Technologica)

基　　金：国家自然科学基金(批准号:12072118,12102138);福建省杰出青年科学基金(编号:2021J06024);厦门青年创新基金(编号:3502Z20206005)资助项目。

摘　　要：深水桥墩属于一类浸没在深水区域中的细长结构,在地震激励下不能忽略动水压力效应以及非线性效应,又鉴于地震激励的随机特性,因而地震激励下深水桥墩的动力学问题可归结为一个非线性随机振动问题,需开展非线性随机振动研究.为此,本文首先建立深水桥墩的非线性随机动力学模型,包括:将桥墩简化为固定在岩石地基上的悬臂梁;采用Kanai-Tajimi过滤白噪声模型模拟地震动加速度过程;利用辐射波浪理论描述动水压力以及凯恩方法推导深水桥墩系统的运动方程.随后,运用标准随机平均法将系统运动方程近似为关于幅值的平均伊藤方程,建立并求解相应的FPK方程以获得该系统的近似稳态概率密度函数.最后,分别考察了激励强度,质量比以及浸入比对系统稳态响应的影响,并采用蒙特卡罗模拟验证理论解析解的有效性.结果表明:理论解析解与蒙特卡罗模拟结果相当吻合,理论解析解具有较高的精度;激励强度的增强、质量比的增加以及浸入比的提高均会对桥墩的稳态响应产生负面影响,即放大了系统的响应;动水压力效应降低了质量比对系统响应的影响程度;桥墩内域水体的存在也会放大系统响应,且这种影响会随着浸没比的增加而增加.本文的研究结果对于深水桥墩的抗震优化设计具有一定的参考价值.A deep-water pier is a slender structure immersed in a deep-water area.The hydrodynamic pressure and nonlinear effects cannot be ignored as a deep-water pier undergoes seismic excitation.Because seismic excitation is stochastic,the dynamic problem of a deepwater pier under seismic excitation is a nonlinear stochastic vibration problem,which must be studied using the theory of nonlinear stochastic vibration.To this end,this paper first established a nonlinear stochastic dynamic model of the deep-water pier structure,including simplifying the pier as a cantilever beam fixed on a rock foundation,simulating the ground motion acceleration process with the Kanai-Tajimi filtering white noise model,describing the hydrodynamic pressure with radiation wave theory,and deriving the system's motion equation by applying Kane's method.Subsequently,the standard stochastic averaging method was used to derive the averaged It?equation for the amplitude envelope,and the corresponding Fokker-Planck-Kolmogorov equation was established and solved to obtain the approximate stationary probability density function of the system in closed form.Finally,the effects of parameters such as excitation intensity,mass ratio,and immersion ratio on the stationary response of the system were examined,and the validity of the theoretical analytical solution was verified using a Monte Carlo simulation.The theoretical analytical solutions agreed perfectly with the Monte Carlo simulation results and had high accuracy.The increase in the excitation intensity,mass ratio,and immersion ratio harmed the stationary response of the pier;that is,the system response was amplified.The hydrodynamic effect reduced the negative effect of mass ratio on structure response.The presence of inner water amplified the response of the system,and the negative effect increased with the immersion ratio.The results obtained in this paper have great application value for the seismic optimization design of deep-water piers.

关 键 词：深水桥墩 随机振动 动水压力 随机地震激励 随机平均法 

分 类 号：U442.55[建筑科学—桥梁与隧道工程]