含有摇摆装置的双层桥墩结构随机振动分析  

Random vibration analysis for double-deck pier structure with rocking device

作　　者：胡慧瑛 陈林聪[1,2] 钱佳敏 HU Hui-ying;CHEN Lin-cong;QIAN Jia-min(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,福建厦门361021 [2]福建省智慧基础设施与监测重点实验室,福建厦门361021

出　　处：《振动工程学报》2023年第3期645-651,共7页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(12072118);福建省自然科学基金资助项目(2019J01049);厦门市青年创新基金资助项目(3502Z20206005);华侨大学研究生科研创新基金资助项目(18013086013)。

摘　　要：基于一种下层含有摇摆装置的双层桥墩结构模型,建立了系统的随机动力学系统模型,其中随机激励选用高斯白噪声模型,自复位恢复力采用经典旗帜形模型。运用广义谐波平衡法将旗帜形滞回力近似分解为幅值依赖的等效拟线性弹性力和拟线性阻尼力,获得原系统的等效随机系统;采用标准随机平均法理论,将等效系统近似为关于幅值的平均伊藤随机微分方程,建立并求解与之对应的Fokker‑Planck‑Kolmogorov(FPK)方程获得系统的稳态响应。探讨系统参数,如能量耗散系数等对系统稳态响应的影响,并通过Monte Carlo数值模拟加以验证。另外,借助Laplace变换,得到等效系统的转换函数及条件功率谱密度,结合下层幅值的稳态概率密度,得到下层幅值响应的功率谱密度估计。In this paper,the random vibration of a double-deck pier structure with a rocking device is studied.A new type of doubledeck pier structure system is designed,and the relevant stochastic dynamics model is established.The Gaussian white noise model is used for random excitation,and the classic flag-shaped model is adopted for self-centering restoring force.Using the generalized harmonic balance method,the flag-shaped hysteresis force is decomposed into the amplitude-dependent equivalent quasi-linear elastic force and quasi-linear damping force to obtain the equivalent system of the original system.With the technique of standard stochastic averaging,the equivalent system is approximated as the averaged Itôstochastic equation of amplitude,and the corresponding Fokker-Planck-Kolmogorov(FPK)equation is established and solved to obtain the stationary response of the system.The effects of system parameters,such as energy dissipation coefficient,on the stationary response of the system are discussed and verified by Monte Carlo simulation.In addition,the transformation function and conditional power spectral density of the equivalent system are derived by Laplace transform.Combining with the stationary response of the lower mass,the power spectral density estimation of the lower structure amplitude is obtained.

关 键 词：摇摆装置 双层桥墩结构 标准随机平均法 稳态概率密度函数 功率谱密度估计 

分 类 号：O324[理学—一般力学与力学基础] U443.22[理学—力学]