车路耦合振动中Galerkin截断收敛阶数的研究

doi:10.3901/JME.2021.12.031

机械工程学报 ›› 2021, Vol. 57 ›› Issue (12): 31-39.doi: 10.3901/JME.2021.12.031

• 特邀专栏：汽车-道路相互作用动力学前沿问题 • 上一篇下一篇

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车路耦合振动中Galerkin截断收敛阶数的研究

陈鸿燕^1,2,3, 丁虎^1,2,3, 陈立群^1,2,3

1. 上海大学力学与工程科学学院上海 200072;
2. 上海应用数学和力学研究所上海 200072;
3. 上海能源工程力学重点实验室上海 200072

收稿日期:2020-07-09 修回日期:2021-01-28 出版日期:2021-08-31 发布日期:2021-08-31
通讯作者: 丁虎(通信作者),男,1978年出生,博士,研究员,博士研究生导师。主要研究方向为非线性动力学、非线性振动与控制。E-mail:dinghu3@shu.edu.cn
作者简介:陈鸿燕,女,1992年出生,博士研究生。主要研究方向为非线性振动与控制。E-mail:hongyan_chen1028@163.com
基金资助:
国家自然科学基金资助项目（11772181）

Analysis of the Galerkin Tuncation Convergence Term in the Vehicle-pavement System

CHEN Hongyan^1,2,3, DING Hu^1,2,3, CHEN Liqun^1,2,3

1. School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072;
2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072;
3. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai 200072

Received:2020-07-09 Revised:2021-01-28 Online:2021-08-31 Published:2021-08-31

摘要/Abstract

摘要： Galerkin截断法是研究车路耦合系统动力学响应的常用方法。将路面假设为非线性黏弹性地基夹层梁模型，车辆假设为匀速运动的弹簧振子，建立车路耦合系统的振动方程。基于路面线性固有频率，提出两种确定Galerkin截断收敛项的有效方案，并分析系统耦合振动响应的收敛性。观察不同车速下的路面响应和车辆振动位移。当车身发生共振时，分析不同路面厚度下Galerkin截断数对系统收敛性的影响。讨论系统达到收敛时，车辆悬架刚度和阻尼，路面不平度波长和幅值对路面变形和车辆振动位移的影响。数值研究表明，提出的方案对车路耦合系统的收敛性判断具有较高的准确性，大大提高了计算效率，对研究人员解决车路耦合系统动力学问题有一定的促进作用。

关键词: Galerkin方法, 收敛性, 耦合振动, 夹层梁

Abstract: The Galerkin truncation method is a commonly used method to study the dynamic response of vehicle-pavement systems. The pavement and the vehicle are modeled as a sandwich beam on the nonlinear viscoelastic foundation and a spring vibrator with uniform speed, respectively. The coupled vibration equation of vehicle-pavement system is established. Two effective schemes for determining the Galerkin truncation convergence term based on the linear natural frequency of the pavement are proposed. The convergence of the coupled vibration response is analyzed. The pavement response and the vehicle vibration displacement at different speeds are observed. The influence of the Galerkin truncation term on the convergence of the system under different pavement thickness is analyzed. The effects of the vehicle suspension stiffness and damping, road roughness wavelength and amplitude on the pavement deformation and the vehicle vibration displacement when the system reaches convergence are discussed. Numerical investigations prove that the proposed schemes have high accuracy for judging the convergence of the vehicle-pavement system, and can greatly improve the calculation efficiency. It has a certain role in promoting researchers to solve the dynamic problems of vehicle-pavement system.

Key words: Galerkin method, convergence, coupled vibration, sandwich beam

中图分类号:

陈鸿燕, 丁虎, 陈立群. 车路耦合振动中Galerkin截断收敛阶数的研究[J]. 机械工程学报, 2021, 57(12): 31-39.

CHEN Hongyan, DING Hu, CHEN Liqun. Analysis of the Galerkin Tuncation Convergence Term in the Vehicle-pavement System[J]. Journal of Mechanical Engineering, 2021, 57(12): 31-39.

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车路耦合振动中Galerkin截断收敛阶数的研究

Analysis of the Galerkin Tuncation Convergence Term in the Vehicle-pavement System

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