基于Chebyshev-Ritz法分析两端固支梁在移动荷载下的动力响应  

Dynamic Responses of Clamped-clamped Beams under Moving Loads Based on Chebyshev-Ritz Method

作　　者：蒋杰 邓安妍 陈继业 JIANG Jie;DENG Anyan;CHEN Jiye(Nanjing Municipal Design and Research Institute Co.,Ltd.,Nanjing 210018,China;School of Civil Engineering and Architecture,Jiangsu University of Science and Technology,Zhenjiang 212100,China)

机构地区：[1]南京市市政设计研究院有限责任公司,江苏南京210018 [2]江苏科技大学土木工程与建筑学院,江苏镇江212100

出　　处：《南京工程学院学报（自然科学版）》2024年第2期69-75,共7页Journal of Nanjing Institute of Technology(Natural Science Edition)

摘　　要：基于小变形、二维弹性力学理论,采用Chebyshev-Ritz法分析两端固支梁在移动集中简谐荷载下的动力响应.利用第一类Chebyshev多项式与边界特征函数的积作为梁位移的试函数,给出求解梁任意阶自振频率的方法,采用Newmark-β法求解振动控制方程得到梁位移响应的数值解.由收敛性分析可知本文方法求解的数值稳定、收敛快速且精度较高,与有限元软件ANSYS建模分析结果对比一致性较好.分析加速、减速和匀速运动下不同速度、荷载频率对于位移响应的影响,可为桥梁损伤检测和计算提供数据支撑和理论参考.Based on the theory of small deformation and two-dimensional elastic mechanics,the Chebyshev-Ritz method was used to analyze the dynamic response of a beam fixed at both ends under a moving concentrated simple harmonic load.The product of the first type of Chebyshev polynomial and the boundary characteristic function was used as the trial function of the beam displacement,and a method for solving the natural frequency of any order of the beam was given.The Newmark-β method was used to solve the vibration control equation and obtain the numerical solution for the beam displacement response.The convergence analysis showed that the numerical value solved by this method was stable with rapid convergence and high accuracy.The comparison with the finite element software ANSYS showed good consistency.Finally,the different speeds under acceleration,deceleration,and uniform motion were analyzed,along with the influence of load frequency on displacement response,providing data support and a theoretical reference for bridge damage detection and calculation.

关 键 词：二维弹性理论 移动荷载 Chebyshev-Ritz法 动力响应 

分 类 号：TV312[水利工程—水工结构工程]