An analytical study on mechanics response of simply supported beams with damages

DONG Wenqi; YANG Yi; WANG Yushuang; HUANG Chihui

doi:10.13471/j.cnki.acta.snus.2018.06.010

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An analytical study on mechanics response of simply supported beams with damages

更新时间：2023-12-11

- An analytical study on mechanics response of simply supported beams with damages
- Acta Scientiarum Naturalium Universitatis SunYatseni Vol. 57, Issue 6, Pages: 77-87(2018)
- 作者机构：
  
  华南理工大学土木与交通学院,广东,广州,510641
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.2018.06.010
  CLC：
- Published：2018，
  
  Published Online：25 November 2018，
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DONG Wenqi, YANG Yi, WANG Yushuang, et al. An analytical study on mechanics response of simply supported beams with damages. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 57(6):77-87(2018)
DOI：

DONG Wenqi, YANG Yi, WANG Yushuang, et al. An analytical study on mechanics response of simply supported beams with damages. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 57(6):77-87(2018) DOI： 10.13471/j.cnki.acta.snus.2018.06.010.

摘要

利用有限元法和U变换法相结合，对带损伤简支梁的力学响应进行了解析研究。首先把简支梁均匀划分为具有n个子结构的周期结构，构造一个等效的循环周期结构系统，将损伤部分看作一个局部荷载项，建立其控制方程，然后对控制方程应用U变换进行解耦，得到节点挠度的解析表达式；在求出损伤单元的位移之后，可以得到整个简支梁的所有节点位移；然后，讨论了单元的损伤程度以及损伤位置对简支梁挠度的影响，并给出了结构固有频率的计算公式。

Abstract

This paper presents an analytical study on the mechanics response of simply supported beams with stiffness damage by combining the finite element method with the U-transformation method. Firstly

a simply supported beam is divided into

substructures

and an equivalent structure with cyclic periodicity is constructed

and the governing equations are established

in which stiffness damage is treated as a loading. Then U-transformation technic is applied to the equations and the analytical expression of nodal deflections of the beam are derived. The influences of damage location and damage degree on these solutions are discussed. Moreover

the natural frequencies of damaged beam are solved.

关键词

简支梁U变换法损伤静力分析固有频率

Keywords

simply supported beamU-transformation methoddamagestatic analysisnatural frequency

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