一种针对多裂纹弹性基础Timoshenko梁振动分析的解析方法  

Analytical method for vibration analysis of multi-cracked Timoshenko beam structures with elastic foundations

作　　者：伍科 彭祺擎 武新峰 刘朋博 寇亚军 WU Ke;PENG Qibo;WU Xinfeng;LIU Pengbo;KOU Yajun(China Astronauts Research and Training Center,Beijing 100094,China;China Manned SpaceAgency,Beijing 100071,China;HTYS Information Technology Co.,Ltd.Shanghai Branch,Shanghai 201107,China)

机构地区：[1]中国航天员科研与训练中心,北京100094 [2]中国载人航天工程办公室,北京100071 [3]航天跃盛(杭州)信息技术有限公司上海分公司,上海201107

出　　处：《航空学报》2024年第22期152-172,共21页Acta Aeronautica et Astronautica Sinica

摘　　要：针对具有弹性基础的任意多开裂纹Timoshenko阻尼梁结构,基于分布传递函数法(DTFM)的基本形式,提出了一种用于振动分析的新颖的解析方法。对于弹性基础,采用了考虑剪切变形和转动变形的二参数连续弹簧模型;对于梁结构上的局部开裂纹,引入了一种描述裂纹处广义位移不连续的局部附加柔度矩阵,然后建立了弹性基础多裂纹阻尼梁的控制方程;采用增强型分布传递函数形式,对裂纹梁组件和非裂纹组件分别建立了局部边界矩阵,并在全局坐标系中组装成全局边界方程;最后,以积分的形式得到了多裂纹阻尼梁的封闭形式的解析解;应用解析表达式,对裂纹梁结构的模态频率、模态振型及频域响应进行分析。在数值仿真算例中,将本文方法得到的动力学响应结果与参考文献和用有限元方法得到的结果进行了对比,验证了提出方法的正确性。与有限元方法相比,提出的方法对于中、高频动力学响应计算具有更高的精度和效率,可以有效地应用于弹性基础梁的裂纹检测问题中。This study proposes a novel analytical method for vibration analysis of arbitrary multi-crack Timoshenko damping beam structures with elastic foundations based on the Distributed Transfer Function Method(DTFM).A twoparameter continuous spring model considering shear and rotational deformation is adopted for the elastic foundation.For local cracks on the beam structure,a local additional compliance matrix induced by the crack is employed,and the governing equation of the multi-cracked Timoshenko damping beam with an elastic foundation established.Using the augmented distributed transfer function method,we establish the local boundary matrices of the non-cracked and cracked beam components,respectively,and then obtain the global boundary equation in the global coordinate system.Finally,a closed-form analytical solution is derived in integral form,and the natural frequencies,mode shapes,and frequency responses of the cracked beam structures can be derived.In numerical examples,the results from previous papers and the Finite Element Method(FEM)are employed to validate the correctness of the proposed method,and the effect of the cracks and the elastic foundations on dynamic behaviors investigated.With higher computational accuracy and efficiency than the FEM for mid-to-high frequency dynamic responses,the proposed method can be used for crack detection of elastic foundation beams.

关 键 词：分布传递函数法 弹性基础 多裂纹梁 模态频率 频域响应 高频动力学 

分 类 号：V414.3[航空宇航科学与技术—航空宇航推进理论与工程]