振动
有限元法
梁(结构)
结构工程
模态分析
帧(网络)
刚度矩阵
传递函数
直接刚度法
刚度
特征向量
传递矩阵
固有频率
计算机科学
声学
工程类
物理
电信
电气工程
计算机视觉
量子力学
作者
Ke Wu,Hailian Zhang,Jianping Zhou
标识
DOI:10.1142/s0219455424501591
摘要
In this paper, based on distributed transfer function method (DTFM), the closed-form analytical solutions for vibrations of Euler–Bernoulli beam and frame structures with arbitrary number of cracks are studied. First, generalized DTFM is employed to characterize the dynamical model for a single cracked beam and its analytical solutions for eigenvalue problem and frequency response are obtained. Then, a new DTFM cracked element that encapsulates one crack of arbitrary location inside the beam is proposed. Using the DTFM cracked element and global dynamic stiffness matrix assembly technique, damaged frame structures of arbitrary form can be modeled for vibration analysis. Previous analytical methods only addressed low-frequency vibration of simple cracked beam structures, the proposed method can yield analytical solutions in the medium- and high-frequency regions, which is critical for the small crack detection in complex frames. Lastly, three numerical examples are given to illustrate the correctness and effectiveness of the DTFM in analyzing natural frequencies, modal shapes and frequency responses for cracked structures. By comparing with the Finite Element Method (FEM) and benchmarks from literatures, we proved that the DTFM has better performances in terms of accuracy and efficiency.
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