Distributed Transfer Function Formulations for Vibration Analysis of Cracked Beam and Frame Structures
-
Published:2023-11-07
Issue:
Volume:
Page:
-
ISSN:0219-4554
-
Container-title:International Journal of Structural Stability and Dynamics
-
language:en
-
Short-container-title:Int. J. Str. Stab. Dyn.
Author:
Wu Ke123,
Zhang Hailian1,
Zhou Jianping1
Affiliation:
1. China Manned Space Agency, Beijing 100071, P. R. China
2. China Astronauts Research and Training Center, Beijing 100094, P. R. China
3. Beijing University of Aeronautics and Astronautics, Beijing 100083, P. R. China
Abstract
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.
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Mechanical Engineering,Ocean Engineering,Aerospace Engineering,Building and Construction,Civil and Structural Engineering