A modal analysis of vibration response of a cracked fluid-filled cylindrical shell

• Published in: Applied Mathematical Modelling 2021-03, Vol.91, p.934-958
• Main Authors: Zheng, Shuihua, Yu, Yankun, Qiu, Mianzhen, Wang, Liumin, Tan, Dapeng
• Format: Article
• Language: English
• Subjects: Condition monitoring; Crack damage detection; Cylindrical shells; Damage detection; Energy flow; Flexibility matrix; Fluid-structure interaction; Fluid-structure interaction (FSI); Forced vibration; Helmholtz equations; Mathematical analysis; Matrix methods; Modal analysis; Partial differential equations; Power flow; Resonant frequencies; Shell theory; Shells; Sound pressure; Structural damage; Thin cylindrical shell; Thin walled shells; Vibration analysis; Vibration response; Wave propagation
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2020.09.040

•According to the Flügge equation, the cylindrical shell vibration response is acquired by wave propagation method.•Considering the surrounding fluid as acoustic medium, the Helmholtz equation is used to describe sound pressure field.•A breathing linear spring model (BLSM) is set up to obtain the crack stress and displacement.•A crack damage detection method based on vibration energy flow is proposed. The shock and vibration response of a thin cylindrical shell is a complex fluid-structure interaction (FSI) dynamic problem, which is very important to the monitoring of the shell condition and the detection of any shell damage. In this paper, the high-order partial differential equation (PDE) of thin shell motion is derived from the Flügge shell theory, and the vibration response of the cylindrical shell system is obtained by the wave propagation method (WPM). In this study, the surrounding fluid of the shell is considered as an ideal acoustic medium and the Helmholtz equation is used to describe the sound pressure field. Using a combination of the above methods, we are able to observe and summarize the patterns regarding the change of the forced vibration response of a thin cylindrical shell under the FSI condition. As far as the crack is concerned, a local flexibility matrix is constructed according to the facture mechanical principles, a breathing linear spring model (BLSM) is set up to obtain the crack stress and displacement. Thus, not only the vibration response of the cracked fluid-filled cylindrical shell is obtained, but also a damage detection method based on the vibration energy flow is presented. This study comes to the following conclusions regarding the fluid-filled thin cylindrical shell: (1) the displacement response of the shell caused by nonlinear excitations vary significantly in the radial, axial and circumferential directions; (2) the crack on the shell cause both local flexibility and natural frequency to decrease; (3) The normalized input power flows prove to be an effective damage detection method for the shell. This study not only makes meaningful contribution to the research field focusing on the vibration response of fluid-filled thin cylindrical shells, but also offers a practical crack damage detection method for structures under the FSI condition.