Modeling and analysis of forced vibration of the thin-walled cylindrical shell with arbitrary multi-ring hard coating under elastic constraint

Thin-walled cylindrical shell structures are widely used in numerous fields owing to their large-bearing capacity, high strength-to-weight ratio and simple structure. However, their in-service life is highly susceptible to external excitation-induced vibrations. Due to the inapplicability of the full hard coating damping technology caused by the appendage and structural weight limitations of the shell structures, multi-ring hard coating damping treatment would be an ideal approach for reducing vibration in cylindrical shells.

The vibration analysis of cylindrical shells with partial coating, has been extensively studied. However, most of these studies are limited to damping treatment with single and double rings or multiple coating patches. In contrast, there is limited research on forced vibration of such cylindrical shell covered partially with arbitrary multi-ring hard coating damping subjected to elastic constraints. Moreover, the stiffness matrix and strain energy of the coated and uncoated regions were determined separately in the previous studies on partial coating. This would be ineffective when multiple rings are involved and constantly changing due to damping optimization.

Although this problem can be solved by developing a unified continuous rectangular pulse thickness function, it significantly reduces computational efficiency. Therefore, developing a more effective method for dealing with multi-ring hard coating treatment is highly desirable. While the connections between main structures and cylindrical shells are generally elastic constraints, forced vibration analysis of the shells remains underexplored. This requires accurate constraint stiffness identification, which is rather difficult because of the micro sliding of elastic constraints under actual loading conditions.

Herein, Dr. Yue Zhang, Professor Hua Song, Professor Xiaoguang Yu and Dr. Jian Yang from University of Science and Technology Liaoning proposed a new parameterized multi-partitioning method for robust modeling and vibration analysis of thin-walled cylindrical shells subjected to elastic constraint. The shells had arbitrary multi-ring hard coating treatment with different coating ratios and ring numbers. Their work is published in the journal, Thin-Walled Structures.

The research team derived admissible displacement and the motion governing equations using Chebyshev orthogonal polynomials and Rayleigh–Ritz method, respectively. They developed a unified external load formulation based on Chebyshev and trigonometric series for improved forced vibration analysis. Furthermore, an enhanced inverse identification procedure was developed for accurate identification of the stiffness coefficients of the elastic constraints with the aid of the genetic and pattern search algorithm. Finally, the effects of the coating ratio and ring number on the damping and vibration characteristics of the shell were examined.

The authors revealed that the rotational and translational stiffness of the elastic constraint could have the inherent frequency dependence property due to the micro sliding effects. This could further lead to soft nonlinearity in the response frequency curves of the shells. Initially, the average strain energy increased rapidly before stabilizing gradually with the increase in the ring number. In contrast, strain energy decreased linearly with an increase in the coating ratio, similar to the average modal loss factor. While the influence of the ring number on the damping and vibration characteristics of the shells mainly depended on the constraint condition and coating scheme, it exhibited less impact than the coating ratio.

In summary, semi-analytical modeling of forced vibration of thin-walled cylindrical shells with arbitrary multi-ring coating was reported. The numerical responses and experiment resonant frequencies were in good agreement, with a relative difference of 27.31% and 1.38%, respectively. These results validated the effectiveness and reliability of the proposed semi-analytical model and stiffness identification methods. In a statement to Advances in Engineering, the authors noted that their study provided valuable insights that would contribute to developing high-performance cylindrical shell structures for different applications.