Applied Mathematics and Mechanics (English Edition) ›› 2026, Vol. 47 ›› Issue (10): 2187-2208.doi: https://doi.org/10.1007/s10483-026-3439-9

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Frequency splitting and vibration evaluation of braided composite toroidal-cylindrical shell with soft coating

Jichuan CAO1, Hui LI1,2(), Jintong HAN3, Xinyu CUI4, Haile YAN5, Bo YANG5, Zeng LIN1,2, Feng ZHAO6, Wei SUN1,2, Bangchun WEN1,2   

  1. 1.School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China
    2.Key Laboratory of Vibration and Control of Aero-Propulsion Systems Ministry of Education of China, Northeastern University, Shenyang 110819, China
    3.Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, U. S. A.
    4.Shi-changxu Innovation Center for Advanced Materials, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China
    5.Key Laboratory for Anisotropy and Texture of Materials, Ministry of Education, Northeastern University, Shenyang 110819, China
    6.College of Mechanical Engineering, Shenyang Ligong University, Shenyang 110159, China
  • Received:2026-05-30 Revised:2026-07-13 Online:2026-10-12 Published:2026-10-12
  • Contact: Hui LI, E-mail: lh200300206@163.com
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Nos. 12472005 and 52175079), the Aerospace Science Foundation of China (No. 2022Z009050002), the Taihang Laboratory Program of China (No. AK023), and the Key Laboratory of Vibration and Control of Aero-Propulsion System Ministry of Education, Northeastern University of China (No. VCAME201603)

Abstract:

To facilitate the design of advanced aero-engine casings, a dynamic analysis framework is developed for the first time for the braided composite toroidal-cylindrical shell with soft coating (BCTCS-SC). The effective material parameters are first evaluated, after which high-order strain-displacement relations are established to describe the deformation of the coupled shell structure. The virtual spring method is adopted to model the rigid connection between the two infrastructures and the end constraints. The displacement fields are then approximated by doubly discrete spectral functions, and the governing dynamic equations are derived via the energy method. The proposed model is validated through comparative studies, and the corresponding mode shapes are visualized. Finally, the effects of key structural and material parameters on the natural characteristics, frequency splitting, and modal exchange are analyzed. The results further clarify the suppression effect of soft coating by modifying the equivalent stiffness and damping distribution. This study establishes a theoretical framework and a technical approach for frequency-splitting prediction and vibration-suppression design of coated braided composite coupled structures.

Key words: structural dynamics, advanced structure, vibration analysis, frequency splitting, soft coating, modal exchange

2010 MSC Number: 

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