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Vibration characteristics analysis of stepped thickness sectorial/annular plates using Chebyshev–Ritz method based on FSDT.

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Title: Vibration characteristics analysis of stepped thickness sectorial/annular plates using Chebyshev–Ritz method based on FSDT.
Authors: Zhao, Zhe1 (AUTHOR), Liang, Ran1 (AUTHOR), Gao, Cong1,2 (AUTHOR), Zou, Yucheng1 (AUTHOR) conggao@hrbeu.edu.cn, Pang, Fuzhen1 (AUTHOR), Li, Haichao1 (AUTHOR)
Source: Acta Mechanica. May2026, Vol. 237 Issue 5, p2195-2217. 23p.
Subjects: Rayleigh-Ritz method, Structural plates, Shear (Mechanics), Iterative methods (Mathematics), Mechanical vibration research, Finite element method
Abstract: This paper establishes a semi-analytical model to investigate the vibration characteristics of sectorial/annular structures with axially stepped thickness. The regional decomposition method and artificial spring technique are employed to construct the mathematical model of such sectorial/annular structures. The energy functional of the plate structure is established based on the first-order shear deformation theory, and five sets of artificial springs are used to simulate the continuity between different segments and the boundary conditions. The Rayleigh–Ritz method is adopted to solve the natural frequencies and mode shapes of the structure. The effectiveness of the proposed method is verified by comparing its results with those from the published literature and finite element method (FEM) calculations. Furthermore, the effects of boundary conditions, structural parameters and stepped thickness distribution on the free vibration characteristics of the sectorial/annular plates are systematically discussed, providing support for the dynamic analysis and vibration control of structures with stepped thickness. The research results show that both the increase in boundary conditions (stiffness) and regional impedance leads to an increase in natural frequencies, while the sector angle has the opposite effect; the radius ratio has no obvious regular influence on the vibration characteristics. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:This paper establishes a semi-analytical model to investigate the vibration characteristics of sectorial/annular structures with axially stepped thickness. The regional decomposition method and artificial spring technique are employed to construct the mathematical model of such sectorial/annular structures. The energy functional of the plate structure is established based on the first-order shear deformation theory, and five sets of artificial springs are used to simulate the continuity between different segments and the boundary conditions. The Rayleigh–Ritz method is adopted to solve the natural frequencies and mode shapes of the structure. The effectiveness of the proposed method is verified by comparing its results with those from the published literature and finite element method (FEM) calculations. Furthermore, the effects of boundary conditions, structural parameters and stepped thickness distribution on the free vibration characteristics of the sectorial/annular plates are systematically discussed, providing support for the dynamic analysis and vibration control of structures with stepped thickness. The research results show that both the increase in boundary conditions (stiffness) and regional impedance leads to an increase in natural frequencies, while the sector angle has the opposite effect; the radius ratio has no obvious regular influence on the vibration characteristics. [ABSTRACT FROM AUTHOR]
ISSN:00015970
DOI:10.1007/s00707-025-04591-4