Unified Approach for Vibration Analyses of Annular Sector and Annular Plates with General Boundary Conditions

doi:10.1007/s12204-017-1848-y

上海交通大学学报（英文版） ›› 2017, Vol. 22 ›› Issue (4): 449-458.doi: 10.1007/s12204-017-1848-y

Unified Approach for Vibration Analyses of Annular Sector and Annular Plates with General Boundary Conditions

SHI Xianjie (石先杰), LI Chunli* (李春丽), WEI Fayuan (魏发远)

(Institute of Systems Engineering, China Academy of Engineering Physics, Mianyang 621999, Sichuan, China)

出版日期:2017-08-03 发布日期:2017-08-03
通讯作者: LI Chunli(李春丽) E-mail:licl@caep.cn

Unified Approach for Vibration Analyses of Annular Sector and Annular Plates with General Boundary Conditions

SHI Xianjie (石先杰), LI Chunli* (李春丽), WEI Fayuan (魏发远)

(Institute of Systems Engineering, China Academy of Engineering Physics, Mianyang 621999, Sichuan, China)

Online:2017-08-03 Published:2017-08-03
Contact: LI Chunli(李春丽) E-mail:licl@caep.cn

摘要/Abstract

摘要： Abstract: This paper presents a unified approach for predicting the free and forced (steady-state and transient) vibration analyses of annular sector and annular plates with various combinations of classical and non-classical boundary supports. In spite of the types of the boundary restraints and the shapes of the plates, the admissible displacement function is described as a modified trigonometric series expansion, and four sine terms are introduced to overcome all the relevant discontinuities or jumps of elastic boundary conditions. Mathematically, the unification of various boundary value problems for annular sector and annular plates is physically realized by setting a set of coupling springs to ensure appropriate continuity conditions along the radial edges of concern. Numerous examples are presented for the free vibration analyses of annular sector and annular plates with different boundary restraints. With regard to the forced vibration analysis, annular sector and annular plates with different external excitations are examined. The accuracy, convergence and numerical robustness of the current approach are extensively demonstrated and verified through numerical examples which involve plates with various shapes and boundary conditions.

关键词: annular sector plates, annular plates, vibration, general boundary conditions

Abstract: Abstract: This paper presents a unified approach for predicting the free and forced (steady-state and transient) vibration analyses of annular sector and annular plates with various combinations of classical and non-classical boundary supports. In spite of the types of the boundary restraints and the shapes of the plates, the admissible displacement function is described as a modified trigonometric series expansion, and four sine terms are introduced to overcome all the relevant discontinuities or jumps of elastic boundary conditions. Mathematically, the unification of various boundary value problems for annular sector and annular plates is physically realized by setting a set of coupling springs to ensure appropriate continuity conditions along the radial edges of concern. Numerous examples are presented for the free vibration analyses of annular sector and annular plates with different boundary restraints. With regard to the forced vibration analysis, annular sector and annular plates with different external excitations are examined. The accuracy, convergence and numerical robustness of the current approach are extensively demonstrated and verified through numerical examples which involve plates with various shapes and boundary conditions.

Key words: annular sector plates, annular plates, vibration, general boundary conditions

中图分类号:

TH 113.1

SHI Xianjie (石先杰), LI Chunli* (李春丽), WEI Fayuan (魏发远). Unified Approach for Vibration Analyses of Annular Sector and Annular Plates with General Boundary Conditions[J]. 上海交通大学学报（英文版）, 2017, 22(4): 449-458.

SHI Xianjie (石先杰), LI Chunli* (李春丽), WEI Fayuan (魏发远). Unified Approach for Vibration Analyses of Annular Sector and Annular Plates with General Boundary Conditions[J]. Journal of shanghai Jiaotong University (Science), 2017, 22(4): 449-458.

参考文献 16

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[14]	SHI X J, SHI D Y, LI W L, et al. A unified method forfree vibration analysis of circular, annular and sectorplates with arbitrary boundary conditions [J]. Journalof Vibration and Control, 2016, 22(2): 442-456.
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Unified Approach for Vibration Analyses of Annular Sector and Annular Plates with General Boundary Conditions

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