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

doi:10.1007/s12204-017-1848-y

Abstract

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

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

CLC Number:

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]. Journal of shanghai Jiaotong University (Science), 2017, 22(4): 449-458.

References 16

[1]	BISADI H, ES’HAGHI M, ROKNI H, et al. Benchmarksolution for transverse vibration of annularReddy plates [J]. International Journal of MechanicalSciences, 2012, 56(1): 35-49.
[2]	BAMBILL D V, REYES J A, LAURA P A A. Anote on transverse axisymmetric vibrations of annularplates of non-uniform thickness [J]. Journal of Soundand Vibration, 1996, 191(4): 584-589.
[3]	YUAN J, DICKINSON S M. On the vibration of annular,circular and sectorial plates with cut-outs oron partial supports [J]. Computers & Structures, 1996,58(6): 1261-1264.
[4]	LEISSA A W. Vibration of plates [M]. WashingtonDC: Government Printing Office, 1969.
[5]	SRINIVASAN R S, THIRUVENKATACHARI V. Freevibration of annular sector plates by an integral equationtechnique [J]. Journal of Sound and Vibration,1983, 89(3): 425-432.
[6]	AGHDAM M M, MOHAMMADI M, ERFANIAN V.Bending analysis of thin annular sector plates usingextended Kantorovich method [J]. Thin-Walled Structures,2007, 45(12): 983-990.
[7]	KIM K, YOO C H. Analytical solution to flexural responsesof annular sector thin-plates [J]. Thin-WalledStructures, 2010, 48(12): 879-887.
[8]	HOUMAT A. A sector Fourier p-element applied tofree vibration analysis of sectorial plates [J]. Journalof Sound and Vibration, 2001, 243(2): 269-282.
[9]	RAMAKRISHNAN R, KUNUKKASSERIL V X. Freevibration of annular sector plates [J]. Journal of Soundand Vibration, 1973, 30(1): 127-129.
[10]	XIANG Y, LIEW K M, KITIPORNCHAI S. Transversevibration of thick annular sector plates [J]. Journalof Engineering Mechanics, 1993, 119(8): 1579-1599.
[11]	WONG W O, YAM L H, LI Y Y, et al. Vibration analysisof annular plates using mode subtraction method[J]. Journal of Sound and Vibration, 2000, 232(4):807-822.
[12]	WANG X W, WANG Y L. Free vibration analyses ofthin sector plates by the new version of differentialquadrature method [J]. Computer Methods in AppliedMechanics and Engineering, 2004, 193(36/37/38):3957-3971.
[13]	SHI D Y, SHI X J, LI W L, et al. Free transversevibrations of orthotropic thin rectangular plates witharbitrary elastic edge supports [J]. Journal of Vibroengineering,2014, 16(1): 389-398.
[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.
[15]	QU Y G, CHEN Y, LONG X H, et al. Free andforced vibration analysis of uniform and stepped circularcylindrical shells using a domain decompositionmethod [J]. Applied Acoustics, 2013, 74(3): 425-439.
[16]	BLEVINS R D. Formulas for natural frequency andmode shape [M]. Florida: Krieger Publishing Company,1979.