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.
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BISADI H, ES’HAGHI M, ROKNI H, et al. Benchmark solution for transverse vibration of annular Reddy plates [J]. International Journal of Mechanical Sciences, 2012, 56(1): 35–49.
BAMBILL D V, REYES J A, LAURA P A A. A note on transverse axisymmetric vibrations of annular plates of non-uniform thickness [J]. Journal of Sound and Vibration, 1996, 191(4): 584–589.
YUAN J, DICKINSON S M. On the vibration of annular, circular and sectorial plates with cut-outs or on partial supports [J]. Computers & Structures, 1996, 58(6): 1261–1264.
LEISSA A W. Vibration of plates [M]. Washington DC: Government Printing Office, 1969.
SRINIVASAN R S, THIRUVENKATACHARI V. Free vibration of annular sector plates by an integral equation technique [J]. Journal of Sound and Vibration, 1983, 89(3): 425–432.
AGHDAM M M, MOHAMMADI M, ERFANIAN V. Bending analysis of thin annular sector plates using extended Kantorovich method [J]. Thin-Walled Structures, 2007, 45(12): 983–990.
KIM K, YOO C H. Analytical solution to flexural responses of annular sector thin-plates [J]. Thin-Walled Structures, 2010, 48(12): 879–887.
HOUMAT A. A sector Fourier p-element applied to free vibration analysis of sectorial plates [J]. Journal of Sound and Vibration, 2001, 243(2): 269–282.
RAMAKRISHNAN R, KUNUKKASSERIL V X. Free vibration of annular sector plates [J]. Journal of Sound and Vibration, 1973, 30(1): 127–129.
XIANG Y, LIEW K M, KITIPORNCHAI S. Transverse vibration of thick annular sector plates [J]. Journal of Engineering Mechanics, 1993, 119(8): 1579–1599.
WONG W O, YAM L H, LI Y Y, et al. Vibration analysis of annular plates using mode subtraction method [J]. Journal of Sound and Vibration, 2000, 232(4): 807–822.
WANG X W, WANG Y L. Free vibration analyses of thin sector plates by the new version of differential quadrature method [J]. Computer Methods in Applied Mechanics and Engineering, 2004, 193(36/37/38): 3957–3971.
SHI D Y, SHI X J, LI W L, et al. Free transverse vibrations of orthotropic thin rectangular plates with arbitrary elastic edge supports [J]. Journal of Vibroengineering, 2014, 16(1): 389–398.
SHI X J, SHI D Y, LI W L, et al. A unified method for free vibration analysis of circular, annular and sector plates with arbitrary boundary conditions [J]. Journal of Vibration and Control, 2016, 22(2): 442–456.
QU Y G, CHEN Y, LONG X H, et al. Free and forced vibration analysis of uniform and stepped circular cylindrical shells using a domain decomposition method [J]. Applied Acoustics, 2013, 74(3): 425–439.
BLEVINS R D. Formulas for natural frequency and mode shape [M]. Florida: Krieger Publishing Company, 1979.
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Foundation item: Foundation item: the National Natural Science Foundation of China (No. 51505445) and the Key Subject “Computational Solid Mechanics” of the China Academy of Engineering Physics
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Shi, X., Li, C. & Wei, F. Unified approach for vibration analyses of annular sector and annular plates with general boundary conditions. J. Shanghai Jiaotong Univ. (Sci.) 22, 449–458 (2017). https://doi.org/10.1007/s12204-017-1848-y
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DOI: https://doi.org/10.1007/s12204-017-1848-y