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.
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
.
DOI: 10.1007/s12204-017-1848-y
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