A Note on Transverse Axisymmetric Vibrations of Annular Plates on Non-Uniform Thickness

Bambill, Diana V.; Reyes, J.A.; Laura, P.A.A.

doi:10.1006/jsvi.1996.0142

Cited by 4 publications

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Although annular, circular and sector plates are used as widely as their rectangular counterparts in practical applications, they are comparatively far less studied in terms of the number of publications in the literature (Leissa et al, 1993;Bambill et al, 1996;Yuan and Dickinson, 1996;Romanelli and Laura, 1997;Singh and Hassan, 1998;So and Leissa, 1998;Houmat, 2001;Cheng et al, 2003;Bashmal et al, 2009;Wong et al, 2000;Bisadi et al, 2012;Fereidoon et al, 2012;Hosseini-Hashemi et al, 2010). A comprehensive review of the earlier research can be found in Leissa's (1973) book.…”

Section: Introductionmentioning

confidence: 99%

A unified method for free vibration analysis of circular, annular and sector plates with arbitrary boundary conditions

Shi

et al. 2014

Journal of Vibration and Control

View full text Add to dashboard Cite

The vibrations of circular, annular, and sector plates are traditionally considered as different boundary value problems and often treated using different solution algorithms and procedures. This problem is further compounded by the fact that the solution for each type of plate typically needs to be adapted to different boundary conditions. In this paper, a simple solution method is proposed for a unified vibration analysis of annular, circular and sector plates with arbitrary boundary conditions. Regardless of the shapes of the plates and the types of boundary conditions, the displacement solutions are invariably expressed as a new and simple form of trigonometric series expansion with an accelerated convergence rate. The unification of seemingly different boundary value problems for the circular and annular plates and their sector counterparts is physically accomplished by applying a set of coupling springs to ensure appropriate continuity conditions along the radial edges. The accuracy, reliability and versatility of the current method are fully demonstrated and verified through numerical examples involving plates with various shapes and boundary conditions. It should be noted that the current method can be easily applied to sector plates with an arbitrary inclusion angle up to 2 π.

show abstract