Advanced Search Many structural parts such as aircraft components, boiler panels, industrial ducts, and machine parts are subjected to loading conditions that are conducive to vibration since they are in close proximity to reciprocating equipment or high fluid velocity. The mechanism of such plate vibration has been studied extensively in the last few decades. Numerous books and articles have been written dealing extensively with this topic. Another book by Gorman Gorman develops detailed equations and solutions to a wide variety of rectangular plates. Other books on plate vibrations are also referenced in subsequent paragraphs.
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Regardless of boundary conditions, the displacement solution is invariably expressed as a new form of trigonometric expansion with accelerated convergence.
The expansion coefficients are treated as the generalized coordinates and determined using the Rayleigh-Ritz technique. This work allows a capability of modeling annular sector plates under a variety of boundary conditions and changing the boundary conditions as easily as modifying the material properties or dimensions of the plates. The reliability and accuracy of the current method are adequately validated through numerical examples.
Introduction Annular sector plates are one of the most important structural components used in industrial applications and civil engineering. The vibrational characteristics of sector plates are thus of great interest to engineers and designers. Although there is a vast pool of studies about vibrations of circular and rectangular plates , relatively few results are reported for annular sector plates. Over the past decades, vibrations of annular sector plates have been investigated using various analytical or numerical methods, such as the energy method , spline element method [3, 4], finite element method , integral equation method , and so on .
In particular, a general technique was developed by Leissa  to obtain exact modal frequencies for plates which are simply supported along the radial edges and have arbitrary boundary conditions at the circumferential edges. This method utilizes the well-known Bessel function solutions for a circular plate by allowing the functions to have noninteger orders.
Liew et al. It is shown that a majority of them are focused on the classical boundary conditions simply supported, clamped, or free edges. In comparison, other more complicated boundary conditions such as elastic boundary supports are rarely attempted. A closed-form solution is proposed by Kim and Yoo  in which the displacements are expressed in terms of trigonometric and.
Teshura Open to the public ; S Public Private login e. Monographs dedicated to the organization and summarization of knowledge existing in the field of continuum vibrations. The University of Melbourne. If you are a seller for this product, would you like to suggest updates through seller support? Amazon Second Chance Pass it on, trade it in, give it a second life.
Vibration Of Plates
In: Journal of Sound and Vibration , Vol. To appropriately describe the stress singularities at the crack tip and show the discontinuities of displacement and slope crossing the crack, previously used corner functions, as well as a new set of functions, are added to the well known admissible functions consisting of regular polynomials. Comprehensive convergence studies on the vibrations of simply supported rectangular plates with horizontal cracks at the symmetry axis are carried out and show that both the corner functions and the proposed new set of functions indeed accelerate the convergence of numerical solutions. Furthermore, the new set of functions is found to be particularly capable in improving convergence of solutions, especially when there is a large crack.
Yozshushura View online Borrow Buy. AmazonGlobal Ship Orders Internationally. The University of Queensland. Amazon Inspire Digital Educational Resources. Nevertheless until today its the best practical book i have seen. Explore the Home Gift Guide. The National Library may be able to supply you with a photocopy or electronic copy of all or part of this item, for a fee, depending on copyright restrictions.