| Summary: | 碩士 === 國立中興大學 === 應用數學研究所 === 81 === A single domain application of the impulse function approach is
used to study the free, flexural vibration problems of Levy-
type plates with arbitrary interior point supports. This
analysis is based on the representation of the concentrated
reactions at the point support locations by a double Fourier
sine series expansion of the impulse function. This study
provides an extension of the classical Levy's solution in the
vibration analysis of plate with interior point supports. The
extended solution allows one to solve the problem in a single
domain in contrast to the multiple domain solutions available
in the literature. This new approach can greatly reduce the
complexities of the problems involving arbitrary multiple point
supports. The versatility and ability of this approach is
demenstrated by considering a rectangular plate with two
opposite edges simply supported and classical boundary
conditions (free, clamped or simply supported) on the other two
edges. The simulation of interior point supports in plates
provides a method for presenting the discrete discontinuities
in the force field, in the interior of plate, into the
governing differential equation and obtaining a concise
representation of the solution in a single domain of plate.
Numerical results are presented for a number of specific
problems, including the convergence and accuracy of the
approach, which include natural frequencies and mode shapes of
some typical plates with interior point supports. The reults
obtained by using the single domain approach are compared with
those obtained by using the multiple domain approaches in the
literature.
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