Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/18626
標題: 含內部點支撐矩形板的自由振動分析
Free Vibration Analysis of Rectangular Plates with Interior Point Supports
作者: 李紹平
Lee, Shaw Pying
關鍵字: Free Vibration;自由振動;Rectangular Plates;Point Supports;矩形板;點支撐
出版社: 應用數學研究所
摘要: 
本文探討了含內部任意點支撐矩形板的自由振動。使用單一區間的分析方
式,將點支撐的集中反力用雙傅立葉級數展開,再利用Levy的平板振動解
,推導出具有任意點支撐矩形板自由振動的級數解。此一單區間的分析方
式,有別於一般多區間的分析方法,可以省去將矩形板分成多個子區間來
分析的麻煩。本文分析的平板,其兩個對邊為簡支,另外兩邊為簡支、自
由或固定三種中的一種,而內部點支撐則為任意數目、任意位置。本文所
推導出來的解,解決了控制方程式中所包含的由點支撐所造成的不連續反
力,為一相當簡便的作法。在數值結果方面,則包括了各種參數及各式邊
界條件下的自然頻率、振動模態和收斂性的討論,與多區間解的自然頻率
亦有所比較。

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.
URI: http://hdl.handle.net/11455/18626
Appears in Collections:應用數學系所

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