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標題: 具厚度變化之環狀板之自由振動分析
Free vibration analysis of annular of annular plate with variable thickness
作者: 孫挺家
關鍵字: frequency;頻率;annular plate;free vibration;variable thickness;mode shape;circular plate;自由振動;厚度變化;環狀板;模態
出版社: 應用數學系
本文主要是分析一具有厚度變化之環狀板之自由震動。探考可分為二部分,一是因為厚度的變化使得板之剛度係數及密度亦隨著厚度變化,這造成振動方程式更加複雜且不易求得解析解。為了簡化振動方程,選擇一些合適的函數,如級數函數、子數函數等,來表示厚度之變化分布將是一重要步驟。 如此,振動方程式將可被簡化為尤拉等式或貝索等式,進而較易求得一般解。最後再根據板之邊界條件解出自然振動頻率及模態。二是根據環狀板之內外半徑比來探討頻率變化情形。一本文方法所得之解析解將可用來比較其他數值方法,如能量法,之數值解。

In this paper, analysis of the natural frequencies and mode shapes for free vibration of annular plates with variable thickness are presented. The governing differential equations for free vibration of annular plates with varying mass density and flexural rigidity are derived. They can be reduced to Bessel's equations or Euler's equation by selecting suitable expressions, such as power functions, for the distributions of flexural rigidity and mass along the radii of the plates. The general solutions of annular plates with variable thickness are obtained. Therefore, frequencies and mode shapes of free vibration of plates with variable thickness are computed and compared for different values of radii ratio and different boundary conditions. Aside from the frequencies and mode shapes for design purposes, these data can be used as test cases for assessing the accuracy of various approximate methods of solution.
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