彈性基礎上環狀板振動分析

Abstract

從工程應用之觀點，有關板之問題是一個很重要的課題。板承受動態外力發生震動需要解決之諸問題，須先求得板之自由振動頻率和振態然始可進一步分析研究。而處理板之有關文獻中大致上可分為解析解法與有限元素法兩種，在解析解法中動力反應分析模式，係藉由運動方程式經解析得一含貝索函數的變位函數。再藉由板之邊界條件推衍得頻率方程式，進而求得頻率參數與振態。而有限元素法，首先求得板元素之勁度矩陣及質量矩陣，再合成為板之勁度矩陣及質量矩陣，並代入邊界條件，其次由解(eigenvalue and eigenvector)求得板之自然振動頻率與振態。 而本文之目的即為使用有限元素法應用之套裝軟體來求得動態反應下板之變形情形，並由解析解法來驗證其準確性。進而分析當考慮彈性基礎時，將板依不同的邊界條件，觀察其對板振態之影響。

In the engineering application point of view, solving the problems of the vibration of plate caused by dynamic forces exerted on plate, in general, is required to obtain the natural vibration frequency and mode shape of the plate first,and then the further analysis. The processing board of the relevant literature can be broadly divided into the analytical solution and finite element method are two types of models in classical mechanics, the system by the equations of motion obtained by the analysis of a deflection function with Bessel function. By plate boundary conditions and then inferring the frequency equation may then obtain the frequency parameters and mode shapes. The finite element method, first obtained by plate element stiffness matrix and mass matrix, and then synthesized for the plate stiffness matrix and mass matrix, and substituted into the boundary conditions, followed by the solution (eigenvalue and eigenvector) obtained the natural frequencies of the plate and mode shapes. The purpose of this paper is to use the Application of the finite element method software package to obtain the dynamic response of the plate deformation case, by the analytical solution to verify its accuracy. Further analysis when considering the elastic foundation, the board according to different boundary conditions, to observe the effect of deformation on the plate.