科氏流量計為一工業應用上相當精確的質量流量計, 其常被應用於測量飛行器燃油之消耗狀況.科氏流量計的數學模式可以藉由振動樑的理論來推導, 並以之分析管流的振動. 在流體為不可壓縮和非黏滯流的假設之下, 則該直管可視為是Timoshenko樑. 再藉由 Hamilton 的原理來推得控制方程式(governing equation). 為了更容易找出自然振動頻率, 本文將四個自由度的形狀函數(shape function)用三階多項式來表示, 再藉由Langrange 方程式 推得樑的運動方程式. 由於經有此方式得到的運動方程式過於複雜, 因此本文採用有限元素法來求解運動方程式. 最後數值結果顯示ANSYS的mode shape很接近Matlab所求的, 也確認了相位差正比於質量流率. Coriolis mass flowmeter is an useful tool to measurement flowrate precisely, the purpose of the research is to analyze a Straight tube Coriolis mass flowmeter, it has been more than fifteen years since finite element method was implemented to the analysis of Coriolis flowmeter. The Coriolis mass flowmeter is modelled by using the theory of vibrating beams. We idealize the fluid as incompressible and inviscid, the tube is represented as Timoshenko beam. The governing equations were derived by Hamilton''s principle. In order to find out natural frequencies easily, we use a third order polynomial shape function for four degrees of freedom including two displacement and two slope and determine the weak form of equation of motion by Lagrange''s equation .The numerical results shows that the mode shape of Matlab is identical to ones of Ansys, and confirm the phase diffenence is proportional to the mass flowrate.
