壓電懸臂樑之有限單元建模與實驗驗證

Finite Element Modeling of the Piezoelectric Cantilever Beam and Experimental Validation

蕭騰蛟(Teng-chiao Hsiao)

指導教授 ： 趙昌博

中原大學/工學院/機械工程研究所/碩士(2004年)

https://doi.org/10.6840/cycu200400714

摘要

本文是以有限元素法模擬壓電懸臂樑之振動並與實驗相互驗證。關於壓電懸臂樑之數值模擬分析，首先建立系統之動態模型，藉由壓電懸臂樑之物理行為與壓電基本方程式得到系統之動能及位能，再利用有限元素法( finite element method )和( Lagrange equation )推導出系統之動態方程式。實際系統方面，利用雷射位移計量測壓電懸臂樑之位移量並將位移訊號傳回頻譜分析儀以得到壓電懸臂樑之頻率響應，透過數值模擬的結果與實際系統互相比較其差異性並探討本研究方法的優缺點。

關鍵字

有限元素 ； 結構 ； 壓電材料 ； 懸臂樑

並列摘要

This study is devoted to model vibrations of the piezoelectric cantilever beam via the finite element method (FEM), which are compared with the experimental results. To this end, the kinetic energy and the potential energy of the system are first derived from the basic physic laws of piezoelectric ceramics, the constitutive equations of the piezoelectric material, in terms of degrees of freedom of nodes. The governing equation of system is established by the uses of FEM technique and Lagrange’s equation for formulation. The case of a bimorph piezoelectric cantilever beam is considered to verify the validness of the modeling technique proposed. Numerical simulations and experimental study are next conducted and compared to ensure the effectiveness of the modeling method. In experiment, the displacement of the piezoelectric cantilever beam is measured by a laser displacement sensor, and then the sensor signal is feedbacked to a spectrum analyzer which is capable of showing the frequency response of the real system. The differences between the numerical simulations and those of experiments are small and non-critical, which confirm the efficacy of the proposed modeling technique.

並列關鍵字

bimorph ； Piezoelectric materials ； finite element modeling ； structure.

參考文獻

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