具多重連續界面之壓電複合致動器分析方法之開發及應用

Abstract

市面上對於壓電材料最廣泛的應用方式就是與其他結構結合，來達成各式工程上的需求，但通常複合結構的模態形狀會比均質結構複雜，這是由於連續條件的緣故，對於工程上是一大挑戰。 本論文主要是從理論出發探討複合結構下的共振頻及模態形狀，在結構的選用上以工程中最常使用的一維結構及圓盤結構，分別套用直角坐標及圓柱座標，須將壓電物性方程式及波傳方程式作結合，並代入連續條件及邊界條件求得。數值模擬的部分將各項參數代入理論並透過運算軟體的輔助得到理論上的共振頻及模態形狀，並同時將相同的結構設定與理論一樣的參數以有限元素法進行模擬，並與理論作比較，最後透過量測儀器來看實際情況下的共振頻及模態，並將以上這三者之結果作比較分析。 一維複合結構主要是想作為能移動載物的壓電馬達來使用，透過電極位置設計讓模態不會被彼此的驅動訊號所干擾，驅動方式採用雙頻雙模態，將兩共振模態進行疊加來產生行進波，其中雙頻率必須為倍數關係才能使結構本身的運動具有固定的週期性，而驅動實驗中載物也確實能被行進波帶動，位移量最長可達50.3mm，最大速度高達3.1mm/s。平面圓盤複合結構則是利用結構於共振頻時快速振動將分布於其表面的水振散成微粒狀逸散至空氣中，能作為高速振盪器及霧化器來使用，都將透過驅動實驗展示複合結構下的運動模式來達成以上的目的。

The major application of piezoelectric ceramic on the market is to attach it to other structures for various engineering requirements. The mode shapes of the composite structures are usually more complicated than the uniform structures, which is due to the continuity conditions. This thesis reports a developed analytical approach to analyze resonance frequencies and mode shapes of the composite structures, including one-dimensional structure and disc structure. They are common engineering structures and are chosen to study in this thesis. The theory was established by combining the piezoelectric constitutive equations and wave equation in Cartesian coordinate and cylindrical coordinate. Methods to solve continuity conditions and boundary conditions were constructed to identify resonant frequencies and mode shapes. Using numerical analysis, theoretical resonance frequencies and mode shapes were obtained. The structure characteristics were also simulated by finite element method to verify developed theory. Finally, a 1-D piezoelectric composite and a circular composite were fabricated to compare with theory and finite element analysis. The one-dimensional composite structure is designed for the application of a piezoelectric motor for carry an object. The positions of piezoelectric actuators are designed so that the resonant mode is not interfered by the other actuator. The driving method adopts the method of dual-frequency-dual-mode to excite two resonant modes in order to generate a traveling wave. Driving frequencies were controlled to have a integer multiplication relationship to create a continuous and steady traveling wave. Experimental results demonstrated that the displacement of a 31mg object can be moved for 50.3 mm and the maximum speed of a 20mg object can reach 3.1mm/s. On the other hand, the disc composite structure operated rapidly through the resonant frequency to atomize water droplets into air. This composite structure can be used as a high-speed oscillator and an atomizer. Both of these composite structures verified the developed analytical approach can be used to study piezoelectric composite for engineering applications.