目前壓電聲子晶體於一維、二維與三維研究上，能帶結果分析方法需要代入表面波條件與邊界條件計算，本研究壓電聲子晶體頻率的計算方式與徹體波頻率計算方式相似，可以直接計算出頻率。另外在壓電聲子晶體以壓電材料的本構方程式(Constitutive Equations)，並結合壓電材料的致動器方程式計算。本研究以兩種主要方程式個別計算；第一種為表面波波動方程式，視無電極的壓電材料為普通材料，分析此聲子晶體複合材料的表面波頻帶；第二種計算為壓電本構方程式結合致動器方程式，分別在壓電材料的表面波頻率代入方程式預測相關位移與電位移後，由逆壓電效應轉換至外加電場調變，以達到壓電材料元件應用，並比較分析結果是否差異性。
本旨研究創新計算方法在一維方向上的聲子晶體(Phononic crystal)波傳的表面聲波(Surface Acoustic Wave, SAW)頻帶(Band gaps)。壓電材料(Piezoelectric Composite)位移與電位移轉換後，藉由此方式得到外加電場對表面聲波的調變。第一個主要為創新的理論分析，第二個為預測相關位移量與電位移量轉換成外加電場的調變影響，並達成設計一維表面聲波的應用。

To date, several piezoelectric phononic crystals research have been described, the band gaps analysis should be into the surface acoustic wave (SAW) condition and boundary condition. In this research, we calculate the frequency of piezoelectric phononic crystals by using the same way of calculating the bulk acoustic wave. In addition, we combine the piezoelectric material constitutive equation and piezoelectric actuator equation to calculate the displacement and electric displacement of piezoelectric phononic crystals.
There are two main types of equations that we calculate individually; the first formula is the equation of SAW. We assumed that the electrode-free piezoelectric are the ordinary materials, and then analysis these materials’ phononic crystal bands of SAW. Second formula is the combination equation of piezoelectric constitutive and actuator. We take the SAW frequency of piezoelectric material into the equation, and the predict the displacement and electric displacement. After the calculation, we modulate the frequency by electric field and take this method for piezoelectric material components applications.
This study creates a novel phenomenon of SAW frequency band gaps of phononic crystals. By using this means, we could obtain the whole new theoretical analysis method and apply it for piezoelectric materials.

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