壓電風扇係一種固態共振裝置，它係利用壓電材料在共振情況來刺激驅動薄葉片，以產生流動的氣流而達到散熱的目的，具有耗能量低、體積小、低噪音、壽命長等優點。
本文主旨在建立有限元素分析模式以探討壓電風扇的靜態和動態特性。首先建立壓電風扇之本構方程式(constitutive equations)，接著使用漢米爾頓原理(Hamilton’s principle)與有限元素的近似解來推導壓電風扇之有限元素運動方程式。本文共使用四種元素，即3D 固體(three-dimensional solid)元素、具壓電效應3D固體 (piezoelectric three-dimensional solid)元素、殼(shell)元素以及固殼過渡(solid-shell transition)元素，以分別模擬壓電風扇塊狀部分與板狀部分結構。固殼過渡元素係介於3D固體元素與殼元素之間，以達成有限元素模型適合性(conformity)的要求。
利用本文之有限元素分析模式及求取特徵值(eigenvalues)與特徵向量(eigenvectors)的方法，可以求得壓電風扇結構之自然振動頻率與模態，並利用Newmark直接積分法來求解有限元素運動方程式，以模擬壓電風扇承受外加交流電壓所產生的動態響應。本文結果並與完全使用3D固體元素模擬壓電風扇的分析結果作比較，以驗證本文分析模型的準確性與效率。

Piezoelectric fans are solid-state resonant devices that use piezoelectric excitation to drive a thin blade into resonance to create a fluid flow for cooling electronic devices. These fans are of low power consumption, small size, low noise and long lifetime.
The objective of the present study is developing a finite element analysis model to investigate the static and dynamic characteristics of the piezoelectric fan. First, this study develops the constitutive equations for the piezoelectric fan. Then use the Hamilton’s principle and finite element approximate solutions to derive the finite element equations of motion for the piezoelectric fan. The present study uses four types of elements, i.e., three-dimensional solid element, piezoelectric three -dimensional solid element, shell element and solid-shell transition element, to model the bulk and plate portions of the piezoelectric fan, respectively. The solid-shell transition element lies between 3-D solid element and shell element to achieve the conformity requirement of a finite element model.
The present finite element model and the method for computing the eigenvalues and eigenvectors are adopted to find the natural frequencies and vibration modes of the piezoelectric fans. The present finite element equations of motion of the fans are solved by the Newmark direct integration scheme to simulate the dynamic responses of the fans subjected to the externally applied alternating voltages. The present results are compared with that of the finite element model with 3-D solid elements only to verify the accuracy and efficiency of the present finite element model of the piezoelectric fan.

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