- 學位論文
複合壓電薄板能量擷取之研究
The Power Harvest of Laminated Piezoelectric Plates
摘要
摘要 本文主旨在估計銅板與PZT壓電薄板所構成的複合板承受基座振動所產生的電流量。探討基座振動頻率、外接電路阻抗值等因子對產生的電流量以及功率之間的關係。 首先以 Kirchhoff 板理論為基礎，對於上下鍍滿電極的情況，壓電薄板可假設只剩下厚度方向之電場，透過壓電本構方程式將力學與電學之間的關係式推導出一套完整的複合壓電薄板之統御方程式。 接著探討在外接電路阻抗為零以及外接電路阻抗為無窮大這兩種特殊情況下，分別以e-form、h-form壓電本構方程式推導複合壓電薄板統御方程式，進而探討在各種型式的邊界條件下此複合壓電薄板系統的自伴隨(Self-Adjoint)性質。 最後在e-form壓電本構方程式、阻抗為零的情況下，求解複合壓電懸臂板在不同外加頻率基底激發下的位移場及電位場。求解出位移場後由壓電本構方程式並給定一外加電場，配合Ohm定律找出正確位移場及電位場的解，即可求得在不同外加頻率基底激發下所產生的電流量，進而探討不同外接電路阻抗下的能量轉換效益。
並列摘要
Abstract The object of this article is to estimate the amount of current generated by laminated piezoelectric plates in base vibration. Discuss the factor of the base vibration frequency and the external circuit impedance value in the relationship between the current and the power. First, based on Kirchhoff plate theory, it can be assumed that only the electric field of thickness direction remains for the upper and lower surfaces covered full electrode. Develop the governing equations of the laminated piezoelectric plates through the piezoelectric constitutive equations. Next, discuss two special situations, the external circuit impedance is zero and the external circuit impedance is infinite. Derive the governing equations from the e-form and h-form of piezoelectric constitutive equations separately. And then discuss the property of self-adjoint in various types of boundary conditions of the laminated piezoelectric plates. Finally, in the situation of e-form piezoelectric constitutive equations and zero impedance, solving the displacement field and the potential field of the laminated piezoelectric cantilever plate under different frequency of base excitation. After solving the displacement field, through piezoelectric constitutive equations and given an applied potential field, with the Ohm's law to find the correct displacement field and the potential field, the amount of current under different frequency of base excitation can be obtained. And then discuss the efficiency of energy transformation under different external circuit impedance.