橢圓形薄膜複合壓電薄板之聲振特性與聲輻射探討

Abstract

本研究探討橢圓形薄膜複合壓電薄板作為揚聲器之振動與聲學特性，並結合理論推導、無網格特雷夫茨法、有限元素法與實驗量測進行綜合分析。首先分析薄膜與壓電薄板在固定與自由邊界條件下之獨立振動行為，進一步探討其複合結構於類自由邊界條件下之結構響應與聲輻射特性，並比較不同幾何與材料組合對其性能之影響。 實驗量測部分，以振動量測為基礎，進一步探討複合結構之聲學特性。振動量測方面，透過電子斑點干涉術獲得面外共振頻率與振動模態，並以雷射都卜勒振動儀搭配振鏡系統掃描整體表面以獲得完整模態；同時使用阻抗分析儀進行壓電之電性阻抗頻譜分析。聲學量測方面，分別於無響室與人工耳中進行，以對應自由音場與封閉音場之聲學行為。在自由音場下，建立有限元素模型模擬聲壓曲線，並與無響室實測數據比對，以驗證模型之準確性；遠場輻射指向性分析則結合理論，包括點聲源與活塞式聲源理論，以及數值模擬與實驗結果進行分析。封閉音場因邊界條件複雜，建構模擬人耳等效電路之有限元素模型，並與人工耳量測數據進行比較，以驗證建模準確性。 綜合振動與聲學分析結果，歸納薄膜複合壓電薄板於不同結構設計下之聲學表現，並將人工耳實驗結果與市售耳機及哈曼曲線比較，展示自製壓電揚聲器具有良好頻響特性。最終建立一套結合理論、數值與實驗方法的聲振分析流程，作為壓電揚聲器結構設計優化與聲音品質標準化之依據，提升壓電揚聲器在市場競爭力。

In this research, the vibration and acoustic characteristics of piezoelectric plates coupled with elliptical membranes for loudspeaker applications through an integrated approach that combines theoretical analysis, the meshfree Trefftz method, the finite element method (FEM), and experimental measurements. Initially, the independent vibration behaviors of membranes and piezoelectric plates under fixed and free boundary conditions are analyzed. Subsequently, the composite structure is examined under quasi-free conditions, with comparisons across different geometries and materials. For experimental measurements, vibration characteristics are evaluated using a Laser Doppler Vibrometer, Electronic Speckle Pattern Interferometry, and an impedance analyzer. Acoustic measurements are performed in both an anechoic room and with an artificial ear, representing free-field and enclosed-field acoustic behavior, respectively. In the free-field condition, the sound pressure level (SPL) curve is simulated using FEM and validated against measurements. Far-field acoustic directivity is evaluated using point and piston source models, as well as numerical and experimental results. In the enclosed field, due to complex boundary conditions, FEM simulations based on equivalent circuit models of the human ear are compared with artificial ear measurements to verify the accuracy of the modeling. Based on the results, acoustic performance across configurations is summarized. SPL results from artificial ear measurements are compared with commercial earphones and the Harman Target Curve, confirming favorable performance. Finally, a standardized vibroacoustic framework is proposed to optimize design and enhance sound quality.