壓電薄板之等效電路模型建構： 一種設計骨傳導耳機發聲元件的方法

Abstract

本論文首先討論了人體聽覺系統，整理了骨傳導聽力的原理，並以設計一款骨傳導耳機為出發點，探討使用壓電薄板作為骨傳導耳機發聲元件的理論與方法。本文採用等效電路的方法對壓電平板進行建模，並進一步利用該模型分析壓電平板在不同邊界條件下的振動響應。 首先，參考前人基於機械—電路類比系統推導出的壓電材料等效電路理論，擴展建立了二維壓電平板的等效電路理論，分別探討了壓電懸臂板和壓電雙邊固定板的邊界條件。在推導過程中，導入樑函數法，計算不同邊界條件下壓電平板的模態振型。另外，利用有限元素法軟體建立相應的壓電平板模型，計算相同條件下的振動響應；同時，使用阻抗分析儀、雷射都卜勒測振儀等量測儀器，對實際的壓電試片進行測量，提供模型化過程中的數據，並驗證模型的準確性。本研究在建立等效電路模型的過程中還使用了系統識別和群體智慧演算法等方法來獲取參數值，這是一種結合理論、實驗與模擬數據的模型建構方法。 最後，以實驗和模擬驗證所建立的壓電致動器模型在施加不同負載情況下的模態、共振頻率、速度和作用力等振動特性的響應表現。本研究特別將人體乳突阻抗以質量—彈簧—阻尼系統的形式建立在有限元素軟體中，藉以模擬在此情況下壓電平板與乳突之間耦合後的作用結果，以便與電路模型進行比較和討論。本文所建立的理論模型與實驗和模擬結果之間呈現出良好的相似性，提供了一種模型化壓電致動器的方法，也提供了一種設計骨傳導耳機的新途徑。

This study first discusses the human auditory system, summarizes the principles of bone conduction hearing, and explores the theory and methods of using piezoelectric plates as sound-producing elements in bone-conduction headphones. The equivalent circuit method is used to model the piezoelectric plates, and this model is further employed to analyze the vibration response of the piezoelectric plates under different boundary conditions. Firstly, the equivalent circuit theory for piezoelectric materials, derived from the mechanical-electrical analogy system, is referenced and expanded to establish a two-dimensional equivalent circuit theory for piezoelectric plates. The boundary conditions of cantilever plates and clamped-clamped plates are investigated separately. The beam function method is introduced during the derivation process to calculate the modal shapes of the piezoelectric plates under different boundary conditions. Additionally, finite element method (FEM) software is used to establish corresponding piezoelectric plate models to calculate the vibration responses under the same conditions. Impedance analyzers, laser Doppler vibrometers, and other measurement instruments are employed to measure actual piezoelectric samples, providing data for the modeling process and verifying the model's accuracy. In establishing the equivalent circuit model, system identification and the HHO (Harris Hawks Optimization) algorithm are used to obtain parameter values. This is a model construction method that integrates theory, experimental data, and simulation results. Finally, experiments and simulations are conducted to verify the response performance of the established piezoelectric actuator model under different load conditions, focusing on modal shapes, resonance frequencies, velocities, and forces. This study particularly establishes the impedance of the human mastoid in the form of a mass-spring-damper system within FEM software to simulate the interaction between the plate and the mastoid under these conditions, allowing for comparison and discussion with the equivalent circuit model. The theoretical model established in this thesis shows good correspondence with the experimental and simulation results, providing a method for modeling piezoelectric actuators and a new approach for designing bone conduction headphones.