口琴簧片之尺寸與流場特性於吹奏時之振動分析

Abstract

本論文旨在應用振動理論與流體力學模型，搭配風洞實驗量測，對口琴的振動發聲原理與條件進行整體性的分析。 口琴由蓋板、琴格、簧板及簧片組成，吹奏時氣流進入琴格並流經簧片帶動其振動並發聲。研究首先單獨針對口琴簧片與簧板進行結構振動探討，簧片一端以鉚釘固定於簧板上形成懸臂梁結構，使用顯微鏡量測獲得簧片尺寸及其與簧板間之縫隙幾何。由於簧片厚度隨長軸方向漸變，本研究採用功能性梯度材料理論推導簧片之自然共振頻率，除與有限元素法模擬有良好對應外，與實驗結果比較也可大幅修正以均勻厚度梁計算之誤差。接著，將簧片與簧板加入琴格形成單一音符之吹奏單元，並參考Laurent Millot所提出之自由簧最小模型，用理論分析使簧片產生穩定振動所需之吹奏條件，可解釋口琴簧片於吹奏時之振動頻率會小於其自然共振頻率之現象。另外，使用商用數值模擬軟體進行雙向流固耦合模擬，得到口琴琴格內部之壓力、流速、簧片位移等時域訊號及全域分布形式，與文獻對應有相同趨勢，並提供更深入之物理解釋，有助於理解口琴中由氣流驅動簧片振動的機制。 實驗部分，以風洞搭配自製縮口治具產生之穩定流場使簧片達穩定振動，使用雷射都卜勒振動儀對簧片進行量測。實驗結果驗證簧片振動頻率確實低於自然共振頻率，並分析不同吹奏條件下簧片振動之時域波形、頻譜響應與倍頻特性，進一步以科學數據深化對簧片發聲行為之理解。

This thesis integrates vibration theory and fluid‐dynamics modeling with wind‐tunnel experiments to deliver a comprehensive analysis of the harmonica’s sound‐production mechanisms. The harmonica comprises a cover plate, comb, reed plate, and free reeds; during play, airstream enters each chamber and passes over its reed, driving it into vibration and producing sound. First, the structural vibration of an individual reed and its reed plate is investigated. Each reed is fixed at one end to the reed plate forming a cantilever beam. Microscopic measurements determine the reed’s dimensions and the gap between reed and plate. Because the reed’s thickness varies along its length, Functionally Graded Material theory is applied to derive its natural frequency. Theoretical predictions significantly reduce errors compared with experimental data inherent in treating the reed as a uniform beam. Next, the reed–plate assembly is embedded in the comb to form a single-note unit. Drawing on Millot’s model, a theoretical analysis identifies the blowing conditions required in stable oscillations and explains the relation between playing and reed’s natural frequency. Subsequently, two-way fluid–structure interaction simulations are performed using commercial software. Time-domain signals of internal pressure, airflow velocity, and reed displacement, along with their spatial distributions, are obtained. The trends correspond closely with literature data and provide deeper physical insight into airflow-driven reed vibration. Experiments was done using a nozzle in a wind tunnel to generate steady flow that excites the reed, and a Laser Doppler Vibrometer measures the its oscillation. The results confirm that the. Spectrum of vibration under varying flow conditions reveal relationships between fundamentals and overtones, offering quantitative insights into the reed’s sound‐production behavior.