研究週期波驅動訊號耦和效應對平板共振譜線及共振模態之影響

Abstract

現今，克拉德尼圖形已被應用於樂器製作上。為了分析聲學腔體的共振，需要建立一套理論模式來決定所對應的克拉德尼圖形。本論文以Kirchhoff -Love平板理論出發，考慮驅動源與平板之間的耦合效應以描述共振平板的波函數。將所推導出的理論形式導入傅立葉分析，實驗上方形平板在單頻弦波及占空比50%、20%之方波週期訊號驅動下的共振譜線及共振模態均可良好重建。接著將此概念推廣，我們進一步利用具有與推導理論模式相同耦合效應的RLC電路網絡成功模擬出小提琴平板的共振譜線及共振模態。

Nowadays, Chladni figures have been used in the industry of musical instruments. To analyze the resonance in the acoustic cavity, a theoretical model is required for resolving the Chladni figures. In this thesis, the coupling effect between the plate and the driving source is considered into the Kirchhoff–Love equation to derive the wave function of the resonant plates. With the concept of Fourier analysis, the derived formula have been confirmed to well reconstructed the resonant spectra and resonant modes of square plates driven by the periodic signals, such as the sinusoidal wave and the square waves with 50% and 20% duty cycles. Furthermore, by using a RLC network with a similar coupling effect as the developed model, the resonant spectra and resonant modes of a violin plate are successfully simulated.