助聽器附著於耳膜後中耳頻率響應函數之研究

Abstract

本文首先由人類聽小骨的剛體模型和韌帶與肌腱等的彈簧模型建立中耳的無阻尼數學模型，接著推導出中耳之運動方程式後解出無阻尼之固有頻率和振形，利用這些固有頻率和振形加入各個模態之阻尼比後推導出人類中耳的頻率響應函數，將調校模態阻尼比的結果和文獻上的實驗數據比較後獲得各個模態適合的阻尼比，如此可獲得符合中耳動態特性的模態參數以及頻率響應函數。 接著將已研發之光電式耳膜附著助聽器的數學模型和所獲得之中耳參數組合。利用次結構合成法將助聽器和中耳之頻率響應函數合成得到助聽器施力傳至內耳位移的頻率響應函數，最後將力和位移的關係換算成電流和位移之關係，即可據以設定助聽器需提供多少電流來達成聽力補償之效果。

This study created a 3D multi-body model of human middle ear structure. First, the ossicels was considered a rigid body and soft tissues was considered a composition of linear spring. Secondly, we ignored damping effect and external force to derive the equation of motions of whole system. Then solved eigenvalue problem and using these natural frequencies、mode shape and damping ratio of each mode, so we can derive the frequency response function of the middle ear. Finally, we tuned the damping ratio of each mode to fit the frequency response function from paper’s experimental data, as a result, we got the frequency response function of the middle ear by theoretical analysis. We used substructure synthesis method to combine the frequency response function of the middle ear and the frequency response function of hearing aid. We obtained the purpose of this study by combining the frequency response function of the two structures. Then, by transforming the electromagnetic force to current hearing aid, we got the frequency response function between the electromagnetic force and current. According to this function we can achieve the settings of hearing aid.