平滑表面銅鐘之振動模態與發聲機制探討

Discussion on Vibration Modes and Sound Generation Mechanism for Smooth Surface Bell

王栢村(Bor-Tsuen Wang) ； 蔡俊郎(Jiun-Lang Tsai) ； 葉明遠(Ming-Yuan Yeh) ； 李致緯(Chih-Wei Li) ； 張博鈞(Bo-Jun Zhang) ； 吳盈輝(Ying-Hui Wu)

《中華民國振動與噪音工程學會論文集》 2016 (2016/06) Pp. 270-277

摘要

鐘聲宏亮而悠揚，常被用為寺院的法器或報時之用途。本文主要探討平滑表面銅鐘振動模態與發聲機制。利用ANSYS有限元素分析(FEA)軟體建構平滑表面銅鐘之有限元素模型，進行理論模態分析，求得銅鐘之理論模態參數，包含自然頻率與模態振型，接著對平滑表面銅鐘進行實驗模態分析(EMA)，實驗中以衝擊鎚為驅動器，加速規為感測器，量測訊號經頻譜分析儀求得量測點之頻率響應函數，透過ME'scopeVES曲線嵌合軟體進行曲線嵌合，可求得銅鐘之實際模態參數，包括自然頻率、模態振型與模態阻尼比，最後將理論與實驗之模態參數進行比較驗證，可明確了解銅鐘之振動模態特性。此外，亦利用麥克風與頻譜分析儀，量測平滑表面銅鐘經敲擊後之聲音頻譜，由對應實際結構之模態振型，可找出銅鐘發聲頻率與振動模態之關聯性。並對銅鐘之不同敲擊位置與不同敲擊鎚進行聲音量測，得到銅鐘之聲音頻譜，結果顯示，銅鐘敲擊位置與敲擊鎚的軟硬度，分別與聲音頻譜之發聲模態數量與聲音之衰減率有很大的關聯性。本文結合有限元素分析與實驗模態分析手法，探討平滑表面銅鐘之振動模態與發聲機制，銅鐘之有限元素分析模型若經適當校正後，將可應用於銅鐘之設計變更。

關鍵字

平滑表面銅鐘 ； 有限元素分析 ； 實驗模態分析 ； 振動模態 ； 發聲機制

並列摘要

Bell sound is bright and melodious and used as religious purpose in temple or just for reporting time. This work is to discuss the vibration modal properties of a smooth surface bell and its sound generation mechanism. The finite element analysis (FEA) software, ANSYS, is adopted to construct the bell FE model and perform theoretical modal analysis (TMA), so as to obtain theoretical modal parameters, including natural frequencies and mode shapes. Experimental modal analysis (EMA) is also conducted on the bell by using the impact hammer and accelerometer as the actuator and sensor, respectively. The frequency response functions (FRFs) can be measured and processed by the curve-fitting software, ME'scopeVES, to obtain the structural modal parameters, i.e. natural frequencies, mode shapes and modal damping ratios. Both theoretically and experimentally obtained modal parameters are compared, respectively, and verified to characterize the bell's vibration modes. The percussion sound of the bell is also measured by using the microphone to get the sound spectrum that can be interpreted with those vibration modes. Different percussion mallets acting on the bell is studied. Results show the percussion location on the bell and the hardness of mallet material will affect the induced vibration modes and the decay rate of percussion sound. This work integrates FEA and EMA to investigate the vibration characteristics and sound generation of the smooth surface bell. The bell FE model can be applied to the design modification after the proper calibration.

並列關鍵字

smooth surface bell ； finite element analysis (FEA) ； experimental modal analysis (EMA) ； vibration mode ； sound generation mechanism