A Theoretical and Experimental Study for Speakers with Anisotropic Beam Pattern

根據聲學理論的基礎，本論文研究一圓柱杯型超聲波傳感器之結構振動，用以發射與接收超聲波而產生空間異向性波束。當結構的發射面積與尺寸很小的時候，其設計參數之間會相互影響。本論文針對超聲波傳感器之主要效能指標：異向性波束、共振頻率、殘響時間與聲源位準等所相應的參數加以分析，並定義結構設計參數，同時引入有限元素法來模擬分析。為了印證有限元素模擬的結果，本論文建構了一套檢測平台，來自動量測超聲波傳感器之遠場空間異向性波束，並以雷射都卜勒干涉儀對其振動板表面位移作驗證。接著透過有限元素分析進行影響超聲波遠場波束之參數研究，由其中發現提高超聲波傳感器的共振頻率是窄化其遠場波束寬度最有效的方法，但是卻要犧牲其遠場波束之異向性。接著，在固定頻率的情況下，振動板形狀對縮小遠場波束寬度影響最小，但若設計得不當，反而會使遠場波束變寬。最後，振動板形態在厚度上於鉛直兩側具有斷差之形態，是另一個對窄化遠場波束寬的重要參數。此外，利用實驗的方法，測定超聲波傳感器內面壓電片之電性阻抗，並以等效電路模擬之。再利用所得之等效參數，與電路模擬軟體接軌來預測殘響時間。此外，將所設計之具空間異向性波束超聲波傳感器實際進行障礙物可偵測範圍測試，以證明其異向性波束可以產生異向性可偵測範圍。此一設計想法與平台可以提供車用超聲波感測器設計之參考。由於壓電超聲波傳感器具高機械品質的特性，因此，將之作為非線性參量陣列之單體，以小面積發射面產生一高聲壓超聲波，並利用振幅調變的方式與空氣非線性的特性產生解調波束。為了精確地量測大動態範圍的超聲波聲壓訊號，本論文以1/3八度音程分析訊號，並利用濾波的功能將高聲壓高頻載波衰減，以釋放多餘的量測動態範圍來研究解調波的特性。並對訊號作可靠度分析。由實驗可以發現，具異向性波束之超聲波傳感器可以發射與載波相同之異向性波束的可聽見聲波。此外，其低頻響應在1kHz以內相當平整。另外，也針對高聲壓之開放型超聲波發射器進行同樣的實驗研究，發現其解調之遠場波束幾乎不受調變頻率之影響。再進一步以超聲波發射器陣列初步驗證其解調聲波可應用於空間局部聲音消除之可行性。最後，將超聲波發射器配合集音罩的結構，以改善其解調波之遠場波束。Based on the fundamental theory of acoustics, we investigated the anisotropic beam pattern induced by a cylindrical pot-like ultrasonic sensor. As the sensor size is small due to its application constraint, the design parameters are thus highly coupled to one another. In this dissertation, we focused on the analysis of parameters related to the four main key performance indices: anisotropic beam pattern, resonance frequency, reverberation time, and source level. Then, we defined the corresponding parameters on the structural design. Furthermore, a finite element analysis was introduced in the development of the structural design. In order to validate the finite element model, an automatic detecting platform was established to measure the spatially anisotropic beam pattern. In addition, a Laser Doppler Interferometer was utilized to determine the displacement of the vibrating plate surface. After validating the finite element model, it was introduced to study the parameters which alter the far-field beam pattern of an ultrasonic sensor. We found that the increase of the resonance frequency of an ultrasonic sensor is an effective method to narrow its far-field beam width, which results in a poor anisotropy of beam pattern. Besides that, the shape of the vibrating plate is an insignificant parameter for narrowing the far-field beam width under a specific frequency. However, if the shape of the vibrating plate was designed unsuitably, it could broaden the far-field beam widths inadvertently. Finally, the thickness discontinuity of the vibrating plate in the two opposite vertical sides is also an important parameter in narrowing the far-field beam width of an ultrasonic sensor. Moreover, by detecting the impedance of the piezoelectric plate stuck on the inner surface of the vibrating plate of an ultrasonic sensor and then calculating its corresponding equivalent circuit parameters, the reverberation time was predicted through the electronic circuit simulation. Finally, we integrated our design which possesses a highly anisotropic beam pattern into the obstacle detection system to determine the detectable region for a standard obstacle. The design thinking and design platform can provide a guideline for the design of an ultrasonic sensor in automotive industry. Due to the highly mechanical quality factor of a piezoelectric based ultrasonic sensor, it can radiate a high-intensity ultrasound beam at its resonance frequency from a small size emitting surface. An amplitude-modulated ultrasound whose carrier is the resonance frequency of the ultrasonic sensor was radiated through air. Using the non-linearity of air, the demodulated audible beam was thus induced at a modest strength. To ensure these sound pressure signals are within a reasonable dynamic range of measuring instruments, a low-pass filter was adopted to condition the detecting signals. Then, using a sound power spectrum analysis through a 1/3 octave band and reliability analysis of the filtered signals, the demodulated audible sound was determined precisely. We found an ultrasonic sensor possessing a spatially anisotropic beam pattern provides a demodulated audible sound with the same beam pattern. In addition, the frequency response of the demodulated audible sound has a plateau in the frequency range below 1kHz. Furthermore, we studied the possibility of the localized sound cancelling through a highly directional sound beam provided by ultrasonic emitter array. Finally, the acoustic dome integrated into the ultrasonic emitter based directional loudspeaker to improve its directivity of demodulated beam was also studied.口試委員會審定書 #謝 i文摘要 iiiBSTRACT v錄 vii目錄 xi目錄 xvi 1 章 緒論 1.1 研究背景 1.2 論文目標 3.3 論文架構 3 2 章 聲學理論 5.1 流體基本物理的數學描述 5.1.1 質量守恆-連續方程式 5.1.2 動量平衡-力平衡方程式 6.1.3 能量守恆-能量方程式 6.1.4 熵平衡-熵方程式 7.1.5 狀態方程式 8.2 聲波行為的數學描述 9.3 非線性聲波行為的數學描述 9 3 章 具異向性波束之超聲波感測器設計 12.1 車用超聲波傳感器 12.1.1 先前文獻回顧 13.1.2 超聲波傳感器單體結構與作動原理 19.1.3 設計需求與限制 20.2 異向性波束 25.2.1 雷利積分 (Rayleigh Integral) 25.2.2 空間傅利葉轉換 27.2.3 異向性聲源 27.3 設計空間與參數化 28.4 模擬方法 31.5 實驗量測架設 33.5.1 共振頻率量測 33.5.2 振形分布量測 34.5.3 聲源位準與波束圖量測 36.6 有效化模擬模型 39.7 參數研究與討論 47 4 章 具異向性波束之超聲波傳感器的其他效能 54.1 接收感度之遠場異向性波束 54.1.1 接收感度之遠場波束圖量測 54.1.2 發射聲壓波束與接收感度波束 56.2 頻率響應與阻抗 57.2.1 頻率響應 57.2.2 阻抗特性 58.3 殘響時間 59.3.1 殘響時間預測 60.3.2 殘響時間量測與結果 62.4 實際車用主機上可偵測範圍 64.4.1 障礙物偵測範圍之測試方法 64.4.2 可偵測範圍與波束異向性 66 5 章 以超聲波發射器為基礎之指向性喇叭 68.1 文獻回顧 69.2 振幅調變與非線性解調 70.2.1 振幅調變 71.2.2 非線性自解調 71.3 實驗量測 72.3.1 頻帶 73.3.2 量測架設 75.4 以超聲波單體為基礎之指向性喇叭 76.4.1 以超聲波傳感器單體為基礎之具異向性波束指向性喇叭 76.4.2 以超聲波發射器單體為基礎之具等向性波束指向性喇叭 83.4.3 反射式超聲波指向性喇叭 94.4.4 空間局部聲音消除的效果 97 6 章 結論與未來展望 101.1 結論 101.2 未來展望 103.2.1 長距離窄波束寬之超聲波傳感器 103.2.2 超聲波式指向性喇叭 104.2.3 聲音消除 104EFERENCE 105錄 A 中央寬大之圓角長方形振動板的超聲波傳感器振形分布 112錄 B 殘響時間測試之統計數據 114者簡歷(Vita) 11