臺灣博碩士論文加值系統

本研究旨在探討移動聲源所引發之聲場，而內容上共分為兩個部份。第一個部份是要建立移動聲源的數學模型，以及對應的數值演算法；第二個部份則是要運用所建立的數值演算法，去探討實際的工程聲學問題。在第一個部份中，首先是推導出一個新的統馭方程式，該方程式可視為是一種修正型的Ffowcs Williams-Hawkings方程式(FW-H方程式)，而其最大的特點為能兼顧內聲場(Interior Domain)與外聲場(Exterior Domain)問題。此外，為了使新的統馭方程式能擴展至移動聲源作非等速運動的情形，也推導出新的聲學位置向量(Acoustic Position Vector)表示法。所謂的聲學位置向量，描述的是聲源點在聲波發射時，與接收點收到聲波時，兩者之間方向與距離的關係。至於統馭方程式的解，則利用格林函數(Green’s Function)將之表示成表面積方程(Surface Integral Formula, SIF)，其目的是為了以時域邊界元素法建立對應的數值演算法(Boundary Element Method in Time Domain, BEMTD)。
在第二個部份中，將以兩個實際個工程案例來展現所建立演算法之特性。第一個案例，是探討變速度移動線聲源，該案例能清楚展現本文所建立的演算法，確實能解除過去相關演算法，其僅能計算等速度移動物體的限制，另外模擬的結果也顯示出，當移動聲源以等加速或等減速運動時，其聲波頻率與振幅的變化率會比等速度運動情況下來的劇烈，而且觀測點接收到最大聲壓振福的時刻也會因此提早或提前。第二個案例則是移動音源聽覺感知的模擬，在該案例中，將利用所建立的演算法計算出耳道入口處之聲壓，並結合黃-希爾伯特轉換(Hilbert Huang Transformation, HHT)作聲壓訊號的時頻分析，以期能了解就感知移動音源之速度與方向而言，不同聽覺感知線索(Cue)之間的權重，結果顯示，雙耳位準差（Interaural Level Difference, ILD）與頻率偏移( Frequencies Shifting )比起雙耳時間差（Interaural Time Difference, ITD）是較為重要的感知線索。此外在相同條件下，移動聲源比靜止聲源對於聽者而言，會感知到較大的響度位準(Loudness Level)。上述兩個工程案例，都確實顯示出移動聲源所引發的聲場，其聲學特性相較靜止聲源所引發的有著很大的不同。而本研究所建立之分析方法，能有效模擬並分析上述類似之聲學問題（無論聲源是處於是靜止狀態或移動狀態），進而從中獲得有意義之物理現象。

Abstract
The Phenomenon of the sound field generated by a moving sound source has
been investigated in the present work with two-part subject. The first part is to establish
the mathematical model and the corresponding numerical scheme; the second part is to
employ the established numerical scheme in practical acoustic problems. In order to
establish the mathematical model, a novel governing equation is derived and it can be
viewed as a modified Ffowcs Williams-Hawkings equation (FW-H-equation). The
major characteristic of the novel governing equation is to include the interior and the
exterior domain. In addition, the acoustic position vector, the quality describes the
relations about the distance and the direction between the observer and the sound
source, is represented for applying to the condition of the sound source moving with
variable speed. As to the solution of the governing equation, it is expressed in the form
of the Surface Integral Formula (SIF) by convoluting the free-space Green’s function in
time domain. Then, this SIF is used to numerical implementation in the concept of the
Boundary Element Method in time domain (BEMTD).
After establishing the numerical scheme and verifying the correctness of the
calculating results, two acoustic problems were investigated for revealing the ability of
the numerical scheme. The first case considers that a moving line source with variable
speed. This case reveals that the restriction of the constant speed is released in the
established numerical scheme. For the simulation results, it shows that the effect of the
variable speed not only influenced the variation rate of the frequency modulation, i.e.,
Doppler effect, but also the time about the maximum acoustic pressure being observed.
In addition, the rate of the amplitude variation is shaper than that in the constant speed
case when the line source is approaching to the observer point. The second case
investigates the binaural hearing perceived by a moving sound source. For
understanding the weighting of the eventful cues about perceiving the direction and the
speed of the moving sound source, the sound pressure at the entrance of the external ear
canal was calculated by the established numerical scheme. Furthermore, the Hilbert
Huang transformation (HHT) is used to find the instantaneous frequencies of acoustic
signal. Results show that the Interaural Level Difference (ILD) and the frequencies
shifting are eventful than Interaural Time Difference (ITD). The perceived loudness
level will be larger in the motional case than that found in the stationary case. These
engineering problems are shown that the acoustic properties are different for
comparing with the sound field generated by a moving sound source and that by a
stationary sound source. As to the analytical methodology developed in the present
work, it turns out that it indeed can be used to simulate and analyze these acoustic
problems whenever the sound source moves or not. Furthermore, some meaningful
phenomenon relating to these problems then can be observed through discussing the
calculating results.

Contents
Abstract i
Acknowledgement iii
Nomenclature vii
List of Figures xi
List of Tables xv
1. Introduction 1
1.1 Motive of Research 1
1.2 Literature Review 1
1.2.1 The theory development 1
1.2.2 The implementation of the numerical scheme 5
1.2.3 The application to the engineering problems 7
1.2.4 Summary 12
1.3 Research Objectives 12
2. Theory of Moving Sound Source 14
2.1 Symbols Definitions and Coordinate Frames 14
2.2 Classical Governing Equation 19
2.3 Novel Governing Equation 24
2.4 The Solution of the Novel Governing Equation 34
2.4.1 General Solution of the nonhomogenous wave equation 34
2.4.2 Surface Integral Formula of the novel governing equation 39
2.5 Formulations for Acoustic Position Vector 47
3. Numerical Implementation 53
3.1 Singular Integrals 53
3.2 Discretisation 55
3.2.1 Temporal Discretisation 57
3.2.2 Spatial Discretisation 58
3.3 Numerical Integration 61
3.4 Point Collocation 64
3.5 Assembly of the System Equation and Solution 68
3.6 Treatment of the Boundary Conditions 72
4. Acoustic Radiation from a Moving Line Source with Variable Speed 76
4.1 Problem Description 76
4.2 Acoustic Pressure Distribution on the Surface 79
4.3 Acoustic Pressure Distribution at the Field Point 82
4.4 Section Conclusions 90
5. Binaural Hearing Caused by a Moving Sound Source 91
5.1 Problem Description 91
5.2 Amplitude Variation for Binaural Hearing 93
5.3 Frequency Variation for Binaural Hearing 102
5.4 Section Conclusions 108
6. Conclusions 110
6.1 Theoretical Contribution about the Moving Sound Source 110
6.2 Practical Application for Moving Sound Source with Variable Speed 111
6.3 Practical Application for Multi-moving Sound Source 111
7. Bibliography 112
Appendix 120
Appendix A Kirchhoff Governing Equation 120
Appendix B The modification of the source terms about Eq. (2.39) under various conditions 124
Appendix C The derivation of Eq. (2.41) 126
Appendix D The solution of the Kirchhoff and Ffowcs Williams-Hawkings Governing Equation 128
Appendix E Detail Expression of Each Term about Eq. (2.61) 131
Appendix F Integral Formula and Calculating Procedure for Turbulence/Body Interaction 135
Appendix G The coefficients of the quartic equation 136
Appendix H Derivation of the coefficient l 137
Appendix I Numerical Implementation of the Singular Integral 142

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