臺灣博碩士論文加值系統

本文發展了一撓性結構同時與多個子系統阻抗耦合的技巧，並將此技巧應用於結構聲學系統之分析與設計。此方法的特色在於每個子結構的動態響應可各別分析計算，再藉由阻抗耦合的技巧將所有子結構的動態響應合成整體結構的動態響應。耦合後的結構特性如自然頻率、阻抗、頻率響應函數和輻射聲能等則可以各別系統之阻抗加以組合。此方法應用於四個範例。首先應用於多組壓電致動器與結構耦合之系統。應用多組壓電致動器使結構產生某特定的位移響應，而壓電致動器的輸出力量則可以由阻抗理論直接計算出。第二個應用則是應用多組結構貼片調整結構多個自然頻率，當指定了結構之自然頻率之後，則可以藉由調整結構貼片的位置及厚度以達到此設定值。第三個應用則是將阻抗耦合的技巧應用於多頻吸振器的設計，此多頻吸振器為一具有不均勻厚度之樑結構，其自然頻率則可以藉由控制結構厚度以調整為與機器所受外力頻率相同，例如旋轉機械的前三個倍頻等等，因此即可吸收多個頻率之振動。最後的應用則是流體承載結構的分析。結構及流體的作用分別以結構阻抗及流體阻抗表示，並且發展了此兩者阻抗耦合的技巧。

An impedance coupling technique for a host structure bonded with multiple substructures to solve various inverse vibro-acoustic problems is introduced. The advantages of the proposed technique lie in that the system is modularized to multiple subsystems. Each subsystem is studied independently of the rest of the system. Then the dynamic response of the integrated system can be obtained by coupling the response of each subsystem through the conditions of compatibility and force equilibrium. The dynamic characteristics of a system, e.g. natural frequency, driving point impedance, frequency response function, radiated acoustic power, etc., can be expressed as the combinations of the impedance of each subsystem. Four applications based on the proposed technique are demonstrated. The first is to synthesize the vibration response using a PZT actuator-driven structure. In the first application, a methodology to synthesize a pre-designated response using a structure bonded with multiple PZT patches is introduced. The actuating force of each PZT can be obtained analytically by using the proposed impedance technique. The second application demonstrates how to manipulate the natural frequencies of a structure by using the structural patches. By adjusting the locations and thickness of each patch, more than one natural frequency of the structure can be shifted to pre-designated values. The third application is to introduce a design technique of vibration absorber whose natural frequencies intentionally coincide with the frequencies of excitation, e.g. the rotating speed of a rotary machine and its harmonic orders. Therefore it can effectively reduce the vibration response due to rotor eccentric, rotor shaft bending, mechanical looseness, etc. The last application is to present a methodology of modeling a fluid-loaded structure. The structural response and the fluid loading are expressed in terms of the structural impedance and the acoustic wave impedance, respectively. Then, the integrated impedance can be calculated from assembling the structural impedance and the acoustic impedance.

Table of Contents
ABSTRACT……………………..….…................…………….….…......I
LIST OF TABLES…………………..….............…………….….….....Ⅵ
LIST OF FIGURES…….……….........….............…………….………Ⅶ
CHAPTER 1 INTRODUCTION
1.1 Motivations and Goal..................................................................................1
1.2 Literature Review.........…………...............................................................3
1.2.1 Modifications of Structural Characteristics......................................3
1.2.2 Development of Mechanical Impedance Concept………………....5
1.2.3 PZT-driven Active Structures………................................................8
1.2.4 Conclusions of Literature Review…………...................................11
1.3 Organization of Chapters...........................................................................12
CHAPTER 2 MULTIPLE PIEZOELECTRIC ACTUATORS DRIVEN STRUCTURES
2.1 Introduction................................................................................................15
2.2 Physical Model…………………………………………………………...16
2.3 Inertial Impedance of PZT patch........................................................……16
2.4 Longitudinal Impedance.............................................................................17
2.5 Modified Longitudinal Impedance.............................................................18
2.6 Impedance of Host Structure.............................................................….....19
2.7 Impedance Coupling of PZT Patch and Host Structure…….……..…......23
2.8 Synthesis of a Given Harmonic Response…………………………….....26
2.9 Response Validation of an Integrated PZT/host Structure System....….....28
2.10 Numerical Examples and Discussion.......................................................30
CHAPTER 3 NATURAL FREQUENCY TUNING USING STRUCTURAL PATCHES
3.1 Introduction................................................................................................41
3.2 Physical Model...........................................................................................41
3.3 Impedance of the Host Structure………………………………………....42
3.4 Impedance Models of Patch/Host Structure Coupling...............................44
3.5 Experimental Validation.............................................................................47
CHAPTER 4 DESIGN OF VIBRATION ABSORBERS FOR STRUCTURES SUBJECT TO MULTIPLE TONAL EXCITATIONS
4.1 Introduction................................................................................................57
4.2 Theory of the SMD Vibration Absorber...…..............................................58
4.3 Design Methodology of a Multiple-Tonal Vibration Absorber..................59
4.4 Impedance of Bock Mass...........................................................................61
4.5 Design of Vibration Absorbers...................................................................63
4.6 Experimental Validation.............................................................................64
4.7 Influences of the Inertia and Stretching Elasticity of the Block Mass on the Vibration Response.................................................................................…66
CHAPTER 5 IMPEDANCE TECHNIQUE FOR A FLUID-LOADED STRUCTURE
5.1 Introduction.....…………………………………………..……………….79
5.2. Mechanical Mobility of Structures………..…………………….......…..80
5.3 Impedance of Fluid……………………………….....................................82
5.4 Impedance Coupling between Structure and Fluid....................................86
5.5 Numerical Validation Using Transformation Method …….......................87
5.6 Impedance Model for a Fluid-loaded Structure Driven by PZT Patches...88
5.7 Numerical Example and Validation……....................................................91
CHAPTER 6 CONCLUSIONS AND FUTURE WORK
6.1 Conclusions………………………………...……………………...……101
6.2 Future Work……………………………………………………..............104
REFERENCES.....................................................................................................105

References
1.Goel, R. P., 1976, “Free Vibrations of a Beam-Mass System with Elastically Restrained Ends,” J. Sound Vib., 47, 9-14.
2.Laura, P. A. A., Pombo, J. L. and Susemihl, E. A., 1975, “A Note on the Dynamics of an Elastically Restrained-Free Beam with a Mass at The Free End,” J. Sound Vib., 41, 397-405.
3.Gurgoze, M., 1984, “A Note On The Vibrations of Restrained Beams and Rods With Point Masses,” J. Sound Vib., 96, 461-468.
4.Manikanahally, D. N., and Crocker, M. J., 1988, “Vibration Analysis of Hysteretically Damped Mass-Loaded Beams,” J. Sound Vib., 132, 177-197.
5.Liu, W. H., Wu, J. R, and Huang, C. C., 1988, “Free Vibration of a Beams with Elastically Restrained Edges and Intermediate Concentrated Masses,” J. Sound Vib., 122(2), 193-207.
6.Wu, J. S., and Lin, T. L., 1990, “Free Vibration Analysis of a Uniform Cantilever Beam with Point Masses By an Analytical-and Numerical-Combined Method,” J. Sound Vib., 136(2), 201-213.
7.Keltie, R. F., and Cheng, C. C., 1995, “Vibration Reduction of a Mass-loaded Beam,” J. Sound Vib., 187(2), pp. 213-228.
8.Keltie, R. F., 1993, “Structural Acoustic Response of Finite-Reinforced Plates,” J. Acoust. Soc. Am., 94(2), pp. 880-887.
9.Koopmann, G. H., and Fahnline, J. B., 1997, Designing Quiet Structures, A Sound Power Minimization Approach, Academic Press, San Diego, California, USA, pp. 154-173.
10.Juang, J. N., 1984, “Optimal Design of a Passive Vibration Absorber for a Truss Beam,” AIAA Guidance and Control Conference, 7(6), 733-739.
11.Ozguven, H. N., and Candir, B., 1986, “Supressing the First and Second Resonances of Beams by Dynamic Vibration Absorbers,” J. Sound Vib., 111(3), 377-390.
12.Cheng, C. C., and Wang, J. K., 2002,“Applications of Unequally Spaced Absorbers on Vibro-Acoustic Response Reduction of a Fluid-Loaded Beam,” Journal of Chinese Society of Engineers, 23(1), pp. 85-91.
13.Nishihara, O., and Asami, T., 2002, “Close-Form Solutions to the Exact Optimizations of Dynamic Vibration Absorbers,” ASME J. Vib. Acoust., 124, pp.576-581.
14.Lamancusa, J. S., 1992, “Numerical Optimization Techniques for Structural-Acoustic Design of Rectangular Panels,” Computer and Structures, 48(4), 661-675.
15.Heavside, 1892, Electrical Papers, Macmillan, London.
16.Kirchhoff, G. R., 1881, Electricität und magnetismusVorlesengen über mathematische Physik, III, B.G. Teubner, Leipzig.
17.Thevenin, M. L., 1883, Rendus hebdomadaires de séances de l''Academie des sciences, XCVⅡ, Gauthier-Villars, Paris, pp. 159–161.
18.Jr, D. F. Tuttle, 1958, Network Synthesis, John Wiley & Sons, Inc, New York pp. 19–20.
19.Guillemin, E. A., 1931, Communication Networks, John Wiley & Sons, Inc., New York.
20.Guillemin, E. A., 1935, Communication Networks, John Wiley & Sons, Inc., New York.
21.Guillemin, E. A., 1953, Introductory Circuit Theory, John Wiley & Sons, Inc., New York.
22.Campbell, G. A., 1922, “Physical Theory of the Electric Wave-filter”, The Bell System Technical Journal, 5, pp. 313–330.
23.Webster, G., 1919, “Acoustical Impedance and Theory of Horns and of The Phonograph”, Proceedings of the National Academy of Science, Washington, 5, pp. 275–282.
24.Maxfield, J. P., and Harrison, H. C., 1926, “Methods of High Quality Recording and Reproducing of Music and Speech Based on Telephone Research”, Transaction of the American Institute Electrical Engineers, 45, pp. 334–348.
25.Firestone, F. A., 1933, “A New Analogy between Mechanical and Electrical Systems”, Journal of the Acoustical Society of America, 4, pp. 249–267.
26.Darrieus, M., 1929, “Les modéles mécaniques en électrotechnique leur application aux problémes de stabilité”, Bulletin de La Societe Francaise d''electriciens, 96, pp. 794–809.
27.Hahnle, W., 1932, “Die darstellung elektromechanischer gebilde durch rein elektrische schaltbilder”, Wiss Verloff and Siemens-Kohzerh, 11, pp. 1–23.
28.Firestone, F. A., 1938, “The Mobility Method of Computing the Vibration of Linear Mechanical and Acoustical Systems: Mechanical–Electrical Analogies”, Journal of Applied Physics, 9, pp. 373–387.
29.Hixson, E. L., 1961, Shock and Vibration Handbook, McGraw-Hill, New York.
30.Harrison, M., Sykes, A. O., and Martin, M., 1952, “Wave Effects in Isolation Mounts”, Journal of the Acoustical Society of America, 24, pp. 62–71.
31.Skudrzyk, E. J., 1958, “Vibrations of a System with a Finite or an Infinite Number of Resonances”, Journal of the Acoustical Society of America, 30, pp. 1140–1152.
32.Skudrzyk, E. J., 1959, “Theory of Noise and Vibration Insulation of a System with Many Resonances”, Journal of the Acoustical Society of America, 31, pp. 68–74.
33.Wright, D. V., 1958,”Impedance Analysis of Distributed Mechanical Systems”, In: R. Plunkett, Editor, Colloquium on Mechanical Impedance Methods for Mechanical Vibrations, The American Society of Mechanical Engineers, pp. 19–42.
34.Ruzicka, J. E., and Cavanaugh, R. D., 1958, “Vibration Isolation of Non-rigid Bodies”, In: R. Plunkett, Editor, Colloquium on Mechanical Impedance Methods for Mechanical Vibrations, The American Society of Mechanical Engineers, pp. 109–124.
35.Soliman, J. I., and Hallam, M. G., 1968, “Vibration Isolation between Non-rigid Machines and Non-rigid Foundations”, Journal of Sound and Vibration, 8, pp. 329–351.
36.Sykes, O., 1971, “Application of Admittance and Impedance Concepts in the Synthesis of Vibrating Systems”, Winter ASME Annual Meeting, Washington DC, pp. 22–37.
37.Bishop, R. E. D., and Johnson, D. C., 1979, The Mechanics of Vibration, Cambridge University Press, Cambridge, UK, pp. 17, 41-54, 245-352, 360.
38.Soedel, W., 1993, Vibrations of Shells and Plates, Marcel Dekker Inc, New York.
39.Bailey, T., and Hubbard, J. E. Jr., 1985, “Distributed Piezoelectric-Polymer Active Vibration Control of a Cantilever Beam,” AIAA Journal 8(5), pp.605-611.
40.Crawley, E. F., and DeLuis, J., 1989, “Use of Piezoelectric Actuators as Elements of Intelligent Structures,” AIAA Journal, 25(10), pp.1373-1385.
41.Hagood, N.W., Ching, W. H., and VonFlotow, A., 1990, “Modeling of Piezoelectric Actuators Dynamics of Active Structure Control,” Proceedings, 31st SDM Conference, Long Beach, CA, AIAA-90-697-CP.
42.Dimitriadis, E. K., Fuller, C. R., and Rogers, C. A., 1991, “Piezoelectric Actuators for Distributed Vibration Excitation of Thin Plates”, ASME J. Vib. Acoust., 113, pp.100-107.
43.Liang, C., Sun, F. P., and Rogers, C. A., 1993, “Dynamic Output Characteristics of Piezoceramic Actuators,” Proceedings of Smart Structures and Intelligent Systems. SPIE. Albuquerque, NM, 1817. pp. 286-298.
44.Rossi, A., Liang, C., and Rogers, C. A., 1993,”Coupled Electric-Mechanical Analysis of a Piezoceramic Actuator Driven System-An Application to Circular Ring,” Proceedings of the AIAA/ASME/ASCE/AHX/ASC 34st Structures, Structural Dynamics and Materials Conference, La Iolla, CA, April 19-22, pp. 3618-3624.
45.Liang, C., Sun, F. P., and Rogers, C. A., 1994, “An Impedance Method for Dynamic Analysis of Active Material System,” ASME J. Vib. Acoust., 116, pp.121-128.
46.Stein, S., Liang, C., and Rogers, C. A., 1993,”Power Consumption of Piezoelectric Actuators in Underwater Active structural Acoustic Control,” Proceedings of the Second Conference on Recent Advances in Active Control of Sound and Vibration, Blacksburg, V.A. April 28-30, pp. 240-251.
47.Zhou, S. W., Liang, C., and Rogers, C. A., 1993, “Impedance Modeling of Two-Dimensional Piezoelectric Actuators Bonded on a Cylinder,” Proceedings of the Adaptive Structures and Material Systems, ASME Winter Annual Meetings, New Orleans, LA, pp. 247-256.
48.Zhou, S. W., Liang, C., and Rogers, C. A., 1996, “An Impedance-Based System Modeling Approach for Induced Strain Actuator-Driven Structures,” ASME J. Vib. Acoust., 118, pp. 323-331.
49.Cheng, C. C., and Wang, P. W., 2001, “Applications of the Impedance Method on Multiple Piezoelectric Actuators Driven Structures,” ASME J. Vib. Acoust., 123(2), pp.262-268.
50.Lin, C. C. and Cheng, C. C., 2004, “An Impedance Approach for Vibration Response Synthesis Using Multiple PZT Actuators,” Sensors and Actuators: A. Physical, 118, pp.116-126.
51.Wang, P. W., and Cheng, C. C., 2005, “Natural Frequencies Tuning Using Structural Patches,” ASME J. Vib. Acoust., 127, pp.28-35.
52.Wang, P. W., and Cheng, C. C., 2003, “應用阻抗法於多頻抑振器之設計,” Proceeding of the 20th National Conference of the Chinese Society of Mechanical Engineers, Taipei, Taiwan.
53.Craig, R. R., Jr., and Bampton, M. C. C., 1968, "Coupling of Substructures for Dynamic Analysis," AIAA Journal, 6 (7), pp.1313-1319.
54.Craig, R. R., Jr., and Chang C.-J., 1977, "On the Use of Attachment Modes in Substructure Coupling for Dynamic Analysis," AIAA Paper No. 77-405, AIAA/ASME 18th Structures, Structural Dynamics and Materials Conference, San Diego, pp. 89-99.
55.Craig, R. R., Jr., 1995, "A New Substructure System Identification Method," Proceedings 36th AIAA/ASME/AHS/ASC Structures, Structural Dynamics, and Materials Conference, New Orleans, LA, pp. 1209-1217.
56. Rao, S. S., 1995, Mechanical Vibration, 3rd edition, Addison-Wesley Publishing Company, Inc., New York, pp. 527, 531-534, 603-607.
57.The Dogbone Vibration Damper Type DB Data Sheet, produced by Dulmision.
58.Hill, S. G., and Snyder, S. D., 2002, ”Design of an Adaptive Vibration Absorber to Reduce Electrical Transformer Structural Vibration,” ASME J. Vib. Acoust., 124, pp.606-611.
59.Maidanik, G., 1966, “The Influence of Fluid Loading on the Radiation from Orthotropic Plate,” J. Sound Vib., 3(3), pp. 288-299.
60.Nayak, P. R., 1970, “Line admittance of Infinite Isotropic Fluid-loaded Plates,” J. Acoust. Soc. Am., 78(2), pp. 763-766.
61.Geers, T., and Felippa, C. A., 1983, “Doubly Asymptotic Approximations for Vibration Analysis of Submerged Structures,” J. Acoust. Soc. Am., 73(1), pp. 1152-1159.
62.Feit, D., and Liu, Y. N., 1985, “The Nearfield Response of a Line-driven Fluid-loaded Plate,” J. Acoust. Soc. Am., 47(1), pp. 191-201.
63.Crighton, D. G., 1989, “Fluid loading: The Interaction between Sound and Vibration,” J. Sound Vib., 133(1), pp. 1-27.
64.Junger, M. G., and Feit, D., 1986, Sound, Structures, and Their Interaction, 2nd ed., MA: MIT Press, Cambridge.
65.Lee, D., Sternberg, R. L., and Schultz, M. H., 1988 “Computational acoustics: algorithms and applications,” Proceedings of the 1st IMACS Symposium on Computational Acoustics, Amsterdam, Holland
66.Ewins, D. J., 2000, Modal Testing Theory, Practice and Application, 2nd ed., Research Studies Press, Baldock, Hertfordshire, England, pp. 163-276.
67.Sneddon, I. N., 1972, The Use of Integral Transformations, McGraw-Hill Inc., New York, pp. 484-504.