本文是以數位光彈法為基礎，架設一套數位動態光彈系統來拍攝動態光彈條紋。首先觀測矩形平板在超音波激振後所形成的駐波及熱應力，以了解均勻喇叭在工作時的應力狀態；超音波的應用範圍極廣，在工業生產領域中常可發現超音波的應用，唯有充分了解並妥善運用，才能提昇製程中的效率與品質。接著研究含切口之矩形平板在超音波激振下的應力波場及其尖端的應力集中現象，藉以開發超音波加工應用於光電半導體製程中。最後，探討常見之T狀結構受到衝擊後的應力波傳；衝擊波對結構產生影響通常發生於撞擊或地震時，常產生關鍵性的破壞，為能確保設計上的安全性，須對衝擊波所產生的應力集中效應有所了解。
當物體受到超音波或衝擊波時所產生的應力波將異於一般傳統的靜態應力分布，非常適合以光彈法來做全域式的即時觀測，再佐以有限單元法的分析結果，可獲得全盤的了解以利研究。如此不但能提高超音波加工的效能，開發新的超音波加工技術，並有助於評估結構在動態負荷下的安全性。
在運用光彈法觀測駐波應力場的過程中，提出均時光彈性(Time-Averaged Photoelasticity)理論，並利用實驗光彈影像的灰階分布來驗證所推導之理論；此實驗方法可有效節省實驗時間及經費。

Based on the conventional digital photoelastic method, this dissertation developed a digital dynamic photoelastic system to record the dynamic photoelastic fringe patterns. First, the system can be used to observe the stress distributions of standing wave and thermal stress generated by the ultrasonic wave. In the field of industrial production, the application of the ultrasonic wave can be found frequently. Only after sufficient understanding and proper practice of the ultrasonic wave, the efficiency and quality of the production can be improved. Next, the states of stresses in several photoelastic strips with different sizes of V-notches under the incidence of the ultrasonic wave were investigated. The obtained results are useful when applying the ultrasonic wave in the optoelectronic semiconductor industry. Finally, the dynamic photoelastic system was used to investigate the stress wave of T-shape structural components under impact. The dynamic loading usually causes critical damage of the structures during impact or earthquake. To ensure safety, it is necessary to analyze the stress concentration effect of structures under impact.
When the object is affected by the ultrasonic wave or impact, the generated stress wave is different from the conventional static stress distribution. For whole field and real time observation, the dynamic photoelastic method is the best method to investigate this problem. With the aid of finite element method, complete understanding can be obtained and further research can be performed. In addition, the efficiency of the ultrasonic machining can be improved, new fields of the ultrasonic machining technology can be developed, and evaluation of the safety of the structures under dynamic load can be facilitated.
In this dissertation, the time-averaged photoelastic method was proposed. By comparing the gray level distributions of the proposed theory and experimentally obtained photoelastic fringe pattern generated by standing wave only, the correctness of the time-averaged photoelastic method was verified. By using this new method, stress characteristics of a harmonic wave motion can be readily obtained and the experimental procedures are much simplified.

[1] D. Ensminger, “Ultrasonics: Fundamentals, Technology, Applications”, 2nd Edition, Marcel Dekker, Inc., New York, U. S. A., 1988.
[2] T. B. Thoe, D. K. Aspinwall, and M. L. H. Wise, “Review on Ultrasonic Machining”, International Journal of Machine Tools and Manufacture, Vol. 38, pp. 239~255, 1998.
[3] J. X. Zeng, “A Brief Introduction of Manufacturing Technique for Gallium-Nitride Monocrystal Substrate” (in Chinese), Electronic Monthly, No. 75, pp. 144~151, 2001.
[4] J. Y. Huang, H. Y. Lin, H. Y. Tsai and C. H. Fan, “Structure of Brittle Material Substrate and Fabricating Process Thereof”, New Invention Patent No. 186553, Republic of China, 2003.
[5] Z. Tuzi, “Photographic and Kinematogrphic Study of Photoelasticity”, Scientific Papers, Inst. Phys. Chem. Research, Tokyo, Vol. 8, pp. 247~267, 1928.
[6] Y. I. Ostrovsky, M. M. Butusov and G. V. Ostrovskaya, “Interferometry by Holography”, Springer-Verlag Book Inc., Berlin Heidelberg, New York, U. S. A., 1980.
[7] W. C. Wang, C. H. Hwang and S. Y. Lin, “Vibration Measurement by the Time-Averaged Electronic Speckle Pattern Interferometry Methods”, Applied Optics, Vol. 35, pp. 1~8, 1996.
[8] A. Asundi, M. R. Sajan and L. Tong, “Dynamic Photoelasticity Using TDI Imaging”, Optics and Lasers in Engineering, Vol. 38, pp. 3~16, 2002.
[9] C. Cranz and H. Schardin, “Kinematographic auf Ruhendem Film und mit Extrem Hoher Bildfrequenz” (in German), Zeitschrift Fur Physik, Vol. 56, pp. 147~183, 1929.
[10] K. F. Graff, “Wave Motion in Elastic Solids”, Dover Publications, Inc., New York, U. S. A., 1991.
[11] W. F. Riley and J. W. Dally, “Recording Dynamic Fringe Patterns with a Cranz-Schardin Camera”, Experimental Mechanics, Vol. 9, pp. 27N~33N, 1969.
[12] C. P. Burger and W. F. Riley, “Effects of Impedance Mismatch on the Strength of Waves in Layered Solids”, Experimental Mechanics, Vol. 14, pp. 129~137, 1974.
[13] J. W. Dally, “Dynamic Photoelastic Studies of Fracture”, Experimental Mechanics, Vol. 19, pp. 349~361, 1979.
[14] J. A. Clark and A. J. Durelli, “An Introduction to Dynamic Photoelasticity”, Experimental Mechanics, Vol. 23, pp. 42~48, 1983.
[15] D. R. Henley, J. L. Turner and C. E. Taylor, “A Hybrid System for Dynamic Photoelasticity”, Experimental Mechanics, Vol. 15, pp. 289~293, 1975.
[16] W. P. T. North and C. E. Taylor, “Dynamic-Stress Concentration Using Photoelasticity and a Laser Light Source”, Experimental Mechanics, Vol. 6, pp. 337~341, 1966.
[17] P. D. Flynn, “Dual-beam Polariscope and Framing Camera for Dynamic Photoelasticity”, Experimental Mechanics, Vol. 13, pp. 178~184, 1973.
[18] A. Shukla and V. Prakash, “Wave Propagation in Porous Media as a Function of Fluid Saturation”, Experimental Mechanics, Vol. 20, pp. 80~87, 1990.
[19] W. J. Zong and L. Y. Ju, “Application of High Speed Photography in Science and Technology”, Proceedings of SPIE, Vol. 348, pp. 168~176, 1982.
[20] W. C. Wang and Y. H. Tsai, “Ultrasonic Stress Analysis of a Strip by the Time-Averaged Photoelastic Method”, Proceedings of the 3rd International Conference on Experimental Mechanics, paper no. 236, 6 pages, Singapore, November 29- December 1, 2004.
[21] M. Ragulskis and L. Ragulskis, “On Interpretation of Fringe Patterns Produced by Time Average Photoelasticity”, Experimental Techniques, Vol. 29, pp. 48~51, 2005.
[22] J. W. Dally, “Data Analysis in Dynamic Photoelasticity”, Experimental Mechanics, Vol. 7, pp. 332~338, 1967.
[23] H. Pih, “Photoelastic Studies of the Two-dimensional Dynamic Stress-Optic Law”, Experimental Mechanics, Vol. 3, pp. 33~40, 1963.
[24] A. B. J. Clark and R. J. Sanford, “A Comparison of Static and Dynamic Properties of Photoelastic Materials”, Experimental Mechanics, Vol. 3, pp. 148~151, 1963.
[25] J. W. Dally, “An Introduction to Dynamic Photoelasticity”, Experimental Mechanics, Vol. 20, pp. 409~416, 1980.
[26] A. Shukla, M. H. Sadd and H. Mei, “Experimental and Computational Modeling of Wave Propagation in Granular Materials”, Experimental Mechanics, Vol. 30, pp. 377~381, 1990.
[27] J. F. Cardenas-Garcia and D. C. Holloway, “On the Lamb Solution and Raylight-Wave-Induced Cracking”, Experimental Mechanics, Vol. 28, pp. 105~109, 1988.
[28] L. W. Zachary and C. P. Burger, “Dynamic Wave Propagation in a Single Lap Joint”, Experimental Mechanics, Vol. 20, pp. 162~166, 1980.
[29] J. L. Rose and P. C. Chou, “Study of Cylindrical Stress Waves Generated by Exploding Wires”, Experimental Mechanics, Vol. 12, pp. 104~106, 1972.
[30] A. W. Miles, “Shock-Front Loading Method for Studies in Dynamic Photoelasticity”, Experimental Mechanics, Vol. 16, pp. 349~355, 1976.
[31] L. V. Brillhart and J.W. Dally, “A Dynamic Photoelastic Investigation of Stress-Wave Propagation in Cones”, Experimental Mechanics, Vol. 8, pp. 145~153, 1968.
[32] K. Kawata, N. Takeda and S. Hashimoto, “Photoelastic-Coating Analysis of Dynamic Stress Concentration in Composite Strips”, Experimental Mechanics, Vol. 24, pp. 316~327, 1984.
[33] A. S. Kobayashi, K. Seo, J. Y. Jou and Y. Urabe, “A Dynamic Analysis of Modified Compact-Tension Specimens Using Homalite-100 and Polycarbonate Plates”, Experimental Mechanics, Vol. 20, pp. 73~79, 1980.
[34] S. Mall, A. S. Kobayashi and Y. Urabe, “Dynamic Photoelastic and Dynamic Finite-Element Analyses of Dynamic-Tear-Test Specimens”, Experimental Mechanics, Vol. 18, pp. 449~456, 1978.
[35] T. Kobayashi and J. W. Dally, “A System of Modified Epoxies for Dynamic Photoelastic Studies of Fracture”, Experimental Mechanics, Vol. 17, pp. 367~374, 1977.
[36] M. Ramulu and A. S. Kobayashi, “Dynamic Crack Curving---A Photoelastic Evaluation”, Experimental Mechanics, Vol. 23, pp. 1~9, 1983.
[37] J. H. Hemann, J. D. Achenbach and S. J. Fang, “A Dynamic Photoelastic Study of Stress-Wave Propagation Through an Inclusion”, Experimental Mechanics, Vol. 16, pp. 291~299, 1976.
[38] J. W. Dally and D. B. Barker, “Dynamic Measurements of Initiation Toughness at Hight Loading Rates”, Experimental Mechanics, Vol. 28, pp. 298~303, 1988.
[39] A. S. Kobayashi and C. F. Chan, “A Dynamic Photoelastic Analysis of Dynamic-Tear-Test Specimen”, Experimental Mechanics, Vol. 16, pp. 176~181, 1976.
[40] K. Kawata and S. Hashimoto, “On Some Differences between Dynamic and Static Stress Distributions”, Experimental Mechanics, Vol. 7, pp. 91~96, 1967.
[41] A. Kuske, “Photoelastic Stress Analysis of Machines under Dynamic Load”, Experimental Mechanics, Vol. 17, pp. 88~96, 1977.
[42] S. Vanlanduit, P. Verboven, P. Guillaume, B. Cauberghe and E. Parloo, “Damage Detection of Airplane Components Using Ultrasonic Surface Waves”, Key Engineering Materials, Vol. pp. 549-556, 2005.
[43] Y. Kudryavtsev and J. Kleiman, “Ultrasonic Technique and Device for Residual Stress Measurement”, Ultrasonics, Vol. 37, pp. 365~372, 1999.
[44] C. L. Ho, H. L. Marcus and O. Buck, “Ultrasonic Surface-wave Detection Techniques in Fracture Mechanics”, Experimental Mechanics, Vol. 14, pp. 42~48, 1974.
[45] F. L. di Scalea, P. Rizzo and A. Marzani, “Propagation of Ultrasonic Guided Waves in Lap-Shear Adhesive Joints”, Journal of the Acoustical Society of America, Vol. 115, pp. 146~156, 2004.
[46] A. S. Eriksson, A Bostron, S. K. Datta, “Ultrasonic Wave Propagation Through a Cracked Solid”, Wave Motion, Vol. 22, pp. 297~310, 1995.
[47] M. E. Baltazar, C. P. Burger, R. Chona and S. Suh, “Study of Wave Motion on the Tubulars Using Broad-band Laser Ultrasound”, Experimental Mechanics, Vol. 45, pp. 427~432, 2005.
[48] J. N. Petzing and J. R. Tyrer, “Analysis of Power Ultrasonic Components Using Shearing Interferometry”, Optics and Lasers in Engineering, Vol. 26, pp. 235~248, 1997.
[49] G. Graham, J. N. Petzing and M. Lucas, “Modal Analysis of Ultrasonic Block Horns by ESPI”, Ultrasonics, Vol. 37, pp. 149~157, 1999.
[50] A. Cardoni and M. Lucas, “Enhanced Vibration Performance of Ultrasonic Block Horns”, Ultrasonics, Vol. 40, pp. 365~369, 2002.
[51] P. M. Kanthale, P. R. Gogate, A. B. Pandit, and A. M. Wilhelm, “Mapping of an Ultrasonic Horn: Link Primary and Secondary Effects of Ultrasound”, Ultrasonics Sonochemistry, Vol. 10, pp. 331~335, 2003.
[52] X. S. Zhu, K. W. Xu, B. Zhao and D. Z. Ma, “Experimental and Theoretical Research on ‘Local Resonance’ in an Ultrasonic Horning System”, Journal of Materials Processing Technology, Vol. 129, pp. 207~211, 2002,
[53] S. G. Amin, M. H. M. Ahmed and H. A. Youssel, “Computer-aided Design of Acoustic Horns for Ultrasonic Machining Using Finite-Element Analysis”, Journal of Materials Processing Technology, Vol. 55, pp. 254~260, 1995.
[54] Z. W. Zhong and K. S. Goh, “Investigation of Ultrasonic Vibrations of Wire-Bonding Capillaries”, Microelectronics Journal, Vol. 37, pp. 107~113, 2006.
[55] S. Sato and R. Ishii, “超音波振動切斷方法及其裝置”, New Invention Patent No. 440484, Republic of China, 2001.
[56] C. F. Chen, “半導體晶片裝置封裝接合之改良”, New Invention Patent No. 471711, Republic of China, 2001.
[57] M. R. Hsu, “光電及半導體製程中聚亞醯胺膜層之剝除方法”, New Invention Patent No. 478016, Republic of China, 2001.
[58] 約翰．歐希諾渥, “處理基板之方法及裝置”, New Invention Patent No. 453905, Republic of China, 1999.
[59] K. Sakaguchi and K. Yanagita, “多孔區域去除方法及半導體基板製造方法”, New Invention Patent No. 440950, Republic of China, 1999.
[60] H. Tomita, N. Soichi, M. Shirakashi, K. Ito and Y. Inoue, “半導體基板清潔裝置及方法”, New Invention Patent No. 466554, Republic of China, 2001.
[61] H. Pih and L. S. Snyders, “Photoelastic Studies of Ultrasonic Waves in a Large Plate”, Experimental Mechanics, Vol. 9, pp. 186~192, 1969.
[62] F. Lanza di Scalea, M. Bonomo and D. Tuzzeo, “Ultrasonic Guided Wave Inspection of Bonded Lap Joints: Noncontact Method and Photoelastic Visualization”, Research in Nondestructive Evaluation, Vol. 13, pp. 153~171, 2001.
[63] Y. H. Nam and S. S. Lee, “A Quantitative Evaluation of Elastic Wave in Solid by Stroboscopic Photoelasticity”, Journal of Sound and Vibration, Vol. 259, pp. 1199~1207, 2003.
[64] C. P. Burger, A. Testa and A. Singh, “Dynamic Photoelasticity as an Aid in Developing New Ultrasonic-Test Methods”, Experimental Mechanics, Vol. 22, pp. 147~154, 1982.
[65] W. C. Wang and Z. Y. Chen, “Photoelastic Investigation of Thermal Stresses in the Horn of an Ultrasonic Machine”, Proceedings of the SEM Annual Conference & Exposition on Experimental and Applied Mechanics, paper no. 120, 8 pages, Portland, Oregon, U. S. A., June 7-9, 2005
[66] M. D. Wu, “The Photoelastic Visualization and Evaluation of Ultrasonic Wave Field” (in Chinese), M. S. Thesis, Department of Physics, National Cheng Kung University, Tainan, Taiwan, R. O. C., 1989.
[67] H. Kolsky, “Stress Waves in Solids”, 2nd Edition, Dove Publications, Inc., New York, U. S. A., 1963.
[68] E. Wu, T. D. Tsai and C. S. Yen, “Two Methods for Determining Impact-force History on Elastic Plates”, Experimental Mechanics, Vol. 33, pp. 11~18, 1993.
[69] R. W. Mortimer, J. L. Rose and P. C. Chou, “Longitudinal Impact of Cylindrical Shells”, Experimental Mechanics, Vol. 11, pp. 25~31, 1971.
[70] R. J. Kroll and C. A. Tatro, “Stress-wave Propagation in Axially Symmetric Test Specimens”, Experimental Mechanics, Vol. 7, pp. 129~544, 1967.
[71] N. P. Suh, “Stress-Wave Propagation in Truncated Cones Against a Rigid Wall”, Experimental Mechanics, Vol. 7, pp. 541~544, 1967.
[72] W. Tong, “Pressure-shear Stress Wave Analysis in Plate Impact Experiments”, International Journal of Impact Engineering, Vol. 19, pp. 147~164, 1997.
[73] J. G. Stephenson and J. C. Wilhoit, “An Experimental Study of Bending Impact Waves in Beams”, Experimental Mechanics, Vol. 5, pp. 16~21, 1965.
[74] B. W. Abbott and R. H. Cornish, “A Stress-wave Technique for Determining the Tensile Strength of Brittle Materials”, Experimental Mechanics, Vol. 5, pp. 148~153, 1965.
[75] Y. C. Angel and A. Bolshakov, “In-plane Waves in an Elastic Solid Containing a Cracked Slab Region”, Wave Motion, Vol. 31, pp. 297~315, 2000.
[76] E. Scarpetta and M. A. Sumbatyan, “On Wave Propagation in Elastic Solids with a Double Periodic Array of Crack”, Wave Motion, Vol. 25, pp. 61~72, 1997.
[77] S. Ganesan, C. S. Man and S. J. Lai-Fook, “Generation and Detection of Lung Stress Waves from the Chest Surface”, Respiration Physiology, Vol. 110, pp. 19~32, 1997.
[78] R. Shea, “Dynamic Stress-concentration Factors”, Experimental Mechanics, Vol. 4, pp. 20~24, 1964.
[79] L. B. Freund, “The Stress Intensity Factor due to Normal Impact Loading of the Faces of a Crack”, International Journal of Engineering Science, Vol. 12, pp. 179~189, 1974.
[80] H. P. Rossmanith, “Dynamic Stress-intensity-factor Determination from Isopachics”, Experimental Mechanics, Vol. 9, pp. 281~285, 1979.
[81] S. Itou and H. Haliding, “Dynamic Stress Intensity Factors around Two Parallel Cracks in an Infinite-Orthotropic Plane Subjected to Incident Harmonic Stress Waves”, International Journal of Solids and Structures, Vol. 34, pp. 1145~1165, 1997.
[82] J. Dominguez and R. Gallego, “Time Domain Boundary Element Method for Dynamic Stress Intensity Factor Computations”, International Journal for Numerical Methods in Engineering, Vol. 33, pp. 635~647, 1992.
[83] L. J. Pyrak-Nolte, S. Roy and B. L. Mullenbach, “Interface Waves Propagated along a Fracture”, Journal of Applied Geophysics, Vol. 35, pp.79~87, 1996.
[84] C. C. Ma and S. K. Chen, “Exact Transient Analysis of an Anti-Plane Semi-infinite Crack Subjected to Dynamic Body Forces”, Wave Motion, Vol. 17, pp. 161~171, 1993.
[85] S. Aoki, K. Kishimoto, H. Kondo and M. Sakata, “Elastodynamic Analysis of Crack by Finite Element Method Using Singular Element”, International Journal of Fracture, Vol. 14, pp. 59~68, 1978.
[86] K. Liu and S. Tanimura, “Numerical Analysis For Dynamic Stress Concentration in a Rectangular Block due to Impact”, International Journal of Impact Engineering, Vol. 19, pp. 653~666, 1997.
[87] W. H. Chen, C. L. Chang, C. H. Tsai, “Elastodynamic Fracture Analysis of Multiple Cracks by Laplace Finite Element Alternating Method”, Journal of Applied Mechanics, Vol. 67, pp. 606~615, 2000.
[88] P. Lazzarin and S. Filippi, “A Generalized Stress Intensity Factor to be Applied to Rounded V-Shaped Notches”, International Journal of Solids and Structures, Vol. 43, pp. 2461~2478, 2006.
[89] A. Seweryn, “Modeling of Singular Stress Fields Using Finite Element Method”, International Journal of Solids and Structures, Vol. 39, pp. 4787~4804, 2002.
[90] N. A. Noda, M. Sera and Y. Takase, “Stress Concentration Factors for Round and Flat Test Specimens with Notches”, International Journal of Fatigue, Vol. 17, pp. 163~178, 1995.
[91] F. J. Gomez and M. Elices, “Fracture of Components with V-Shaped Notches”, Enginering Fracture Mechanics, Vol. 70, pp. 1913~1927, 2003.
[92] W. Xu, X. F. Yao, M. Q. Xu, G. C. Jin and Y. H. Yeh, “Fracture Characterizations of V-Notch Tip in PMMA Polymer Material”, Polymer Testing, Vol. 23, pp. 509~515, 2004.
[93] X. F. Yao, H. Y. Yeh and W. Xu, “Fracture Investigation at V-Notch Tip Using Cogerent Gradient Sensing”, International Journal of Solids and Structures, Vol. 43, pp. 1189~1200, 2006.
[94] D. H. Kim, J. H. Kim and S. Moon, “Evaluation of Intrinsic Fracture Toughness from the Apparent Toughness of Notched Specimen”, Materials Science and Engineering, Vol. 387, pp. 381~384, 2004.
[95] M. Filippini, “Stress Gradient Calculations at Notches”, International Journal of Fatigue, Vol. 22, pp. 397~409, 2000.
[96] A. W. Leissa, O. G. McGee and C. S. Huang, “Vibrations of Circular Plates Having V-Notches or Sharp Radial Cracks”, Journal of Sound and Vibration, Vol. 162, pp. 227~239, 1993.
[97] O. G. McGee, A. W. Leissa, C. S. Huang and J. W. Kim, “Vibrations of Circular Plates with Clamped V-Notches or Rigidly Constrained Radial Cracks”, Journal of Sound and Vibration, Vol. 181, pp. 185~201, 1995.
[98] J. W. Dally and W. F. Riley, “Experimental Stress Analysis”, 3rd Edition, McGraw-Hill Book Inc., New York, U. S. A., 1991.
[99] C. R. Wylie and L. C. Barett, “Advanced Engineering Mathematics”, McGraw-Hill Book Inc., New York, U. S. A., 1982.
[100] R. N. Kar, “Stress Intensity Factors in Glass Plates with Edge Cracks by Half Fringe Photoelasticity”, M. S. Thesis, Iowa state University, Iowa, U. S. A., 1977.
[101] Gamma Correction, Optical Microscopy Primer: Digital Image Processing, National High Magnetic Field Laboratory, The Florida State University, Tallahassee, Florida, U. S. A., http://www.micro.magnet.fsu.edu/primer/java/ digitalimaging/processing/gamma/index.html, 2006.
[102] A. Voloshin and C. P. Burger, “Half-Fringe Photoelasticity: A New Approach to Whole-Field Stress Analysis”, Experimental Mechanics, Vol. 23, pp. 304~313, 1983.
[103] W. C. Wang, T. L. Chen and S. H. Lin, “Digital Photoelastic Investigation of Transient Thermal Stresses of Two Interacting Defects”, Journal of Strain Analysis for Engineering Design, Vol. 25, pp. 215~228, 1990.
[104] W. C. Wang and T. L. Chen, “Half-Fringe Photoelastic Determination of Opening Mode Stress Intensity Factor for Edge Cracked Strips”, Engineering Fracture Mechanics, Vol. 32, pp. 111~122, 1989.
[105] K. H. Huebner and E. A. Thornton., “The Finite Element Method for Engineers”, 2nd Edition, Wiley Inc., New York, U. S. A., 1982.
[106] Website of DALSA Semiconductor Co., Canada, http://www.dalsa.com
[107] J. N. Walker, “Laboratory Applications of Time Delay and Integration (TDI) Image Acquisition”, Electrim Corporation, Princeton, New Jersey, U. S. A., 2001.
[108] M. J. Madou, “Fundamentals of Microfabrication”, CRC Press, Florida, U. S. A., 1997.
[109] Measuerments Group, Inc., Raleigh, North Carolina, U. S. A., 1986.
[110] PhotoImpact 8, Ulead Systems, Inc., Taipei, Taiwan, R. O. C., 2003.
[111] ANSYS User’s Manual for Revision 5.1, Swanson Analysis System, Inc., Houston, Pennsylvania, U. S. A., 1993.
[112] PCB piezotronics Inc., New York, U. S. A., 2003.
[113] Matlab, Version 6.5, The MathWorks, Inc., Massachusetts, U. S. A., 2002.
[114] Surfer, Version 5.01, Surface Mapping System, Golden Software, Inc., Golden, Colorado, U. S. A., 1993.
[115] Visio 2003, Microsoft Corporation, Washington, U. S. A., 2003.
[116] Photoshop, Version 7.0, Adobe Systems Inc., San Jose, U. S. A., 2002.
[117] Origin, Version 7.0, Original Lab Co., Massachusetts, U. S. A., 2002.