本論文以自製之高頻、寬頻聚焦式超音波換能器，搭配改良式藍姆波分析法，以測量薄板及鍍層材料之機械性質為目標，其中薄板厚度為100~500μm；鍍層材料厚度則為20~40μm。本論文目的在於建立一套快速且簡單的系統，精準地量測等項性薄板及鍍層材料之彈性係數。由於材料機械性質與藍姆波的波傳特性有直接的關係，因此本論文利用聚焦式超音波換能器及V(f,z)散焦量測法量測材料的藍姆波頻散曲線，用於材料機械性質的反算；除了以散焦量測的方式測量材料之表面波波速，另一方面，亦以自製小張角之高頻超音波換能器直接量測薄板之縱波波速，也因此可得到更快速、準確量測薄板機械性質的驗證方法。
本論文製作P(VDF-TrFE)無鏡頭聚焦式換能器，可精準量測寬頻之藍姆波頻散曲線，於加工成曲面之鋁金屬背層材料上，直接旋鍍一層高分子P(VDF-TrFE)膜，並利用負載電壓的方式極化此高分子薄膜，使之具有壓電性質。換能器的操作頻率為5～110MHz之間、中心頻率為20～50MHz不等，搭配V(f,z)量測法建構出快速且完整的藍姆波頻散曲線量測系統。
此外，為了有效地計算材料的機械性質，本論文以數位影像處理及最佳化分析為基礎，開發一套改良式V(f,z)分析法，藉由藍姆波理論及實驗量測的方式，得到玻璃、不鏽鋼薄板與鎳鍍層材料之彈性係數，也因此提供了一個以非破壞性的方式，快速、準確地得到薄板及鍍層之機械性質的方法。

This thesis investigates a nondestructive method for determining elastic constants of a thin plate using ultrasound transducers and Lamb wave measurements. The samples under consideration are thin plates of thickness from 100 to 500 micrometers and coating layer of thickness 20 ~ 40 micrometers. The goal is to develop a fast and easily implemented method for accurate measurements of all elastic constants of the plates and the coatings. Due to the nature of thin plates, Lamb waves are chosen and the dispersion curves of Lamb waves are used for the purpose of inversely determination of elastic constants. Focusing ultrasound transducers and V(f,z) defocusing measurement methods are applied for measuring the dispersion curves of thin plates and coatings over a wide range of frequency spectrum.
To achieve high accuracy and wideband measurements of Lamb waves, several lensless PVDF focusing transducers are fabricated. The transducers are prepared using spin-coated copolymer P(VDF-TrFE) on aluminum backing and following by electrical poling processes. With a wide range of operating frequency from 5 MHz up to 110 MHz, a defocusing and V(f,z) measurement system is constructed which allows quick and complete measurements of Lamb wave dispersion curves.
For the determination of elastic constants from measured Lamb wave dispersion curves, numerical calculation and digital image process are performed. Thin glass and stainless steel plates and coatings are measured and both Young’s modulus and Poisson’s ratio are successfully determined from few low order fundamental modes of Lamb waves. Discussions on the measurement accuracy as well as potential applications for other types of nondestructive evaluation using the proposed PVDF transducers and measurement system will be addressed.

[1] D. Xiang, N. N. Hsu, and G. V. Blessing, “The Design, Construction and Application of a Large Aperture Lens-Less Line-Focus PVDF Transducer,” Ultransonics 34, pp.641-647 (1996)
[2] D. Xiang, N. N. Hsu, and G. V. Blessing, “Material Characterization by a Time-Resolved and Polarization-Sensitive Ultrasonic Technique,” QNDE 15, pp.1431-1438 (1996)
[3] N. N. Hsu, D. Xiang, S. E. Fick and G. V. Blessing, “Time and Polarization Resolved Ultrasonic Measurements Using A Lensless Line-Focus Transducer,” Proceeding IEEE Ultrasonics Symposium, pp.867-871 (1995).
[4] D. Xiang, N. N. Hsu, and G. V. Blessing, “Ultrasonic Leaky Wave Measurements for Materials Evaluation,” in Nondestructive Characterization of Materials, C.O. Rund and R.E. Green, eds., Plenum Press, New York (1997).
[5] D. Xiang, N. N. Hsu, and G. V. Blessing, “Time Domain Waveforms of a Line-Focus Transducer Probing Anisotropic Solids,” in Nondestructive Characterization of Materials, C.O. Rund and R.E. Green, eds., Plenum Press, New York (1997).
[6] C. H. Yang, “Characterization of Piezoelectrics Using Line-Focus Transducer,” in Proceedings of 15th Conference of Chinese Society of Mechanical Engineering, pp.785-790 (1998).
[7] J. Kushibiki and N. Chubachi, “Material Characterization by Line-Focus Beam Acoustic Microscopy,” IEEE Trans. Sonics Ultrason. 32, pp.189-22 (1985)
[8] Y. C. Lee, “Measuements of Multimode Leaky Lamb Waves Propagation in Metal Sheets,“ Japanese Journal of Applied Physics 40, pp.359-363 (2001).
[9] Y. C. Lee, “Measurements of Dispersion Curves of Leaky Lamb Waves Using a Lensless Line-Focus Transducer,” Ultrasonics 39, pp.297-396 (2001).
[10] Y. C. Lee, and S. P. Ko, ”Measuring Dispersion Curves of Acoustic Waves Using PVDF Line-Focus Transducer,” NDT&E Int. 34, pp.191-197 (2001).
[11] Y. C. Lee, and S. W. Cheng, ”Measuring Lamb Wave Dispersion Curves of Bi-Layered Plate and Its Application on Material Characterization of Coating,” IEEE Tran. Ultrason. Ferroelect. Freq. Control 48(3), pp.830-836 (2001).
[12] H. R. Gallantree, “Review of Transducer Applications of Polyvinylidene,” IEE Procssdings 190, Pt. I, No.5, pp.219-224 (1983).
[13] A. Ambrosy and K. Holdik, “Piezoelectric PVDF Films as Ultrasonic Transducers,” J. Phys. E : Sci. Instrum. 17, pp856-859 (1984).
[14] M. Platte, ”PVDF Ultrasonic Transducers,” Ferroelectrics 75, pp.327-373 (1987).
[15] M. D. Sherar and F. S. Foster, “The Design and fabrication of high frequency PVDF transducers,” Ultrasonic Imaging 11, p.75-94 (1989).
[16] G. R. Lockwood, D. H. Turnbull, D. A. Christopher, and F. S. Foster, “Beyonf 30 MHz,” IEEE Engineering in Medicine and Biology, Nov./Dec., p.60-71 (1996).
[17] S. Smolorz and W. Grill. “Focusing PVDF Transducers for Acoustic Microscopy,“In Res. Nondestr. Eval. 7, pp.195-201 (1996).
[18] L. F. Brown, R. L. Carlson and J. M. Sempsrott, "Spin-cast(VDF-TrFE) films for high performance medical ultrasound transducers," Proc. 1997 IEEE Ultrasonics Symposium, pp.1725-1727.
[19] M. Z. Sleva, R.D. Briggs and W. D. Hunt, ”A Micromachined Poly(vinylidene fluoride-trifluoroethylene) Transducer for Pulse-Echo Ultrasound Applications,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 43, no. 2,Mar., 1996, pp.257-262
[20] M. F. Robert, G. Molingou, K. Snook, J. Cannata, K. K. Shung. “Fabrication of focused poly(vinylidene fluoride-trifluoroethylene) P(VDF-TrFE) copolymer 40-50 MHz ultrasound transducers on curved surfaces,” J App Physics 2003; 96(1):252–256.
[21] 鄭勝文, 聚焦式超聲波換能器之藍姆波量測分析與應用, 國立成功大學機械工程學系碩士論文 (2000).
[22] 柯馨蘋，”線聚焦式超聲波換能器之表面波量測與分析 ”，國立成功大學機械工程學系碩士論文，pp. 21~27(1999)。
[23] I. A. Viktorov, Rayleigh and Lamb Waves: Physical Theory and Application, Plenum Press, New York (1967).
[24] H. P. William, P. F. Brian, T. A. Saul and V. T. William,”Numerical Recipes: The Art of Scientific Computing,” Cambridge University Press, New York.