本研究探討積層製造材料的異向性力學材料機械性質，使用熱融擠製成型的3D列印機分別列印出三種不同材料排向之試片，利用動態試驗的方法量測三個方向的材料常數，再將其材料常數帶回正交性材料常數裡，完成正交性材料力學模型，接著利用3D列印機列印出不同堆疊方向試片，欲驗證其模型的準確性，利用動態試驗得到樑結構的共振頻率實驗量測結果，同時以正交性材料力學模型輸入有限元素軟體裡，將計算結果與實驗量測值進行比較，得知3D列印材料確實具有材料正交性的特性；除此之外，也利用3D列印機製作功能性梯度材料，同樣將製作出來的試片進行動態試驗，並利用材料力學的振動模型對厚度變化的材料變化性質進行理論推導，經由白努利-尤拉樑模型反算共振頻率，最後比較功能性梯度材料理論模型與等向性模型試片於動態測試結果的差異。

This study is to analyze anisotropic material properties of additive manufacture, which used on the fused deposition modeling of 3D printer to measure the vibration characteristics of Bernoulli-Euler beam. In order to evaluate the property of the additive manufacturing specimen modeled as cross-ply fiber reinforced material, use 3D printer to process the specimens which mixed different tool-path directions. The beam’s specimens made of additive manufacture were determined on their mechanical properties, and the orthogonal material constants were obtained by dynamic tests. The orthogonal material constants measured by dynamic tests imported into the Finite element method (FEM) and the results of the resonant frequencies from experimental measurements were compared with FEM calculation. Therefore, the vibration characteristics of additive manufacturing with orthotropic material properties is perform in good agreements between experimental measurements and theoretical analysis.
The functional gradient structure was made of additive manufacturing material and its resonant frequencies were determined on dynamic tests. The isotropic mechanical properties of the layered specimens were measured by inverse calculation from impact loading. Quadratic and linear theoretical models of functional graded material were established by varying stiffness along the thickness direction. The resonant frequencies can be calculated being according to Bernoulli-Euler beam theory and good consistence was shown in comparison with the results of experiment measurements.

[1] Li, L., Sun, Q., Bellehumeur, C., and Gu, P., Composite Modeling and Analysis for Fabrication of FDM Prototypes with Locally Controlled Properties. Journal of Manufacturing Processes, 2002. 4(2): p. 129-141.
[2] Sung-Hoon Ahn, M.M., Dan Odell, Shad Roundy and Paul K. Wright, Anisotropic material properties of fused deposition modeling ABS. Rapid Prototyping Journal, 2002. 8(4): p. 248-257.
[3] Lee, C.S., Kim, S. G., Kim, H. J., and Ahn, S. H., Measurement of anisotropic compressive strength of rapid prototyping parts. Journal of Materials Processing Technology, 2007. 187–188(0): p. 627-630.
[4] Scholz, M.S., B.W. Drinkwater, and R.S. Trask, Ultrasonic assembly of anisotropic short fibre reinforced composites. Ultrasonics, 2014. 54(4): p. 1015-1019.
[5] Vallittu, P.K., High-aspect ratio fillers: Fiber-reinforced composites and their anisotropic properties. Dental Materials, 2015. 31(1): p. 1-7.
[6] Tymrak, B.M., M. Kreiger, and J.M. Pearce, Mechanical properties of components fabricated with open-source 3-D printers under realistic environmental conditions. Materials & Design, 2014. 58(0): p. 242-246.
[7] Yamanouchi M., Hirai T., Shiota I., “Proceedings of First International Symposium on Functionally Gradient Materials”, FGM Forum, Tokyo, 1990,Japan.
[8] T.R. Jackson, H. Liu, N.M. Patrikalakis, E.M. Sachs, and M.J. Cima, Modeling and designing functionally graded material components for fabrication with local composition control. Materials and Design 20, 1999, p.63-75.
[9] Zheng Zhong, and Tao Yu, Analytical solution of a cantilever functionally graded beam, Composites Science and Technology 67,2007, p.481-488.
[10] Metin Aydogdu, and Vedat Taskin, Free vibration analysis of functional graded beams with simple supported edges, Materials & Design, Materials and Design 28, 2007, p.1651-1656.
[11] X.-F.Li, A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler–Bernoulli beams, JOURNAL OF SOUND AND VIBRATION, Journal of Sound and Vibration 318 (2008), p.1210–1229.
[12] S.A Sina, H.M. Navazi, and H. Haddadpour, An analytical method for free vibration analysis of functionally graded beams, Materials & Design,Materials and Design 30, 2009, p.741-747.
[13] Pierre Muller, Fean-Yues Hascoet, and Pascal Mognol, Toolpaths for additive manufacturing of functionally graded material(FGM) part, Rapid Prototyping Journal(2014), p.511-522.
[14] Sugavaneswaran, M., Arumaikkannu, G., Analytical and experimental investigation on elastic modulus of reinforced additive manufactured structure, Materials & Design, Materials and Design 66, 2015, p.29-36.
[15] 鄭明昌, 碳纖複合材料吸水性質及應變量測方法研究. 國立雲林科技大學工程科技研究所博士論文, 2005年12月.
[16] Ronald F.Gibson, PRINCIPLE OF COMPOSITE MATERIAL MECHANICS, CRC Press.
[17] Signal conditioner model 2775AM4. ENDEVCO Corporation, 2008.
[18] Polytec, PDV-100 Vibrometer Education Kit.
[19] Ma, C.C., Y.H. Huang, and S.Y. Pan, Investigation of the transient behavior of a cantilever beam using PVDF sensors. Sensors, 2012. 12(2): p. 2088-2117.
[20] 劉泓嶔, PVDF感測器應用於結構系統之動態量測能力探討. 國立臺灣大學機械工程研究所碩士論文, 100年7月.
[21] 潘善盈, 應用PVDF感測器於懸臂梁之主動抑振與揚聲器音壓之控制. 國立臺灣大學機械工程研究所碩士論文, 98年7月.
[22] Andrew Pytel, J.K.著. and 余念一譯,材料力學.高立圖書有限公司, 2013年.
[23] Bent, A.A. and N.W. Hagood, Piezoelectric fiber composites with interdigitated electrodes. Journal of Intelligent Material Systems and Structures, 1997. 8(11): p. 903-919.
[24] McMahon, G.W., Measurement of Poisson's Ratio in Poled Ferroelectric Ceramics. Ultrasonics Engineering, IEEE Transactions on, 1963. 10(2): p. 102-103.
[25] IEEE Standard Definitions and Methods of Measurement for Piezoelectric Vibrators. IEEE Std No.177, 1966: p. 1.
[26] Maeda, R., Tsaur, J. J., Lee, S. H., and Ichiki, M., Piezoelectric Microactuator Devices. Journal of Electroceramics, 2004. 12(1-2): p. 89-100.
[27] Park, J.-M., Joung-Man, Kong, Jin-Woo, Kim, Dae-Sik, and Yoon, Dong-Jin, Nondestructive damage detection and interfacial evaluation of single-fibers/epoxy composites using PZT, PVDF and P(VDF-TrFE) copolymer sensors. Composites Science and Technology, 2005. 65(2): p. 241-256.
[28] Campoli, G., et al., Mechanical properties of open-cell metallic biomaterials manufactured using additive manufacturing. Materials & Design, 2013. 49(0): p. 957-965.
[29] Chuang, K.C., Lin, S. H., Ma, C. C., and Wu, R. H., Application of a fiber bragg grating-based sensing system on investigating dynamic behaviors of a cantilever beam under impact or moving mass loadings. IEEE Sensors Journal, 2013. 13(1): p. 389-399.
[30] Amin Yavari, S., Ahmadi, S. M., van der Stok, J., Wauthle, R., Riemslag, A. C., Janssen, M., Schrooten, J., Weinans, H., and Zadpoor, A. A., Effects of bio-functionalizing surface treatments on the mechanical behavior of open porous titanium biomaterials. Journal of the Mechanical Behavior of Biomedical Materials, 2014. 36(0): p. 109-119.
[31] 蔡富吉 and 蔡坤哲, 3D印表機自造全書. 碁峰出版社, 2014年4月.
[32] Saada, A.S., Elasticity: Theory and Applications. J. ROSS PUBLISHING, Second Edition, Revised & Updated.
[33] 許明發, 柯哲豪, 劉顯光, and 郭文雄, 複合材料入門. 中華民國尖端材料科技協會, 94年8月.
[34] Rao, S.S., Vibration of Continuous Systems. JOHN WILEY & SONS, INC.
[35] 黃泰榮, 積層製造材料與噴頭壓電陶瓷之異向性力學材料常數量測,國立臺灣科技大學機械工程系碩士論文, 104年6月.