臺灣博碩士論文加值系統

本文延伸具內質量共振結構球之理論研究，以兩種實驗探討具內質量共振結構球於低速衝擊下之反應。實驗試體是以三維成型機製作而成，並改良模型的外球殼構造，於外球殼上挖鑿數個孔洞，除了可降低外球殼的重量外，也易於觀察試體內部的現象。實驗先藉由高速攝影機比較均質球與具內質量共振結構球反彈高度的差異，結果顯示具內質量共振結構球的反彈高度明顯低於均質球，由此可知具內質量共振結構球能抑制衝擊外力。接著進一步探討具內質量共振結構球之自然頻率與反彈高度的關係，並根據實驗結果建立恢復係數相對自然頻率之趨勢線，藉由趨勢線預測具不同自然頻率之內質量共振結構球的恢復係數。除此之外，也根據牛頓擺之概念懸掛不同試體，觀察尺寸相近的不同試體相互撞擊之情形，可以發現撞擊後內質量共振器會產生振盪，由此可知撞擊後內質量共振器會吸收部分的衝擊能。
本文也參考多孔結構的相關研究，並以三維成型機製作具挫曲特性結構，再利用自行設計與製作的落摔衝擊試驗機進行實驗探討。最後，結合內質量共振特性與結構的挫曲特性，提出具內質量共振與挫曲特性結構，實驗結果顯示該結構具有較佳的抑制衝擊能力。

This thesis extends the theoretical study of the mass-in-mass structure. Low-velocity impact response of mass-in-mass unit cell is investigated by two experimental methods. The mass-in-mass unit cell is manufactured by 3D printing technology. Modification is made by drilling holes on the shell for easiness of observation of the internal motion, and for decreasing the mass of the shell. In the first step of experiment, the bounce height of mass-in-mass ball and equivalent ball is recorded by high-speed camera for comparison. The result shows that the bounce height of mass-in-mass ball is lower than equivalent ball which means the mass-in-mass ball has impact-mitigation capability. Second, the relation between resonance frequency of mass-in-mass ball and bounce height is investigated. To predict the COR (coefficient of restitution) of mass-in-mass ball with different resonance frequency, trend line is built according to the experimental results. In addition, the impact response of two different specimens are observed.
According to the research of cellular solids, structure with buckling property is fabricated by 3D printing technology. The self-designed drop impact tester is used to perform impact test, and the deformation of structure is recorded. Finally, a structure combining local resonance and buckling property is introduced. The experimental results show that the structure has a better impact-mitigation capacity.

口試委員會審定書 i
誌謝 ii
中文摘要 iii
ABSTRACT iv
目錄 v
圖目錄 viii
表目錄 xii
第1章 緒論 1
1.1 研究動機 1
1.2 文獻回顧 1
1.3 本文研究方法 10
1.4 論文架構 11
第2章 具內質量共振結構球受衝擊之反應 12
2.1 落摔反彈試驗實驗設置與試體製作 12
2.1.1 實驗設置與試體製作-初版 13
2.1.2 實驗設置與試體製作-改良版 16
2.2 均質球與具內質量共振結構球反彈高度比較 18
2.2.1 實驗試體 19
2.2.2 實驗結果與討論 20
2.3 具不同自然頻率之內質量共振結構球撞擊彈簧面 21
2.3.1 具不同自然頻率之內質量共振結構球試體 22
2.3.2 實驗結果與討論 24
2.3.3 恢復係數與趨勢線 26
2.3.4 以新試體驗證趨勢線方程式 28
2.4 具不同自然頻率之內質量共振結構球撞擊銅板面 30
2.4.1 實驗結果與討論 31
2.4.2 恢復係數與趨勢線 33
2.4.3 以新試體驗證趨勢線方程式 34
2.5 以矽利康取代圓錐形塔簧 36
2.5.1 均勻塗佈矽利康球 36
2.5.2 線狀塗佈矽利康球 38
2.6 牛頓擺試驗 40
2.6.1 實驗設置與試體製作 41
2.6.2 彈出角度與入射角度之關係 44
2.6.3 撞擊反應(30°) 47
2.6.4 撞擊反應(45°) 50
2.6.5 撞擊反應(60°) 53
2.7 小結與討論 56
第3章 具挫曲特性結構受衝擊之反應 58
3.1 實驗試體 58
3.1.1 試體幾何構造 58
3.1.2 試體尺寸 60
3.2 落摔衝擊試驗實驗設置 62
3.3 實驗結果與討論 64
3.3.1 衝擊速度0.99m/s 64
3.3.2 衝擊速度1.4m/s 66
3.3.3 衝擊速度1.715m/s 67
3.3.4 衝擊速度1.98m/s 69
3.4 小結與討論 70
第4章 具內質量共振與挫曲特性結構受衝擊之反應 71
4.1 實驗設置與試體製作 71
4.2 實驗結果與討論 73
4.2.1 衝擊速度0.99m/s 73
4.2.2 衝擊速度1.4m/s 74
4.2.3 衝擊速度1.715m/s 76
4.2.4 小結與討論 78
第5章 結論及未來展望 79
5.1 結論 79
5.1.1 落摔反彈試驗 79
5.1.2 牛頓擺試驗 80
5.1.3 落摔衝擊試驗 80
5.2 未來展望 82
參考文獻 83

[1]H. H. Huang, C. T. Sun, and G. L. Huang, "On the negative effective mass density in acoustic metamaterials," International Journal of Engineering Science, vol. 47, pp. 610-617, 2009.
[2]J. M. Manimala, H. H. Huang, C. T. Sun, R. Snyder, and S. Bland, "Dynamic load mitigation using negative effective mass structures," Engineering Structures, vol. 80, pp. 458-468, 2014.
[3]B. A. Gama, T. A. Bogetti, B. K. Fink, C. J. Yu, T. D. Claar, H. H. Eifert, et al., "Aluminum foam integral armor: a new dimension in armor design," Composite Structures, vol. 52, pp. 381-395, 2001.
[4]C. L. Ding, L. M. Hao, and X. P. Zhao, "Two-dimensional acoustic metamaterial with negative modulus," Journal of Applied Physics, vol. 108, p. 074911, 2010.
[5]H. J. Chen, H. C. Zeng, C. L. Ding, C. R. Luo, and X. P. Zhao, "Double-negative acoustic metamaterial based on hollow steel tube meta-atom," Journal of Applied Physics, vol. 113, p. 104902, 2013.
[6]H. C. Zeng, C. R. Luo, H. J. Chen, S. L. Zhai, C. L. Ding, and X. P. Zhao, "Flute-model acoustic metamaterials with simultaneously negative bulk modulus and mass density," Solid State Communications, vol. 173, pp. 14-18, 2013.
[7]Z. X. Liang and J. S. Li, "Extreme acoustic metamaterial by coiling up space," Physical review letters, vol. 108, p. 114301, 2012.
[8]V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ϵ and μ," Physics-Uspekhi, vol. 10, pp. 509-514, 1968.
[9]J. B. Pendry, "Negative refraction makes a perfect lens," Physical review letters, vol. 85, p. 3966, 2000.
[10]S. H. Lee, C. M. Park, Y. M. Seo, Z. G. Wang, and C. K. Kim, "Acoustic metamaterial with negative density," Physics Letters A, vol. 373, pp. 4464-4469, 2009.
[11]N. Fang, D. Xi, J. Xu, M. Ambati, W. Srituravanich, C. Sun, et al., "Ultrasonic metamaterials with negative modulus," Nature materials, vol. 5, pp. 452-456, 2006.
[12]S. H. Lee, C. M. Park, Y. M. Seo, Z. G. Wang, and C. K. Kim, "Acoustic metamaterial with negative modulus," Journal of Physics: Condensed Matter, vol. 21, p. 175504, 2009.
[13]G. W. Milton and J. R. Willis, "On modifications of Newton''s second law and linear continuum elastodynamics," Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, vol. 463, pp. 855-880, 2007.
[14]H. H. Huang and C. T. Sun, "Theoretical investigation of the behavior of an acoustic metamaterial with extreme Young''s modulus," Journal of the Mechanics and Physics of Solids, vol. 59, pp. 2070-2081, 2011.
[15]尤建勳, "彈性超穎材料 (負楊氏模數模型) 波傳行為探討與實驗分析," 臺灣大學工程科學及海洋工程學研究所學位論文, pp. 1-72, 2014.
[16]Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, et al., "Locally resonant sonic materials," Science, vol. 289, pp. 1734-6, 2000.
[17]Z. Liu, C. T. Chan, and P. Sheng, "Analytic model of phononic crystals with local resonances," Physical Review B, vol. 71, p. 014103, 2005.
[18]S. S. Yao, X. M. Zhou, and G. K. Hu, "Experimental study on negative effective mass in a 1D mass–spring system," New Journal of Physics, vol. 10, p. 043020, 2008.
[19]Z. Yang, H. M. Dai, N. H. Chan, G. C. Ma, and P. Sheng, "Acoustic metamaterial panels for sound attenuation in the 50–1000 Hz regime," Applied Physics Letters, vol. 96, p. 041906, 2010.
[20]H. H. Huang and C. T. Sun, "Wave attenuation mechanism in an acoustic metamaterial with negative effective mass density," New Journal of Physics, vol. 11, p. 013003, 2009.
[21]R. Zhu, G. L. Huang, H. H. Huang, and C. T. Sun, "Experimental and numerical study of guided wave propagation in a thin metamaterial plate," Physics Letters A, vol. 375, pp. 2863-2867, 2011.
[22]J. S. Chen and C. T. Sun, "Dynamic behavior of a sandwich beam with internal resonators," Journal of Sandwich Structures and Materials, vol. 13, pp. 391-408, 2011.
[23]R. Zhu, G. K. Hu, M. Reynolds, and G. L. Huang, "An elastic metamaterial beam for broadband vibration suppression," SPIE Smart Structures and Materials+ Nondestructive Evaluation and Health Monitoring, vol. 8695, p. 86952J, 2013.
[24]G. Gantzounis, M. Serra-Garcia, K. Homma, J. M. Mendoza, and C. Daraio, "Granular metamaterials for vibration mitigation," Journal of Applied Physics, vol. 114, p. 093514, 2013.
[25]G. L. Huang and C. T. Sun, "Band gaps in a multiresonator acoustic metamaterial," Journal of Vibration and Acoustics, vol. 132, p. 031003, 2010.
[26]K. T. Tan, H. H. Huang, and C. T. Sun, "Negative Effective Mass Density of Acoustic Metamaterial using Dual-Resonator Spring-Mass Model," Conference Proceeding for Metamaterials, pp. 17-20, 2012.
[27]K. T. Tan, H. H. Huang, and C. T. Sun, "Blast-wave impact mitigation using negative effective mass density concept of elastic metamaterials," International Journal of Impact Engineering, vol. 64, pp. 20-29, 2014.
[28]劉建均, "多振態聲學超材料之計算與模擬," 成功大學土木工程學系學位論文, pp. 1-73, 2012.
[29]X. N. Liu, G. K. Hu, C. T. Sun, and G. L. Huang, "Wave propagation characterization and design of two-dimensional elastic chiral metacomposite," Journal of Sound and Vibration, vol. 330, pp. 2536-2553, 2011.
[30]E. Baravelli, M. Carrara, and M. Ruzzene, "High stiffness, high damping chiral metamaterial assemblies for low-frequency applications," SPIE Smart Structures and Materials+ Nondestructive Evaluation and Health Monitoring, vol. 8695, p. 86952K, 2013.
[31]P. Wang, F. Casadei, S. Shan, J. C. Weaver, and K. Bertoldi, "Harnessing buckling to design tunable locally resonant acoustic metamaterials," Physical review letters, vol. 113, p. 014301, 2014.
[32]J. T. B. Overvelde, S. Shan, and K. Bertoldi, "Compaction through buckling in 2D periodic, soft and porous structures: effect of pore shape," Advanced Materials, vol. 24, pp. 2337-2342, 2012.
[33]J. T. B. Overvelde and K. Bertoldi, "Relating pore shape to the non-linear response of periodic elastomeric structures," Journal of the Mechanics and Physics of Solids, vol. 64, pp. 351-366, 2014.
[34]K. Bertoldi, P. M. Reis, S. Willshaw, and T. Mullin, "Negative Poisson''s ratio behavior induced by an elastic instability," Advanced Materials, vol. 22, pp. 361-366, 2010.
[35]J. Shen, S. Zhou, X. Huang, and Y. M. Xie, "Simple cubic three‐dimensional auxetic metamaterials," physica status solidi (b), vol. 251, pp. 1515-1522, 2014.
[36]S. Babaee, J. Shim, J. C. Weaver, E. R. Chen, N. Patel, and K. Bertoldi, "3D soft metamaterials with negative Poisson''s ratio," Advanced Materials, vol. 25, pp. 5044-5049, 2013.
[37]D. T. Queheillalt and H. N. G. Wadley, "Cellular metal lattices with hollow trusses," Acta Materialia, vol. 53, pp. 303-313, 2005.
[38]H. F. Cheng and F. S. Han, "Compressive behavior and energy absorbing characteristic of open cell aluminum foam filled with silicate rubber," Scripta materialia, vol. 49, pp. 583-586, 2003.
[39]H. Zhao and G. Gary, "Crushing behaviour of aluminium honeycombs under impact loading," International Journal of Impact Engineering, vol. 21, pp. 827-836, 1998.
[40]R. Cross, "Grip-slip behavior of a bouncing ball," American Journal of Physics, vol. 70, pp. 1093-1102, 2002.
[41]R. Cross, "Dynamic properties of tennis balls," Sports Engineering, vol. 2, pp. 23-34, 1999.
[42]R. Cross, "Measurements of the horizontal coefficient of restitution for a superball and a tennis ball," American Journal of Physics, vol. 70, pp. 482-489, 2002.
[43]K. Arakawa, T. Mada, H. Komatsu, T. Shimizu, M. Satou, K. Takehara, et al., "Dynamic contact behavior of a golf ball during an oblique impact," Experimental mechanics, vol. 46, pp. 691-697, 2006.
[44]K. Arakawa, T. Mada, H. Komatsu, T. Shimizu, M. Satou, K. Takehara, et al., "Dynamic deformation behavior of a golf ball during normal impact," Experimental mechanics, vol. 49, pp. 471-477, 2009.
[45]M. J. Carre, D. M. James, and S. J. Haake, "Impact of a non-homogeneous sphere on a rigid surface," Proceedings of the Institution of Mechanical Engineers, part C: Journal of mechanical engineering science, vol. 218, pp. 273-281, 2004.
[46]R. Cross, "The bounce of a ball," American Journal of Physics, vol. 67, pp. 222-227, 1999.
[47]P. A. Maurone and F. J. Wunderlich, "Bouncing ball experiment," American Journal of Physics, vol. 46, pp. 413-415, 1978.
[48]E. Falcon, C. Laroche, S. Fauve, and C. Coste, "Behavior of one inelastic ball bouncing repeatedly off the ground," The European Physical Journal B-Condensed Matter and Complex Systems, vol. 3, pp. 45-57, 1998.
[49]Q. He, "Stiffness and static elongation of a cone-shaped spring " Physics Experimentation, vol. 4, p. 011, 2004.
[50]F. Herrmann and P. Schmälzle, "Simple explanation of a well-known collision experiment," Am. J. Phys, vol. 49, pp. 761-764, 1981.
[51]D. Simanek, "Newton''s Cradle," 2012.