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  1. NTU Theses and Dissertations Repository
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請用此 Handle URI 來引用此文件: http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/98921
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dc.contributor.advisor劉立偉zh_TW
dc.contributor.advisorLi-Wei Liuen
dc.contributor.author洪鈺豪zh_TW
dc.contributor.authorYuh-Hao Hungen
dc.date.accessioned2025-08-20T16:17:35Z-
dc.date.available2025-08-21-
dc.date.copyright2025-08-20-
dc.date.issued2025-
dc.date.submitted2025-08-14-
dc.identifier.citation[1] S. Alavi, J. Ganghoffer, M. Sadighi, M. Nasimsobhan, and A. Akbarzadeh. Continualization method of lattice materials and analysis of size effects revisited based on cosserat models. International Journal of Solids and Structures, 254-255:111894, 2022.
[2] S. E. Alavi, M. Sadighi, M. D. Pazhooh, and J.-F. Ganghoffer. Development of size-dependent consistent couple stress theory of timoshenko beams. Applied Mathematical Modelling, 79:685–712, 2020.
[3] R. Bengtsson, M. Mousavi, R. Afshar, and E. K. Gamstedt. Viscoelastic behavior of softwood based on a multiscale computational homogenization. Mechanics of Materials, 179:104586, 2023.
[4] M. A. Boucher, C. W. Smith, F. Scarpa, R. Rajasekaran, and K. Evans. Effective topologies for vibration damping inserts in honeycomb structures. Composite Structures, 2013.
[5] M. Chen, N. Hu, C. Zhou, X. Lin, H. Xie, and Q. He. The hierarchical structure and mechanical performance of a natural nanocomposite material: The turtle shell. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 520:97–104, 2017.
[6] Q. Cheng, L. Jiang, and Z. Tang. Bioinspired layered materials with superior mechanical performance. Accounts of chemical research, 47(4):1256–1266, 2014.
[7] L. J. Gibson, M. F. Ashby, G. S. Schajer, and C. I. Robertson. The mechanics of two-dimensional cellular materials. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 382(1782):25–42, 1982.
[8] A. R. Hadjesfandiari and G. F. Dargush. Couple stress theory for solids. International Journal of Solids and Structures, 48(18):2496–2510, 2011.
[9] L. Iorio, J. De Ponti, A. Corigliano, and R. Ardito. Bandgap widening and resonator mass reduction through wave locking. Mechanics Research Communications, 134:104200, 2023.
[10] Z. E. Jian. Micromechanical modeling and collapse surface of cellular materials. Master’s thesis, National Taiwan University, Taipei, Taiwan, 2024. Advisor: Li-Wei Liu.
[11] W. Koiter. Couple-stress in the theory of elasticity. In Proc. K. Ned. Akad. Wet, volume 67, pages 17–44. North Holland Pub, 1964.
[12] S. Kong, S. Zhou, Z. Nie, and K. Wang. The size-dependent natural frequency of bernoulli-euler micro-beams. International Journal of Engineering Science, 46(5):427–437, 2008.
[13] D. Lam, F. Yang, A. Chong, J. Wang, and P. Tong. Experiments and theory in strain gradient elasticity. Journal of the Mechanics and Physics of Solids, 51(8):1477–1508, 2003.
[14] E. H. Lee and I. Kanter. Wave Propagation in Finite Rods of Viscoelastic Material. Journal of Applied Physics, 24(9):1115–1122, 06 2004.
[15] C. Lim, G. Zhang, and J. Reddy. A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation. Journal of the Mechanics and Physics of Solids, 78:298–313, 2015.
[16] S. Malek and L. Gibson. Effective elastic properties of periodic hexagonal honeycombs. Mechanics of Materials, 91:226–240, 2015.
[17] R. Mindlin and N. Eshel. On first strain-gradient theories in linear elasticity. International Journal of Solids and Structures, 4(1):109–124, 1968.
[18] R. Mindlin, H. Tiersten, et al. Effects of couple-stresses in linear elasticity. Archive for Rational Mechanics and analysis, 11(1):415–448, 1962.
[19] R. D. Mindlin et al. Microstructure in linear elasticity. Columbia University New York, 1963.
[20] B. Niu and B. Wang. Directional mechanical properties and wave propagation directionality of kagome honeycomb structures. European Journal of Mechanics A/Solids, 2016.
[21] P. Onck, E. Andrews, and L. Gibson. Size effects in ductile cellular solids. part i: modeling. International Journal of Mechanical Sciences, 43(3):681–699, 2001.
[22] S. Park and X. Gao. Bernoulli–euler beam model based on a modified couple stress theory. Journal of Micromechanics and Microengineering, 16(11):2355, 2006.
[23] F. Rahimidehgolan, J. Magliaro, and W. Altenhof. Influence of specimen profile size and thickness on the dynamic compressive behavior of rigid pvc foams. International Journal of Impact Engineering, 179:104676, 2023.
[24] D. T. Reilly and A. H. Burstein. The mechanical properties of cortical bone. JBJS, 56(5):1001–1022, 1974.
[25] R. Toupin. Elastic materials with couple-stresses. Archive for rational mechanics and analysis, 11(1):385–414, 1962.
[26] A. J. Wang and D. L. McDowell. In-Plane Stiffness and Yield Strength of Periodic Metal Honeycombs . Journal of Engineering Materials and Technology, 126(2):137–156, 03 2004.
[27] A. J. Wang and D. L. McDowell. Yield surfaces of various periodic metal honeycombs at intermediate relative density. International Journal of Plasticity, 21(2):285–320, 2005.
[28] S. Wang, M. Wang, and Z. Guo. Adjustable low-frequency bandgap of flexural wave in an euler-bernoulli meta-beam with inertial amplified resonators. Physics Letters A, 417:127671, 2021.
[29] F. Yang, A. Chong, D. Lam, and P. Tong. Couple stress based strain gradient theory for elasticity. International Journal of Solids and Structures, 39(10):2731–2743, 2002.
[30] G. Zhang and X. L. Gao. Band gaps for wave propagation in 2-d periodic three-phase composites with coated star-shaped inclusions and an orthotropic matrix. Composites Part B: Engineering, 182:107319, 2020.
[31] Z. Zhu, Z. Deng, and J. Du. Elastic Wave Propagation in Hierarchical Honeycombs With Woodpile-Like Vertexes. Journal of Vibration and Acoustics, 2019.
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dc.identifier.urihttp://tdr.lib.ntu.edu.tw/jspui/handle/123456789/98921-
dc.description.abstract本研究針對六角與三角蜂巢結構,建立彈性動態模型與頻率帶隙模型。彈性動態模型基於固體力學的四級理論架構,納入材料組成律、變形機制與幾何特性,並考慮尺寸效應;頻率帶隙模型則透過傳遞矩陣法與Bloch理論建構,用以識別特定頻率範圍內的帶隙區域。此外,亦進行參數化分析,探討相對密度、傾角與牆厚等幾何參數對動態響應與帶隙行為的影響。為佐證理論模型,本研究亦自製哈金森衝擊桿測試儀,並以3D列印製作試體,實際觀察不同微結構配置下之波傳行為。透過理論與實驗結合之方式,建立了一套分析蜂巢材料動態行為的完整架構,可作為未來設計高強度、高韌性與具消能潛力之蜂巢結構材料的基礎。zh_TW
dc.description.abstractThis study develops elastodynamic models and frequency bandgap models for hexagonal and triangular honeycomb structures. The elastodynamic model is constructed based on a four-level solid mechanics framework, incorporating constitutive behavior, deformation mechanisms, and geometric features, while accounting for size effects. The frequency bandgap model is formulated using the transfer matrix method and Bloch's theorem to identify the bandgap regions across a specified frequency range. Parametric studies are conducted to evaluate the effects of microstructural parameters, such as relative density, inclined angle, and wall thickness, on the dynamic response and bandgap characteristics. To support the theoretical analysis, a Hopkinson bar apparatus is constructed, and 3D-printed specimens are prepared to experimentally investigate wave propagation in cellular structures with various geometries. This integrated modeling and testing framework provides a foundation for designing lightweight, high-strength, and energy-dissipative cellular materials.en
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dc.description.tableofcontentsAcknowledgements i
摘要iii
Abstract v
Contents vii
List of Figures xi
List of Tables xvii
Notations and Conventions xxi
Chapter 1 Literature review 1
1.1 Mechanics of cellular materials . . . . . . . . . . . . . . . . . . . . 1
1.2 Theoretical studies of strain gradient and couple stress . . . . . . . . 2
1.3 Experimental studies of size-dependent behavior in cellular materials 4
1.4 Wave propagation and frequency bandgaps . . . . . . . . . . . . . . 5
Chapter 2 Elastodynamic Model of Hexagonal Honeycombs 7
2.1 Hexagonal Honeycombs . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Decoupling of biaxial stress inputs applied to hexagonal honeycombs 9
2.3 Hierarchical modeling of hexagonal honeycombs . . . . . . . . . . . 9
2.3.1 Material point level . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3.2 Cross section level . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.3 Cell wall level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.4 Cellular material level . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4 Influence factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.5 Dynamic responses under cyclic stress inputs . . . . . . . . . . . . . 26
2.5.1 Scenario I: influence of the relative density . . . . . . . . . . . . . 29
2.5.2 Scenario II: influence of the thickness . . . . . . . . . . . . . . . . 32
2.5.3 Scenario III: influence of the inclined angle . . . . . . . . . . . . . 35
Chapter 3 Elastodynamic model of triangular honeycombs 41
3.1 Triangular honeycombs . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2 Decoupled stress states of triangular honeycombs . . . . . . . . . . . 43
3.3 Hierarchical modeling of triangular honeycombs . . . . . . . . . . . 43
3.3.1 Material point level . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.3.2 Cross section level . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.3.3 Cell wall level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.3.4 Cellular material level . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.4 Responses under cyclic stress inputs . . . . . . . . . . . . . . . . . . 53
3.4.1 Scenario I: influence of the relative density . . . . . . . . . . . . . 56
3.4.2 Scenario II: influence of the inclined angle . . . . . . . . . . . . . . 57
Chapter 4 Dispersion analysis of cellular mateials 61
4.1 Frequency bandgap model of hexagonal honeycombs . . . . . . . . . 61
4.2 Investigation on the influence of microstructures of hexagonal honeycombs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.2.1 Scenario I: influence of the relative density . . . . . . . . . . . . . 67
4.2.2 Scenario II: influence of the thickness . . . . . . . . . . . . . . . . 69
4.2.3 Scenario III: influence of the inclined angle . . . . . . . . . . . . . 70
4.3 Frequency bandgap model of triangular honeycombs . . . . . . . . . 72
4.4 Investigation on the influence of microstructures of triangular honeycombs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.4.1 Scenario I: influence of the relative density . . . . . . . . . . . . . 77
4.4.2 Scenario II: influence of the inclined angle . . . . . . . . . . . . . . 79
Chapter 5 Experimental studies of cellular materials 81
5.1 Hopkinson bar testing machine . . . . . . . . . . . . . . . . . . . . . 81
5.2 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.3 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Chapter 6 Conclusions and future works 91
6.1 Comparative conclusions of microstructural influences on dynamic responses in hexagonal and triangular honeycombs . . . . . . . . . . 91
6.2 Comparative conclusions of microstructural influences on frequency bandgaps in hexagonal and triangular honeycombs . . . . . . . . . . 92
6.3 Future works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
References 95
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dc.language.isoen-
dc.subject頻率帶隙模型zh_TW
dc.subject彈性動態模型zh_TW
dc.subject自製哈金森衝擊桿測試儀zh_TW
dc.subject微結構zh_TW
dc.subjectElastodynamic modelen
dc.subjectMicrostructural architectureen
dc.subjectFrequency bandgap modelen
dc.subjectSelf-made Hopkinson bar testing machineen
dc.title孔隙材料頻散特性之探討zh_TW
dc.titleInvestigation on dispersion of cellular materialsen
dc.typeThesis-
dc.date.schoolyear113-2-
dc.description.degree碩士-
dc.contributor.oralexamcommittee陳正宗;郭茂坤;張為光zh_TW
dc.contributor.oralexamcommitteeJeng-Tzong Chen;Mao-Kuen Kuo;Wei-Kuang Changen
dc.subject.keyword彈性動態模型,頻率帶隙模型,微結構,自製哈金森衝擊桿測試儀,zh_TW
dc.subject.keywordElastodynamic model,Frequency bandgap model,Microstructural architecture,Self-made Hopkinson bar testing machine,en
dc.relation.page99-
dc.identifier.doi10.6342/NTU202504275-
dc.rights.note未授權-
dc.date.accepted2025-08-15-
dc.contributor.author-college工學院-
dc.contributor.author-dept土木工程學系-
dc.date.embargo-liftN/A-
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