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系統識別號 U0026-1406201423415500
論文名稱(中文) 奈米碳管加勁複合材料三明治壓電板承受雙軸向壓力作用下之挫屈與自然振動解析解
論文名稱(英文) Exact solutions for the stability and free vibration of sandwich piezoelectric plates with an embedded carbon nanotube-reinforced composite core and under bi-axial compressive loads
校院名稱 成功大學
系所名稱(中) 土木工程學系
系所名稱(英) Department of Civil Engineering
學年度 102
學期 2
出版年 103
研究生(中文) 李維宸
研究生(英文) Wei-Chen Li
學號 N66011142
學位類別 碩士
語文別 英文
論文頁數 94頁
口試委員 指導教授-吳致平
口試委員-黃炯憲
口試委員-廖為忠
口試委員-王永明
口試委員-方中
中文關鍵字 Reissner混合變分原理  振動  挫屈  奈米碳管加勁複合材料核心層  功能性梯度材料  壓電板 
英文關鍵字 Reissner’s mixed variational theorem  vibration  buckling  carbon nanotube-reinforced composite core  functionally graded materials  piezoelectric plates 
學科別分類
中文摘要 本文改良傳統文獻中之Pagano方法,應用於三明治混合奈米碳管加勁核心層與壓電材料面層板結構,探求具完全簡支承邊界及承受雙軸壓力作用下之相關三維挫屈與自然振動之解析解。文中考慮奈米碳管於核心加勁層中,沿厚度方向具不同的函數分佈,諸如:均勻函數分佈、功能性梯度菱型與X型函數分佈,其相關之有效材料係數則以二相混合法則評估之。文中亦引入Reissner混合變分原理、連續近似法、傳遞矩陣法與系統方程實數解之轉換,求解奈米碳管加勁複合材料三明治壓電板受雙軸壓力作用下之自然振動頻率與模態。結果顯示本文求得之解析解與文獻中多層疊合壓電板材料板之三維解析解一致,其奈米碳管加勁複合材料三明治壓電板之解析解則可作為評估各種二維理論與數值方法解之準則。
英文摘要 Exact three-dimensional (3D) stability and free vibration analyses of bi-axially loaded and simply-supported, sandwich piezoelectric plates with an embedded either functionally graded (FG) carbon nanotube-reinforced composite (CNTRC) core or multilayered fiber-reinforced composite (FRC) one are presented. Three different distributions of carbon nanotubes (CNTs) through the thickness of the CNTRC core, i.e., uniformly distributed and FG V-, rhombus- and X-type variations, are considered, and the effective material properties of the CNTRC core are estimated by the rule of mixtures. The Pagano method, which is conventionally used for the analysis of multilayered FRC plates, is modified to be feasible for the study of sandwich hybrid CNTRC and piezoelectric ones, in which Reissner’s mixed variational theorem, the successive approximation and transfer matrix methods, and the transformed real-valued solutions of the system equations are used. The modified Pagano solutions for the stability and free vibration of multilayered hybrid FRC and piezoelectric plates are in excellent agreement with the exact 3D ones available in the literature, and those for sandwich hybrid CNTRC and piezoelectric plates may be used as the benchmark solutions to assess the ones obtained using various two-dimensional theories and numerical models.
論文目次 Abstract I
摘要 II
誌謝 III
Contents (目錄) IV
List of tables (表目錄) VI
List of figures (圖目錄) IX
Chapter 1 Introduction 1
Chapter 2 Carbon nanotube-reinforced composite layer 6
Chapter 3 Pre-buckling state in the multilayered plate 9
Chapter 4 Hamilton’s principle 14
4.1. RMVT-based Lagrangian functional 14
4.2. Euler-Lagrange equations 17
Chapter 5 The modified Pagano method 20
5.1. Nondimensionalization 20
5.2. The double Fourier series expansion method 22
5.3. Theories of the homogeneous linear systems 24
5.4. The successive approximation method 25
Chapter 6 Illustrative examples 27
6.1. Stability of multilayered hybrid elastic and piezoelectric plates 27
6.2. Stability of sandwich piezoelectric plates with an FG CNTRC core 28
6.3. Free vibration of axially-loaded, multilayered hybrid elastic and piezoelectric plates 30
6.4. Free vibration of axially-loaded, sandwich hybrid CNTRC and piezoelectric plates 32
Chapter 7 Concluding remarks 34
第一章 緒論 36
第二章 奈米碳管加勁複合材料層 39
第三章 多層疊合壓電板挫屈前狀態 42
第四章 Hamilton定理 47
4.1基於RMVT的Lagrangian泛函 47
4.2 Euler-Lagrange方程 50
第五章 改良Pagano方法 52
5.1無因次化 52
5.2雙重傅立葉級數展開法 54
5.3齊性線性系統理論 56
5.4連續近似法 57
第六章 數值範例 58
6.1壓電材料疊層板之挫屈 58
6.2功能性奈米碳管核心層加勁三明治壓電材料板之挫曲 59
6.3壓電彈混合疊層板承受軸向壓力之自然振動 60
6.4功能性奈米碳管加勁三明治壓電材料板承受軸向壓力之自然振動 62
第七章 結語 64
References (參考文獻) 65
Appendix A 72
附錄 A 73
Appendix B 74
附錄 B 76
參考文獻 [1] Noor AK, Burton WS. Assessment of computational models for multilayered anisotropic plates. Compos Struct 1990;14:233-65.
[2] Noor AK, Burton WS. Assessment of computational models for multilayered anisotropic shells. Appl Mech Rev 1990;43: 67-97.
[3] Noor AK, Burton WS, Peters JM. Assessment of computational models for multilayered composite cylinders. Int J Solids Struct 1991;27:1269-86.
[4] Carrera E. An assessment of mixed and classical theories on global and local response of multilayered orthotropic plates. Compos Struct 2000;50:183-98.
[5] Carrera E. Historical review of zig-zag theories for multilayered plates and shells. Appl Mech Rev 2003;56:287-308.
[6] Carrera E. Assessment of theories for free vibration analysis of homogeneous and multilayered plates. Shock Vib 2004;11:261-70.
[7] Carrera E, Ciuffreda A. Bending of composites and sandwich plates subjected to localized lateral loading: A comparsion of various theories. Compos Struct 2005;68:185-202.
[8] Carrera E, Brischetto S. A survey with numerical assessment of classical and refined theories for the analysis of sandwich plates. Appl Mech Rev 2009;62:1-17.
[9] Saravanos DA, Heyliger PR. Mechanics and computational models for laminated piezoelectric beams, plates, and shells. Appl Mech Rev 1999;52:305-20.
[10] Tang YY, Noor AK, Xu K. Assessment of computational models for thermoelectroelastic multilayered plates. Comput Struct 1996;61:915-33.
[11] Soldatos KP. Review of three dimensional dynamic analyses of circular cylinders and cylindrical shells. Appl MechRev 1994;47:501-16.
[12] Liu S, Soldatos KP. Futher assessment of a generalized plate model: Stress analysis of angle-ply laminates. Int J Solids Struct 2003;40:4125-33.
[13] Kapania RK. A review on the analysis of laminated shells. J Press Vessel Tech 1989;111:88-96.
[14] Kapuria S, Sengupta S, Dumir PC. Assessment of shell theories for hybrid piezoelectric cylindrical shell under electromechanical load. Int J Mech Sci 1998;40:461-77.
[15] Nath JK, Kapuria S. Assessment of improved zigzag and smeared theories for smart cross-ply composite cylindrical shells including transverse normal extensibility under thermoelectric loading. Arch Appl Mech 2012;82:859-77.
[16] Wu CP, Chiu KH, Wang YM. A review on the three-dimensional analytical approaches of multilayered and functionally graded piezoelectric plates and shells. CMC: Comput Mater Continua 2008;8:93-132.
[17] Pagano NJ. Exact solutions for composite laminates in cylindrical bending. J Compos Mater 1969;3: 398-411.
[18] Pagano NJ. Exact solutions for rectangular bidirectional composites and sandwich plates. J Compos Mater 1970; 4:20-34.
[19] Heyliger P. Exact solutions for simply supported piezoelectric plates. J Appl Mech 1997;64:299-306.
[20] Heyliger P, Brooks S. Exact solutions for laminated piezoelectric plates in cylindrical bending. J Appl Mech 1996; 63:903-10.
[21] Heyliger P, Brooks S. Free vibration of piezoelectric laminates in cylindrical bending. Int. J Solids Struct 1995;32:2945-60.
[22] Heyliger P, Saravanos DA. Exact free-vibration analysis of laminated plates with embedded piezoelectric layers. J Acoust Soc Amer 1995;98:1547-57.
[23] Chen WQ, Ding HJ, Xu RQ. Three-dimensional static analysis of multilayered piezoelectric hollow spheres via the state space method. Int J Solids Struct 2001;38:4921-36.
[24] Chen WQ, Ding HJ. On free vibration of a functionally graded piezoelectric rectangular plate. Acta Mech 2002;153:207-16.
[25] Chen WQ, Ying J, Cai JB, Ye GR. Benchmark solution of imperfect angle-ply laminated rectangular plates in cylindrical bending with surface piezoelectric layers as actuator and sensor. Comput Struct 2004;82:1773-84.
[26] Kapuria S, Achary GGS. Exact 3D piezoelectricity solution for buckling of hybrid cross-ply plates using transfer matrices. Acta Mech 2004;170:25-45.
[27] Kapuria S, Achary GGS. Exact 3D piezoelectricity solution of hybrid cross-ply plates with damping under harmonic electromechanical loads. J Sound Vib 2005;282:617-34.
[28] Wu CP, Liu KY. A state space approaches for the analysis of doubly curved functionally graded elastic and piezoelectric shells. CMC: Comput Mater Continua 2007;6:177-99.
[29] Xu RQ. Three-dimensional exact solutions for the free vibration of laminated transversely isotropic circular, annular and sectorial plates with unusual boundary conditions. Arch Appl Mech 2008;78:543-58.
[30] Dube GP, kapuria S, Dumir PC. Exact piezothermoelastic solution of simply-supported orthotropic circular cylindrical panel in cylindrical bending. Arch Appl Mech 1996;66:537-54.
[31] Dumir PC, Dube GP, Kapuria S. Exact piezoelectric solution of simply-supported orthotropic circular cylindrical panel in cylindrical bending. Int J Solids Struct 1997;34:685-702.
[32] Kapuria S, Dumir PC, Sengupta S. Exact axisymmetric solution for a simply supported piezoelectric cylindrical shell. Arch Appl Mech 1997; 67:260-73.
[33] Kapuria S, Dumir PC, Sengupta S. Nonaxisymmetric exact piezothermoelastic solution for laminated cylindrical shell. AIAA J 1997;35:1792-5.
[34] Zenkour AM. Benchmark trigonometric and 3D elasticity solutions for an exponentially graded thick rectangular plate. Arch Appl Mech 2007;77:197-214.
[35] Wu CP, Lo JY. Anasymptotic theory for dynamic response of laminated piezoelectric shells. Acta Mech 2006;183:177-208.
[36] Wu CP, Lo JY, Chao JK. A three-dimensional asymptotic theory of laminated piezoelectric shells. CMC: Comput Mater Continua 2005;2:119-37.
[37] Wu CP, Syu YS. Asymptotic solutions for multilayered piezoelectric cylinders under electromechanical loads. CMC: Comput Mater Continua 2006;4:87-108.
[38] Wu CP, Syu YS. Exact solutions of functionally graded piezoelectric shells under cylindrical bending. Int J Solids Struct 2007;44:6450-72.
[39] Wu CP, Syu YS, Lo JY. Three-dimensional solutions for multilayered piezoelectric hollow cylinders by an asymptotic approach. Int J Mech Sci 2007;49:669-89.
[40] Wu CP, Tsai YH. Cylindrical bending vibration of functionally graded piezoelectric shells using the method of perturbation. J Eng Math 2009;63:95-119.
[41] Coleman JN, Khan U, Blau WJ, Gun’ko YK. Small but strong: A review of the mechanical properties of carbon nanotube-polymer composites. Carbon 2006;44:1624-52.
[42] Chou TW, Gao L, Thostenson ET, Zhang Z, Byun JH. An assessment of the science and technology of carbon nanotube-based fibers and composites. Compos Sci Technol 2010;70:1-19.
[43] Esawi AMK, Farag MM. Carbon nanotube reinforced composites: Potential and current challenges. Mater Des 2007;28:2394-401.
[44] Ramaratnam A, Jalili N. Reinforcement of piezoelectric polymers with carbon nanotubes: Pathway to next-generation sensors. J Intell Mater Sys Struct 2006;17:199-208.
[45] Thostenson ET, Ren Z, Chou TW. Advanced in the science and technology of carbons and their composites: A review. Compos Sci Technol 2001;61:1899-912.
[46] Shen HS. Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments. Compos Struct 2009;91:9-19.
[47] Shen HS, Xiang Y. Nonlinear vibration of nanotube-reinforced composite cylindrical shells in thermal environments. Comput Methods Appl Mech. Engrg 2012;213:196-205.
[48] Wang ZX, Shen HS. Nonlinear vibration and bending of sandwich plates with nanotube-reinforced composite face sheets. Compos Part B 2012;43:411-21.
[49] Hill R. A self-consistent mechanics of composite materials. J Mech Phys Solids 1965;13:213-22.
[50] Mori T, Tanaka K. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metallurgica 1973;21:571-4.
[51] Shen HS. Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments, Part I: Axially-loaded shells. Compos Struct 2011;93:2096-108.
[52] Shen HS. Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments, Part II: Pressure-loaded shells. Compos Struct 2011;93:2496-503.
[53] Shen HS, Xiang Y. Postbuckling of nanotube-reinforced composite cylindrical shells under combined axial and radial mechanical loads in thermal environment. Compos Part B 2013;52:311-22.
[54] Zhu P, Lei ZX, Liew KM. Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory. Compos Struct 2012;94:1450-60.
[55] Lei ZX, Liew KM, Yu JL. Buckling analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method. Compos Struct 2013;98:160-8.
[56] Rasool MD, Foroutan M, Pourasghar A. Dynamic analysis of functionally graded nanocomposite cylinders reinforced by carbon nanotube by a mesh-free method. Mater Des 2013;44:256-66.
[57] Heshmati M, Yas MH. Dynamic analysis of functionally graded multi-walled carbon nanotube-polystyrene nanocomposite beams subjected to multi-moving loads. Mater Des 2013;49:894-904.
[58] Yas MH, Pourasghar A, Kamarian S, Heshmati M. Three-dimensional free vibration analysis of functionally graded nanocomposite cylindrical panels reinforced by carbon nanotube. Mater Des 2013;49:583-90.
[59] Brischetto S, Carrera E. Analysis of nano-reinforced layered plates via classical and refined two-dimensional theories. Multid Model Mater Struct 2012;8:4-31.
[60] Brischetto S, Carrera E. Classical and refined shell models for the analysis of nano-reinforced structures. Int J Mech Sci 2012;55:104-17.
[61] Carrera E. Developments, ideas and evaluation based upon Reissner’s mixed variational theorem in the modelling of multilayered plates and shells. Appl Mech Rev 2001;54:301-29.
[62] Carrera E. Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking. Arch Comput Methods Eng 2003;10:215-96.
[63] Carrera E, Brischetto S. Analysis of thickness locking in classical, refined and mixed multilayered plate theories. Compos Struct 2008;82:549-62.
[64] Wu CP, Chen SJ, Chiu KH. Three-dimensional static behavior of functionally graded magneto-electro-elastic plates using the modified Pagano method. Mech Res Commun 2010;37:54-60.
[65] Wu CP, Lu YC. A modified Pagano method for the 3D dynamic responses of functionally graded magneto-electro-elastic plates. Compos Struct 2009; 90:363-72.
[66] Wu CP, Tsai TC. Exact solutions of functionally graded piezoelectric material sandwich cylinders by a modified Pagano method. Appl Math Model 2011;36:1910-30.
[67] Wu CP, Jiang RY. The 3D coupled analysis of FGPM circular hollow sandwich cylinders under thermal loads. J Intell Mater Sys Struct 2011;22:691-712.
[68] Carrera E, Boscolo M. Classical and mixed finite elements for static and dynamic analysis of piezoelectric plates. Int J Numer Methods Eng 2007;70:1135-81.

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