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研究生:陳弦
研究生(外文):HsuanChen
論文名稱:應用改良Pagano方法於功能性壓電材料三明治圓柱殼之自由振動解析
論文名稱(外文):Exact solutions of free vibration of functionally graded piezoelectric material sandwich circular hollow cylinders using a modified Pagano method
指導教授:吳致平
指導教授(外文):Chih-Ping Wu
學位類別:碩士
校院名稱:國立成功大學
系所名稱:土木工程學系碩博士班
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2013
畢業學年度:101
語文別:中文
論文頁數:45
中文關鍵詞:三維解析解自由振動功能性梯度材料Pagano 方法
外文關鍵詞:Exact solutionsFree vibrationFunctionally graded materialsPagano’s method
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本文以改良Pagano方法探討具簡支承邊界之多層疊合功能性壓電材料中空圓柱殼之三維自由振動分析。其中考量三種表面條件,並使用非均質性且厚度座標方向隨指數律變化之功能性壓電材料。傳統Pagano方法多用來分析多層疊合複合材料板和殼,然而經由四部分改良後,即可應用於多層疊合功能性圓柱殼,其改良部分分別如下:以Reissner 混合變分原理替代以位移為基礎的虛位移原理進行解析;利用Euler公式將系統方程式之解由複數解型態轉換為實數解型態;應用連續近似法,將功能性材料圓柱殼藉由切割成多個離散層結構,且各單層之厚度相較於圓心至中曲面的半徑長度微小;使用傳遞矩陣法,可逐層求解系統方程式,提升計算效能;藉由以上四部分的改良,便可拓展Pagano方法的應用層面。此外,本文亦著重探討多層疊合功能性圓柱殼的中曲面之寬厚比、表面條件、各層厚度、材料參數梯度指標對頻率結果的影響,並將改良Pagano方法求得之頻率參數和既有文獻之精確解進行探討。
The three-dimensional (3D) free vibration analysis of simply-supported, functionally graded piezoelectric material (FGPM) sandwich circular hollow cylinders with different surface conditions is presented. The material properties of each FGPM layer are regarded as heterogeneous through the thickness coordinate, and obey an exponent-law dependent on this. Pagano’s method is modified to be feasible for this study of FGPM sandwich cylinders, in which a displacement-based formulation is replaced by a mixed one; a set of the complex-valued solutions of the system equations is transferred to the corresponding set of real-valued solutions using Euler’s formula; a successive approximation method is adopted to approximately transform each FGPM layer into homogeneous piezoelectric layers with an equal and small thickness for each layer in comparison with the mid-surface radius, and with the homogeneous material properties determined in an average thickness sense; and a transfer matrix method is developed so that the general solutions of system equations can be obtained layer-by-layer, which is significantly less time-consuming than usual. A parametric study of the influence of the mid-surface radius-to-thickness ratio, open- and closed-circuit surface conditions, the thickness ratio of each layer, and the material-property gradient index on the natural frequencies of FGPM sandwich cylinders is carried out.
目錄
中文摘要 I
英文摘要 II
誌謝 III
目錄 IV
表目錄 VI
圖目錄 VII
第一章 緒論 1
第二章 三維壓電力學 5
2.1 基本方程式 5 2.2 無因次化 8
第三章 改良Pagano法 12
3.1 雙傅立葉級數展開法 12
3.2 線性齊性系統理論 13
3.3 連續近似法 14
3.4 傳遞矩陣法 15
第四章 數值範例 19
4.1 多層疊合均質壓電材料中空圓柱殼 19
4.2 多層疊合功能性壓電材料中空圓柱殼 21
第五章 結論 23
參考文獻 24
表 33
圖 39
附錄A 43
附錄B 44
自述 45
[1] A.K. Noor, W.S. Burton, Assessment of computational models for multilayered anisotropic plates, Compos. Struct. 14 (1990) 233_265.
[2] A.K. Noor, W.S. Burton, Assessment of computational models for multilayered anisotropic shells, Appl. Mech. Rev. 43 (1990) 67_97.
[3] A.K. Noor, W.S. Burton, C.W. Bert, Computational model for sandwich panels and shells, Appl. Mech. Rev. 49 (1996) 155_199.
[4] A.K. Noor, W.S. Burton, J.M. Peters, Assessment of computational models for multilayered composite cylinders, Int. J. Solids Struct. 27 (1991) 1269_1286.
[5] W.S. Burton, A.K. Noor, Assessment of computational models for sandwich panels and shells, Comput. Methods Appl. Mech. Eng. 124 (1995) 125_151.
[6] D.A. Saravanos, P.R. Heyliger, Mechanics and computational models for laminated piezoelectric beams, plates, and shells, Appl. Mech. Rev. 52 (1999) 305_320.
[7] S.V. Gopinathan, V.V. Varadan, V.K. Varadan, A review and critique of theories for piezoelectric laminates, Smart Mater. Struct. 9 (2000) 24_48.
[8] E. Carrera, An assessment of mixed and classical theories on global and local response of multilayered orthotropic plates, Compos. Struct. 50 (2000) 183_198.
[9] E. Carrera, Historical review of zig-zag theories for multilayered plates and shells, Appl. Mech. Rev. 56 (2003) 287_308.
[10] E. Carrera, Assessment of theories for free vibration analysis of homogeneous and multilayered plates, Shock Vib. 11 (2004) 261_270.
[11] E. Carrera, A. Ciuffreda, Bending of composites and sandwich plates subjected to localized lateral loading: A comparsion of various theories, Compos. Struct. 68 (2005) 185_202.
[12] E. Carrera, S. Brischetto, A survey with numerical assessment of classical and refined theories for the analysis of sandwich plates, Appl. Mech. Rev. 62 (2009) 1_17.
[13] C.P. Wu, K.H. Chiu, Y.M. Wang, A review on the three-dimensional analytical approaches of multilayered and functionally graded piezoelectric plates and shells, Comput. Mater. Continua, 8 (2008) 93_132.
[14] N.J. Pagano, Exact solutions for composite laminates in cylindrical bending, J. Compos. Mater. 3 (1969) 398_411.
[15] N.J. Pagano, Exact solutions for rectangular bidirectional composites and sandwich plates, J. Compos. Mater. 4 (1970) 20_34.
[16] H. Bufler, Theory of elasticity of a multilayered medium, J. Elasticity 1 (1971) 125_143.
[17] V.Z. Vlasov, The method of initial functions in problems of theory of thick plates and shells, Proc. Ninth Int. Congress Appl. Mech., Brussels, 321_330.
[18] J.Q. Ye, Laminated composite plates and shells, Springer-Verlag, London, Great Britain.
[19] E. Pan, Exact solutions for functionally graded anisotropic elastic composite laminates, J. Compos. Mater. 37 (2003) 1903_1920.
[20] J.G. Ren, Exact solutions for laminated cylindrical shells in cylindrical bending, Compos. Sci. Tech. 29 (1987) 169_187.
[21] J.G. Ren, Analysis of simply-supported laminated circular cylindrical shell roofs, Compos. Struct. 11 (1989) 277_292.
[22] T.K. Varadon, K. Bhaskar, Bending of laminated orthotropic cylindrical shells-An elasticity approach, Compos. Struct. 17 (1991) 141_156.
[23] G.P. Dube, S. Kapuria, P.C. Dumir, Exact piezothermoelastic solution of simply-supported orthotropic flat panel in cylindrical bending, Int. J. Mech. Sci. 38 (1996) 1161_1177.
[24] P.C. Dumir, G.P. Dube, S. Kapuria, Exact piezoelectric solution of simply-supported orthotropic circular cylindrical panel in cylindrical bending, Int. J. Solids Struct. 34 (1997) 685_702.
[25] T.G. Rogers, P. Watson, A.J.M. Spencer, An exact three-dimensional solution for normal loading of inhomogeneous and laminated anisotropic elastic plates of moderate thickness, Proc. Royal Soc. A437 (1992) 199_213.
[26] T.G. Rogers, P. Watson, A.J.M. Spencer, Exact three-dimensional elasticity solution for bending of moderately thick inhomogeneous and laminated strips under normal pressure, Int. J. Solids Struct. 32 (1995) 1695_1673.
[27] C.P. Wu, J.Q. Tarn, S.M. Chi, Three-dimensional analysis of doubly curved laminated shells, J. Eng. Mech. 122 (1996) 391_401.
[28] C.P. Wu, J.Q. Tarn, S.M. Chi, An asymptotic theory for dynamic response of doubly curved laminated shells, Int. J. Solids Struct. 33 (1996) 3813_3841.
[29] C.P. Wu, J.Q. Tarn, P.Y. Chen, Refined asymptotic theory of doubly curved laminated shells, J. Eng. Mech. 123 (1997) 1238_1246.
[30] C.P. Wu, J.Q. Tarn, S.C. Tang, A refined asymptotic theory for dynamic analysis of doubly curved laminated shells, Int. J. Solids Struct. 35 (1998) 1953_1979.
[31] P. Heyliger, Exact solutions for simply supported piezoelectric plates, J. Appl. Mech. 64 (1997) 299_306.
[32] P. Heyliger, S. Brooks, Exact solutions for laminated piezoelectric plates in cylindrical bending, J. Appl. Mech. 63 (1996) 903_910.
[33] P. Heyliger, S. Brooks, Free vibration of piezoelectric laminates in cylindrical bending, Int. J. Solids Struct. 32 (1995) 2945_2960.
[34] P. Heyliger, D.A. Saravanos, Exact free-vibration analysis of laminated plates with embedded piezoelectric layers, J. Acoust. Soc. Amer. 98 (1995) 1547_1557.
[35] F. Ramirez, P.R. Heyliger, E. Pan, Static analysis of functionally graded elastic anisotropic plates using a discrete layer approach, Compos. Part B: Eng. 37 (2006) 10_20.
[36] F. Ramirez, P.R. Heyliger, E. Pan, Discrete layer solution to free vibrations of functionally graded magneto-electro-elastic plates, Mech. Adv. Mater. Struct. 13 (2006) 249_266.
[37] C.P. Wu, C.H. Wu, Asymptotic differential quadratic solutions for the free vibration of laminated conical shells, Comput. Mech. 25 (2000) 346_357.
[38] C.P. Wu, Y.H. Tsai, Asymptotic DQ solutions of functionally graded annular spherical shells, Eur. J. Mech. A/Solids 23 (2004) 283_299.
[39] C.P. Wu, Y.M. Wang, Y.C. Hung, Asymptotic finite strip analysis of doubly curved laminated shells, Comput. Mech. 27 (2001) 107_118.
[40] G. Akhras, W.C. Li, Three-dimensional static, vibration and stability analysis of piezoelectric composite plates using a finite layer method, Smart Mater. Struct. 16 (2007) 561_569.
[41] G. Akhras, W.C. Li, Three-dimensional thermal buckling analysis of piezoelectric composite plates using the finite layer method, Smart Mater. Struct. 17 (2008) 1_8.
[42] C.P. Wu, H.Y. Li, The RMVT- and PVD-based finite layer methods for the three-dimensional analysis of multilayered composite and FGM plates, Compos. Struct. 92 (2010) 2476_2496.
[43] C.P. Wu, H.Y. Li, RMVT- and PVD-based finite layer methods for the quasi-3D free vibration analysis of multilayered composite and FGM plates, Comput. Mater. Continua, 19 (2010) 155_198.
[44] C.P. Wu, K.H. Chiu, Y.M. Wang, RMVT-based meshless collocation and element-free Galerkin methods for the quasi-3D analysis of multilayered composite and FGM plates, Compos. Struct. 93 (2011) 923_943.
[45] C.P. Wu, K.H. Chiu, RMVT-based meshless collocation and element-free Galerkin methods for the quasi-3D free vibration analysis of multilayered composite and FGM plates, Compos Struct. 93 (2011) 1433_1448.
[46] C.P. Wu, S.W. Yang, RMVT-based meshless collocation and element-free Galerkin methods for the approximate 3D analysis of multilayered composite and FGM circular hollow cylinders, Compos. Part B: Eng. 42 (2011) 1683_1700.
[47] C.P. Wu, S.W. Yang, A semi-analytical element-free Galerkin method for the 3D free vibration analysis of multilayered FGM circular hollow cylinders, J. Intell. Mater. Sys. Struct. (2011) DOI: 10.1177/1045389X11421822.
[48] Y.L. Yeh, M.J. Jang, C.C. Wang, Analyzing the free vibrations of a plate using finite difference and differential transformation method, Appl. Math. Comput. 178 (2006) 493_501.
[49] H.S. Yalcin, A. Arikoglu, I. Ozkol, Free vibration analysis of circular plates by differential transformation method, Appl. Math. Comput. 212 (2009) 377_386.
[50] M. Dehghan, G.H. Baradaran, Buckling and free vibration analysis of thick rectangular plates resting on elastic foundation using mixed finite element and differential quadrature method, Appl. Math. Comput. (2011) DOI: 10.1016/j.amc.2011.08.020.
[51] C.P. Wu, S.J. Chen, K.H. Chiu, Three-dimensional static behavior of functionally graded magneto-electro-elastic plates using the modified Pagano method, Mech. Res. Commun. 37 (2010) 54_60.
[52] C.P. Wu, Y.C. Lu, A modified Pagano method for the 3D dynamic responses of functionally graded magneto-electro-elastic plates, Compos. Struct. 90 (2009) 363_372.
[53] C. P. Wu, T.C. Tsai, Exact solutions of functionally graded piezoelectric material sandwich cylinders by a modified Pagano method, Appl. Math. Modell. (2011) DOI:10.1016/j. apm.2011.07.077.
[54] C.P. Wu, R.Y. Jiang, The 3D coupled analysis of FGPM circular hollow sandwich cylinders under thermal loads, J. Intell. Mater. Sys. Struct. 22 (2011) 691_712.
[55] K.P. Soldatos, V.P. Hadjigeorgiou, Three-dimensional solution of the free vibration problem of homogeneous isotropic cylindrical shells and panels, J. Sound Vib. 137 (1990) 369_384.
[56] A.K. Noor, P.L. Rarig, Three-dimensional solutions of laminated cylinders, Comput. Methods Appl. Mech. Eng. 3 (1974) 319_334.
[57] E. Carrera, Theories and finite elements for multilayered plates and shells: A unified compact formulation with numerical assessment and benchmarks, Arch. Comput. Methods Eng. 10 (2003) 215_296.

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