臺灣博碩士論文加值系統

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。

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.

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

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