研究生: |
林宏儒 Lin, Hong-Ru |
---|---|
論文名稱: |
應用Reissner混合變分原理有限層板法於奈米碳管加勁複合材料核心與壓電材料面層積層板之三維自然振動分析 Three-dimensional free vibration analysis of carbon nanotube-reinforced composite plates withsurface-bonded piezoelectric layers using RMVT-based finite layer methods |
指導教授: |
吳致平
Wu, Chih-Ping |
學位類別: |
碩士 Master |
系所名稱: |
工學院 - 土木工程學系 Department of Civil Engineering |
論文出版年: | 2014 |
畢業學年度: | 102 |
語文別: | 英文 |
論文頁數: | 62 |
中文關鍵詞: | 三維分析 、振動 、Reissner混合變分原理 、有限層板法 、奈米碳管 、壓電板 |
外文關鍵詞: | three-dimensional analysis, dynamic responses, mixed theories, finite layer methods, carbon nanotubes, piezoelectric plates |
相關次數: | 點閱:107 下載:2 |
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本文基於三維壓電力學,發展Reissner混合變分原理(Reissner’s mixed variational theorem, RMVT)有限層板法(finite layer methods, FLMs),並應用於具簡支承邊界開放(或封閉)迴路表面條件,功能性梯度(functionally graded, FG)奈米碳管加勁複合材料(carbon nanotube-reinforced composite, CNTRC)三明治壓電板之三維自然振動分析。文中將板人為切割成若干矩形層;其中,三角函數和Lagrange多項式用於內插各層面內和面外主變數之變化,諸如:彈性位移、橫向剪應力和正向應力、電位勢和法線方向之電位移(電通量)分量。而厚度座標各變數之模擬階數可自由組合,諸如:線性、二次或三次式。本文考慮四種沿厚度方向分佈之奈米碳管加勁複合材料,分別為均勻分佈、功能性梯度V型、菱形和X型分佈,各層有效材料性質由二相混合法則予以評估。文中將本有限層板法應用於奈米碳管加勁複合材料核心與壓電材料面層組合板之自然振動分析,求得之頻率參數將和文獻中三維精確解進行綜合比較,驗證本有限層板法之精確性和收斂性,並進行各參數間之綜合分析。
A unified formulation of finite layer methods (FLMs) based on the Reissner’s mixed variational theorem (RMVT) is developed for the three-dimensional (3D) dynamic responses of simply-supported, functionally graded (FG) carbon nanotube-reinforced composite (CNTRC) plates with surface-bonded piezoelectric sensor and actuator layers and closed- and open-circuit surface conditions. In the formulation, the plate is divided into a number of finite rectangular layers, in which the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-plane variations of the primary field variables of each individual layer, respectively, such as the elastic displacement, transverse shear and normal stress, electric potential, and normal electric displacement (flux) components. The relevant orders used for expansion of these variables in the thickness coordinate can be freely chosen, such as linear, quadratic or cubic ones. Four different through-thickness distributions of carbon nanotubes in the CNTRC layer are considered, and the effective material properties of the layer are estimated using the rule of mixtures. The accuracy and convergence rate of the frequency parameters of the sandwiched hybrid CNTRC and piezoelectric plates obtained using assorted RMVT-based FLMs are assessed by comparing their solutions with the exact 3D solutions available in the literature.
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