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系統識別號 U0026-3005202005470700
論文名稱(中文) 以Levenberg-Marquardt反向傳播神經網絡進行功能性材料梁之材料成分識別
論文名稱(英文) Identification of material compositions of functionally graded beams using a Levenberg-Marquardt backpropagation neural network
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 108
學期 2
出版年 109
研究生(中文) 張守傑
研究生(英文) Shou-Chieh Chang
學號 N66071045
學位類別 碩士
語文別 中文
論文頁數 44頁
口試委員 口試委員-徐德修
口試委員-蘇于琪
指導教授-吳致平
口試委員-王永明
口試委員-方中
中文關鍵字 類神經網路  功能性梯度梁  分層梁理論  高階剪切變形理論  Hamilton原理 
英文關鍵字 neural network  functionally graded beam  layer-wise beam theory  higher-order shear deformation theory  Hamilton principle 
學科別分類
中文摘要 本文應用混合分層(Layerwise, LW)高階剪切變形理論(Higher-order shear deformation theory, HSDT)進行受軸向載重之功能性梯度簡支梁的振動頻率及臨界載重分析。文中假設 FG 梁的材料性質隨厚度座標變化,FG 梁之有效材料性質可用二相材料混合法則(The rule of mixtures)來進行計算。數值範例結果顯示與文獻中提供精確解相吻合。本文亦使用類神經網路進行受軸向載重 FG 簡支梁振動頻率之預測和材料性質之辨識。在訓練類神經網路的過程中,預先依混合分層高階剪切變形理論產生訓練組及測試組,前者用於訓練神經網路,後者用於測試類神經網路精確度。經過適當訓練後,類神經網路所預測之振動頻率有相當不錯的精確度,而運算時間相較混合分層高階剪切變形理論解法大幅節省,亦達成本理論解法無法實現之材料辨識。
英文摘要 This paper uses Layerwise (LW) Higher-order Shear Deformation Theory (HSDT) to analyze the vibration frequency and critical load of a functionally graded simply supported beam under axial load. It is assumed that the material properties of the FG beam change with the thickness coordinates, and the effective material properties of the FG beam can be calculated by the rule of mixtures of two phases. The numerical example results show that they are in agreement with the exact solutions provided in the literature. This paper also uses neural network to predict the vibration frequency of the FG simply supported beam under axial load and identify the material properties. In the process of training neural networks, a training group and a test group are generated in advance according to the mixed layered high-order shear deformation theory. The former is used to train the neural network, and the latter is used to test the accuracy of the neural network. After proper training, the vibration frequency predicted by the neural network has quite good accuracy, and the calculation time is greatly saved compared with the mixed layered high-order shear deformation theoretical solution, which also achieves the material identification that can not be achieved by the theoretical solution.
論文目次 摘要 I
目錄 VIII
表目錄 IX
圖目錄 X
第一章 緒論 1
第二章 混合分層高階剪切變形梁理論 4
2-1強型式數學方程式 4
2-2應用 13
第三章 類神經網路演算法 17
3-1前向傳遞作業 17
3-2 倒傳遞程序 18
第四章 數值範例 21
4-1 FG 樑的振動和挫屈分析 21
4-2以多層倒傳遞神經網路分析軸向載重 FG 簡支梁 23
4-3使用人工神經網絡識別FG梁的材料成分 24
第五章 結論 25
參考資料 26
附錄A 30
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