臺灣博碩士論文加值系統

本文探討壓電材料貼覆或內埋於平板，施予電壓對平板產生的靜態撓曲變形和簡諧振動。結合彈性力學理論與壓電原理推導壓電材料和平板接觸面作用力或力矩，再以此力或力矩為負載作用於平板，應用板理論求解平板撓曲位移或簡諧振動。並以簡支撐平板為例，比較推導所得解析解和有限元素數值解兩者相當吻合，驗證推導的準確性。藉由參數分析探討壓電片大小及放置位置之影響，表面貼覆與內埋之差異，再由改變施予之電壓頻率了解共振與非共振頻率對平板之激振效果。壓電材料為智慧結構常見的感測和致動元件，本文推導所得可作為此類型智慧結構分析的理論基礎。

In this investigation, the static deflection and harmonic vibration of a simply supported plate induced by piezoelectric actuators are examined two piezoelectric actuators are surface bonded or embedded in the plate and are symmetric with the mid-plane. Electric voltage with the same amplitude and opposite sign are applied to the two symmetric piezoelectric actuators, results to the bending effect on the plate. The bending moment is derived by using the theories of elasticity and piezoelectricity. This bending moment is then applied to the plate. Following the classical plate theory, the analytical solution of flexural displacement on a simply supported plate subjected to bending moment can be obtained. The analytical solution are compared with the finite element results to show the validation of present approach. The effects of size and location of actuators on the response of a plate are presented through parametric study. The response can be static or harmonic according to the static or sinusoidal voltage applied to the actuators. Piezoelectric actuators are common used in smart structures. The analytical model presented in this research demonstrates the capability of predicting the responses of smart structures to a command voltage applied to the piezoelectric actuators.

摘 要……………………………………..……………………………I
英文摘要………………………………………………………………..II
誌謝……………………………………………………………………..III
目 錄…………………..………………………………………………IV
表目錄…………………………………………………………………..VI
圖目錄…………………………………………………………………..XI
符號說明……………………………………………………………....XX
第一章 緒論……………………………………………………………1
1.1 前言……………………………...………………………1
1.2 研究概念……………………………...………………………2
1.3 文獻回顧………………………...……………………2
第二章 壓電原理…………..…………………………………………..4
2.1 壓電理論………………………………………..…………….4
2.2 壓電方程式...…………………………………………………5
第三章 力學分析………………………………………………………..9
3.1貼覆式壓電致動器作用力…………………………………….9
3.2內埋式壓電致動器作用力………..………………………….13
3.3簡支撐平板靜態響應………………………………………...17
3.4簡支撐平板簡諧分析……………………………..………….20
第四章 例題探討………...…………………………………………….23
4.1靜態分析……………………………………………………...23
4.2簡諧分析…………………………...…………………………25
第五章 內含壓電材料平板三維有限元素分析…………………… 30
5.1壓電元素….…………...……………………………………...30
5.2靜態撓曲分析……………….…………………………...…...33
5.2.1 壓電片貼覆於表面………………………………………...33
5.2.2 壓電片內埋於平板…………...……………………………36
5.3 平板簡諧振動分析…………………………………………..38
5.3.1 壓電片貼覆於表面………………………………………...39
5.3.2 壓電片內埋於平板………………………………………...43
第六章 結論……………………………………………………………48
參考文獻..………………………………………………………………50

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