臺灣博碩士論文加值系統

考慮一個長方形平板，受光電致動器產生的外力影響,且四端均為簡支撐之平板的振動分析。依據 Tzou and Fu，得到長方形平板的運動方程式，在振動受到光電致動器的作用為了清楚地看致動器對長方形平板的影響力則不考慮平板阻尼係數的影響。本文中運用Galerkin 的方法，將統御方程式化簡為一個以時間為變數的 Mathieu 方程式，至於暫態振動的部分，則使用四階 Runge-Kutta 的方法來描述振動對時間時的關係表分別繪出，藉此來探討其致動器的擺放位置對長方形平板振動的影響關係。

The analysis of vibration for the rectangular plate under out-plane moment from opto-electromechanical actuators are considered. The rectangular plate is simply supported at all edges. The equation of rectangular plate motion including out-plane moment based on Tzou and Fu is presented. In order to show clearly the effects of active damping, structural damping is not considered. The equations of vibration are reduced to an ordinary differential equation by assuming mode shape and Galerkin’s procedure. Using Runge-Kutta method, the amplitude-time is determined. By discussing the effective control moments depend on the locations of actuators to the vibration of a rectangular plate.

中文摘要 ………………………………………………………………………… i
Abstract …………………………………………………………………………. ii
誌 謝 ………………………………………………………………………….. iii
Contents ………………………………………………………………………….. iv
List of table ……………………………………………………………………… vi
List of figures ……………………………………………………………………. vi
Nomenclature …………………………………………………………………... viii
Chapter 1 Introduction ………………………………………………………... 1
Chapter 2 Governing Equations ………………………………………………. 3
2.1 An opto-electromechanical actuator …………………………………… 3
2.2 Equations of photovoltaic, pyroelectric , thermal , and piezoelectric effect..5
2.3 Distributed opto-electromechanical actuator …………………………... 7
2.4 Equations of motion for simply supported rectangular plate ………….. 8
Chapter 3 Analysis of vibration ……………………………………………..... 9
3.1. Displacement function ………………………………………………... 9
3.2 Applying Galerkin’s method …………………………………………. 10

Chapter 4 Results and discussion ……………………………………………. 12
4.1 The time history temperature response and displacement response .....13
4.2 The transient vibration for case 1 and case 2 ………………............... 14
Chapter 5 Conclusions ………………………………………………………. 16
References ………………………………………………………………………. 17
Table …………………………………………………………………………….. 20
Figures …………………………………………………………………………... 21

LIST OF TABLE
Table 1. Parameters. .......……………………………………........................... 20

LIST OF FIGURES
Fig .1. Opto-electromechanical actuator ………………………….................. 21
Fig.2. Plate with opto-electromechanical actuators ………………................... 22
Fig.3 Opto-electromechanical actuators under irradiation of light … ................23
Fig.4. Temperature response ( ) of the optical actuator for ........ 24
Fig.5. Temperature response ( ) of the optical actuator for I= ........ 25
Fig.6. Temperature response ( ) of the optical actuator for I= ........ 26
Fig.7. Displacement response of the optical actuator for I= .................. 27
Fig.8. Displacement response of the optical actuator for I= ................ 28
Fig.9. Displacement response of the optical actuator for I= ............... 29
Fig.10. (a) Case1 (b) Case2 ………………………………………...................... 30
Fig.11. Mode (1,1) response for I= , Case 1 ……………................... 31
Fig.12.Mode (1,1) response for I= , Case 1 …………….................. 32
Fig.13.Mode (1,2) response for I= , Case 1 ……………................. 33
Fig.14.Mode (2,1) response for I= , Case 1 ……………..................34
Fig.15.Mode (1,1) response for I= , Case 1 ……………................ 35
Fig.16. Mode (1,1) response for I= , Case 2 …………................... 36
Fig.17.Mode (1,1) response for I= , Case 2 …………................... 37
Fig.18.Mode (1,2) response for I= , Case 2 ……….…….............. 38
Fig.19.Mode (2,1) response for I= , Case 2 ……………............... 39
Fig.20.Mode (1,1) response for I= , Case 2 …………................... 40

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