請用此 Handle URI 來引用此文件: http://hdl.handle.net/11455/18221
標題: 新型智慧結構之形狀、振動及噪聲輻射控制
A New Configuration of Smart Structures for Shape, Vibration and Sound Radiation Controls
作者: 許志宇
Hsu, Chih-Yu
關鍵字: smart strucrures
智慧結構
shape control
vibration control
sound radiation control
形狀控制
振動控制
噪聲控制
出版社: 應用數學系
摘要: 本研究旨在提出一種新型之智慧結構能夠針對環境的改變作出適當的反應 。本論文以理論分析方法探討此一新型智慧結構之形狀、振動及噪聲輻射 控制效果。此一新型智慧結構以層疊方式結合正向性層疊板以及可作為感 測器及致動器的壓電材料層片,其中壓電材料層片的電極外形可設計成正 弦函數或模態函數的二次導函數。採用適當數目的壓電材料層片並針對實 際上的需求選用控制法則得到所期望的控制結果,使得結構在受到任何靜 態外力的情況下,都能夠接近原來之形狀並且控制在所要求的精密度範圍 之內。此外,當結構受到動態外力擾動時,也能夠避免共振現象的發生, 縮短暫態反應所需之安定時間,並且能將振動降低到最小的程度,同時也 使得結構之輻射噪聲隨之下降。本文採用漢彌頓 (Hamilton) 原理推導此 一含壓電材料的新型智慧結構樑的運動方程式及邊界條件,再採用傅氏級 數 (Fourier series) $ 及司托克變換 (Stokestransformation) 分析靜 態位移,以及利用感測器電壓負回授的動態頻率響應。此外,用模態分析 法 (modal analysis)求各個模態座標之二階動態方程式。 利用座標轉換 成連續時間的狀態方程式,藉此可利用克利-漢彌頓 (Caley Hamilton) 定理求得暫態矩陣之後得到離散時間的狀態方程式。數值模擬針對靜態之 形狀控制,以及動態外力在單頻率、雙頻率與含有白色噪聲等不同情況影 響下的控制效果。本文採用 Wallace所提出關於簡支樑振動時所產生的輻 射噪聲關係式,來求出遠場的聲壓分佈,以此評估在控制前後,簡支樑振 動所產生的輻射噪聲的改善程度。
A new configurationof smart structures which could adjust itself according to changes ofenvironments is proposed. Theoreticalsimulations are formulated and performed without physical experimentationfor evaluating its feasibility.\vskip 0.5pc\indentThe new configuration is a laminated beam-plate or wide beamcomposed of layers of piezoelectric sensors and actuators. Their electrodeshapes are trimmed to desirable shapes in conjunction with propercontrol algorithm, to achieve expected control effects. Shapes of sinefunctions are used for controling static deformation to within a desiredtolerance, and resonance control of beam-plates of any boundaryconditions by the new configuration itself.For dynamic analysisof beam-plates, electrodes trimmed to theshapes of the second derivative of modal functions are used toreduce the settling timeof the transient state, suppress deformation of beam-platesand reduce sound radiation.The Hamilton''s principle is used to derive the governing equationand boundary conditions. While Fourier series with Stokestransformation used for static and free vibration analysis ofbeam-plates of any supporting conditions is convenient for establishing shapeand resonance control algorithms, modal functions are used for dynamicanalysis.The state equation in continuous time domain transformed into discretetime domain on the basis of Caley Hamilton theorem is used in thefeedforward control analysis.Numerical simulations for beam-plates under staticloading, and single as well as dual frequency and white noise excitationsare investigated.The control of the sound radiation for reducing the far-field pressureradiated from beam vibration using the relation given by Wallace [49]is examined.
URI: http://hdl.handle.net/11455/18221
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