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研究生:林孝哲
研究生(外文):Lin Shiaw Jer
論文名稱:含壓電感測器與制動器之複合材料樑之振動控制
論文名稱(外文):Vibration Control of Composite Beams with Piezoelectric Sensors and Actuators
指導教授:張銘永先生林忠逸先生
指導教授(外文):Mr. Chang Min YungMr. Lin Jong Yih
學位類別:碩士
校院名稱:國立中興大學
系所名稱:機械工程研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:1993
畢業學年度:81
語文別:中文
論文頁數:150
中文關鍵詞:複合材料壓電材料斜角
外文關鍵詞:Composite MaterialPiezoelectric MaterialSkew angle
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含壓電材料撓性樑之振動控制問題,一般均採用 Bernoulli-Euler樑理論
與 Timoshenko 樑理論,且大多僅探討橫向位移之振動,較少論及扭轉角
之控制。而本文採用改進樑模式,及使用壓電制動器與感測器同時控制懸
臂樑之扭轉角與橫向位移。本文以漢彌爾頓原理(Hamilton's
principle) 結合有限元素法推導懸臂樑之改進樑模式的運動方程式,求
其動態系統之狀態空間描述。然後利用 LQG 控制架構之方法,設計控制
器抑制懸臂樑振動,並以改良估測器及調整感測器位置等方式提高控制效
率。同時本文提出兩種控制懸臂樑扭轉角之方法。其一為利用複合材料耦
合特性,直接控制橫向位移,而間接影響扭轉角,以達到橫向位移與扭轉
角皆能控制的目的。第二種方法則為利用壓電材料主軸方向與樑結構主軸
方向之斜角 (skew angle) 放置,使能同時觀察並控制樑之橫向位移與扭
轉角。

Although many researches had been done on the vibration control
of elastic beams using piezoelectric sensors and actuators , in
most of these works either Bernoulli-Euler or Timoshenko beam
theory is adopted. As a result, the emphasis is on the
suppression of the bending vibration, leaving out the important
issue of the control of the torsional vibration. The main goal
of this thesis is to develop methods of controlling the bending
and torsional vibration of composite beam simultaneously with
piezoelectric sensors and actuators. Toward this end, first, an
improved beam theory incorporating both bending and torsional
deformation effects is employed. Next, the Hamilton principle
and finite element method are used to derive the equations of
sensor and of motion of beams containing driving source from
the piezoelectric actuator. These equations are then
transformed into state-space form convenient for control
design. Linear quadratic Gaussian (LQG) technique is applied to
design the controller for vibration suppression. It is shown
that through the design of the observer or by choosing
appropriate sensor's locations, the performance of the
controller can be improved significantly. As for the control of
the torsional vibration, two schemes are proposed. One approach
is making use of the mechanical deformation coupling effect
existing in the composite materials. Since if there exists a
coupling between the bending and torsional vibration, the
torsional vibration can be suppressed through the control of
the bending vibration. The other approach is to arrange the
piezoelectric material in such a way that its principal
material direction form an angle (often called skew angle) with
beam axis. Then if, furthermore, the dielectric constants d31
and d32 are not equal, the piezoelectric sensors and actuators
are able to sense and control both bending and torsional motion.

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