片段環感測器之模態敏感度的空間訊號分佈及片段環 致動器的控制效應

Modal sensitivities, spatial signal distribution and average of segmented ring sensors and control effect of segmented ring actuators

林裕昇(Yu-Sheng Lin)

指導教授 ： 朱錦洲 ； 張建成

國立臺灣大學/工學院/應用力學研究所/碩士(2009年)

https://doi.org/10.6342/NTU.2009.03168

摘要

對於薄殼類型之結構的分佈控制，必須要有效的致動和動態
分析。本研究是估算片段分佈的電-機械性質的壓電薄殼感測器
應用在環薄殼。由於感測器的訊號是模態決定，所以必須先學習
自然模態的特性而且特別強調於環向之模態。其次，在分佈片段
的感測器使用分割的技巧且設計不同的長度，使得藉著模態形變
而估算訊號。
因此，全部的輸出訊號總共包含了四個部份：1)環向之振動
的振幅所造成彎曲應變而感生訊號，2)徑向之振動的振幅所造成
彎曲應變而感生訊號，3)環向之振動的振幅所造成膜應變而感生
訊號，4)徑向之振動的振幅所造成膜應變而感生訊號。膜應變與
彎曲應變主要分別由環向與徑向之自然頻率伴隨而生。所以感測
器的敏感度可以在分成：1)徑向型態敏感度與2)環向型態敏感
度。
使用參數學習(例如：環的半徑、感測器的厚度、環的厚度
和片段感測器的大小)而引導計算出在自然振動之下，所產生在
環的壓電片感測器所得之訊號。所有的資料指示著，產生的總訊
號主要是由環向分量貢獻為較多，而不是徑向分量。
其次，在環薄殼上包覆致動層，藉著推導致動片之控制效
應，瞭解在徑向模式時，彎曲控制效應支配整個控制效應，反之
在環向模式時，膜控制效應會是主要控制效應的主幹。
最後，使用參數學習（例如：環的半徑、致動器的厚度、環
的厚度和片段致動器的大小與施加電壓大小）而瞭解這些幾何參
數影響控制效應之大小。

關鍵字

環向模態 ； 徑向模態 ； 分割技巧 ； 彎曲應變感生訊號 ； 膜應變感生訊號 ； 感測器敏感度總產生訊號 ； 彎曲控制效應 ； 膜控制效應

並列摘要

Distributed monitoring is essential to effective actuation and
vibration control of shell-type structures. In this thesis, electro-mechanics
of the segmented distributed piezoelectric shell sensors applied to ring
shells are evaluated. Since sensor signals are modal dependent, natural
modal characteristics, emphasizing the circumferential mode, are studied
first. Then, with the segmentation technique, distributed segmented
sensors with various lengths are designed and their signal generations
resulting from modal strains are evaluated.
The total output signal includes four components: 1) a bending strain
induced signal by the circumferential oscillatory amplitude, 2) a bending
strain induced signal by the transverse oscillatory amplitude, 3) a
membrane strain induced signal by the circumferential oscillatory
amplitude and 4) a membrane strain induced signal by the transverse
oscillatory amplitude respectively at the transverse and circumferential
component frequencies. Furthermore, the sensor sensitivities are divided
into: 1) the transverse modal sensitivity and 2) the circumferential modal
sensitivity.
Parametric studies (e.g., ring radius, sensor thickness, ring thickness
and sensor segment length) are conducted to evaluate the spatial signal
distributions and component signal generations of segmented ring sensors.
All data indicate that ring’s circumferential, not transverse, component
mode dominates the total signal generation.
Then, distributed control actions induced by electrostrictive actuator
segments are evaluated the total effect can be divided into two
microscopic control actions: the circumferential membrane and bending
control actions. The bending control action in total control action is major
contribution at the transverse mode. The membrane control action in total
VI
control actions is major contribution at the circumferential mode.
Finally, parametric studies (e.g., ring radius, actuator thickness, ring
thickness, actuator segment length and applied voltage) are conducted to
evaluate control effect.

並列關鍵字

Circumferential modal ； transverse modal ； segmentation technique ； bending strain induced signal ； membrane strain induced signal ； sensor sensitivity ； total signal generation ； bending control action ； membrane control action

參考文獻

[1] A. E. H. Love, “On the small free vibrations and deformations of a thin elastic

shell”, Philosophical Transactions of the Royal Soc. Of London, Ser. A, 179,

[2] W. Flugge, “stresses inShells”, 2nd ed., Springer-Verlag, New Tork, 1973.

[3] W. Soedel, Vibrations of Shells and Plates, Dekker, 1993.

[4] H. S. Tzou, Piezoelectric Shells: Distributed Sensing and Control, Kluwer