本文主要研究扭轉波在含拘束層的電流變流體（ER）和磁流變流體（MR）軸的波傳現象，首先以有限元素模型來推導其運動方程式，再配合轉移矩陣來計算系統的能隙結構圖，希望能藉由外加電場或磁場的不同來改變電流變流體和磁流變流體的剪力模數，來達到調整能隙範圍大小的變化，形成一個可主動控制的濾波器。同時利用了電流變流體和磁流變流體來設計一超常材料柱，將其置於夾層中，視為一個不計質量的彈簧，來進行扭轉波在此結構上的波傳分析，並利用此材料在剪力模數上可調變的特性，同樣的來進行能隙範圍大小的變化。
加入兩種智能材料方面確實可以利用外加電場和磁場的改變，來使此系統的能隙的位置和範圍產生變化，並可利用系統結構參數的改變加以配合，來達到主動的調變機制。在超常材料柱方面，有效負質量確實可以讓波傳在能隙內具有較大的衰退速度，也確實可以利用電流變流體和磁流變流體來達到〝停止帶位置和範圍〞的控制，利用結構參數的變化也可以達到停止帶大小的控制。

In this study, the wave propagation of torsional wave in three-layer with electrorheological（ER） or magnetorheological（MR） fluids have been investigated. First, we use finite element model to derive the governing question and then follow the transfer matrix method to plot the band-gap diagram. The approach utilizes the property of ER and MR materials, that can change the material properties to control the stop and pass band regions in the frequency spectra. Then, we use the electrorheological and magnetorheological to construct a metamaterial bar, and tune the shear modulus to control the propagation of torsional wave.
With the two smart materials ER fluid and MR fluid, it can really change the position and the frequency of the stop band by tune the electrical field or magnetic field and the parameter of structure. In metamaterial bar, when effective mass density occurs in the gap it yields significant spatial attenuation of the wave amplitude. By tune the electrical field or magnetic field and the parameter of structure can also be changed the position and the frequency of the stop band.

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