本論文主要研究電變流體應用於智能結構之自由振動、阻尼行為與動態穩定特性的行為，並配合原有的振動分析模組，加以分析此種智能週期結構的波動傳遞特性。在本文中振動與動態穩定部份將以三明治方板為研究模型，而週期結構之波傳分析模型則以三明治樑為分析對象。首先以漢米爾頓原理推導其運動方程式，其中包含轉動慣量、剪力變形、外力作功及剪力層等效應，方板系統中所使用的電變流體以線性阻尼材料來近似，其材料性質是以複數的形式來加以描述，再以有限元素法方式來得到系統的馬修方程式，最後藉此複數形式的特徵值問題即可解得系統的自然振動頻率、模態損失因子，在動態穩定性問題方面，將利用Bolotin的方法計算系統動態穩定與不穩定區域間的邊界。接著利用有限元素分析的基礎，配合轉移矩陣法的應用，分析在週期結構下波動的特性行為，並研究在不同週期與材料的組合下，對於系統的波傳能隙分布的影響。

　　本文探討了數種參數，例如拘束層與電變流體層的材料特性和厚度，以及施加的電場強度等等，對三明治方板系統的自然振動頻率、模態損失因子及系統動態不穩定區域的影響變化；最後亦探討在不同貼覆面積下，此種週期系統的波傳特性。由數值分析的結果中可以得知，較厚的拘束層或是電變流體層的貼覆並不一定能得到較佳的阻尼特性，而系統的模態損失因子也會隨著施加電場強度的改變而產生變化。因此，在此方板系統上貼覆此種主動式智能材料阻尼層除了可使系統更加的穩定外，也可達到主動控制的效果。最後亦針對聲波在週期結構下的特性來討論其波傳現象，從數據分析的結果中可以得知，可以藉由不同週期的材料組合以及貼覆的材料特性，達到類似光纖波導的效果。

　In this thesis, an investigation has been carried out on the dynamic characteristics of an sandwich plate with an electrorheological (ER) fluid core. The isotropic or orthotropic rectangular plate is covered an electrorheological fluid core and a constraining layer to improve the stability of the system. In this study, the finite element method and the harmonic balance method are used to calculate the vibration characteristics and the principal instability regions of the sandwich plate. Numerical results are presented to study the effects of various parameters, such as thickness ratio, stiffness ratio, and applied electric field on the vibration behaviors and principal instability regions of the sandwich plate. Rheological property of the electrorheological fluid materials, such as viscosity, plasticity, and elasticity can be changed when applying an electric field. When the electric field is applied on the sandwich structure, the damping of the system is more effective. The ER fluid core is found to have a significant effect on the location of the boundaries of the dynamic instability regions.

　Periodic structures can act as filters for wave propagation within certain bands of frequency called stop bands. The partially constrained layer damping (CLD) treatments are placed periodically along the beam and covered with a constrained layer to control the longitudinal wave propagation in this beam. The CLD placed on the beams act as the sources of impedance mismatch with viscoelastic characteristics. The location and width of the stop bands can be changed with different configurations of the periodic structure.

　The finite element model and the transfer matrix method are developed to study the one-dimensional, periodically structural problems to predict the performance of the system. The behaviors of the periodic structure are evaluated at different length ratios and base beam materials. The investigation in the present study provides the basic guidelines to design periodic structures with smart materials to achieve desired filtering characteristics.

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