由於地震來臨時，雷利波於表面能量集中的行為與撓曲板的振動有某些特徵上的相似，近年來，在抗震領域中已有眾多學者們針對板中的彈性波傳控制進行研究。在本文中，基於Kirchhoff-Love薄板理論，我們利用薄板的撓曲波傳來模擬半空間表面波傳，主要研究了局部共振薄板中的撓曲波傳遞並且考慮預應力作用於板的影響，局部共振薄板是由週期性排列的質量彈簧阻尼諧振器連接於薄板上所組成，過程中以平面波展開法來處理這種二維週期性結構的問題，透過諧振器和預應力的參數變化來分析對頻帶結構的影響，討論帶隙的衰減程度、位置以及寬度。文獻中表示，週期性結構的帶隙是頻帶結構之間阻擋波傳遞的頻率範圍，局部共振結構存在著由布拉格散射及局部共振機制所產生的布拉格帶隙與共振帶隙，由於共振帶隙受其諧振器參數控制，透過適當的諧振器參數調配可與布拉格帶隙形成寬偽帶隙，在我們的分析結果中顯示，預應力的施加會導致布拉格頻率的改變，因此我們表示，針對低頻彈性波的傳遞，可以藉由引入預應力行為使帶隙達到低頻的寬偽帶隙來阻擋。

In this thesis, we are concerned with the control of the propagation of elastic waves in thin plate. Based on Kirchhoff-Love thin plate theory, the propagation of flexural waves in the thin plate is studied. Specifically, we investigate the propagation of flexural waves in a locally resonant thin plate, which is made of a periodic array of mass-spring-damped resonators attached on a thin homogeneous plate. In addition, the effect of prestress is also examined. The plane wave expansion method is used to deal with the plate system with a periodic array of lumped resonant elements. Through numerical analysis based on finite element calculations (MATLAB), the objective of this work is to explore the effects of prestress on band structures and band gaps in locally resonant thin plates. It is found that different values of prestress affect the Bragg frequency. The propagation of low-frequency elastic waves can be blocked by introducing a pre-stress to achieve a low-frequency wide pseudo-gap.

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