本論文系統性地綜述了薄膜型超材料在隔聲與振動控制應用中的最新研究進展。首先，在聲學部分建構理論模型，針對兩種不同形狀的質量體（弧形質量體和片狀質量體），深入探討其非對稱的物理機制，並分析各種參數組合對聲學損失的影響。
其次在振動方面，本研究重點揭示了與相同重量的集中質量體結構相比，方框形質量體（Square Frame-Shaped Mass）能更有效地產生寬廣且導致波衰減的頻段。隨後提出了一個可行的數學模型，成功預測了承受張力的彈性薄膜及附加於薄膜表面的多個ARCH-MASS的局部共振系統，並準確預估該局部共振系統的第一和第二個初始頻率，此外，本文所提出的局部共振系統能將有效帶隙頻率移至300 Hz以下，通過調整ARCH-MASS的幾何參數（如厚度、寬度和位置），甚至增加ARCH-MASS的數量，該理論均能有效預測帶隙的初始頻率，顯示出所提出數學模型的準確性。
最後我們提出了一種新型薄膜超材料板，其結構包含兩個不等重的質量體（M₁、M₂）。通過有限元素分析，獲得了該材料的頻散關係圖及有效質量密度分佈，並以此為基礎深入探討其彎曲波的傳遞特性。在研究中，通過調整質量體M₁的位置，成功調控了局部結構的模態行為，從而實現了帶隙位置的可控調節。通過振動實驗對理論模型進行驗證，實驗結果與有限元素（FE）分析結果高度吻合，充分證明了該超材料板在多頻率振動衰減抑制方面的潛在應用價值。
以上研究不僅為聲學和振動超材料的理論基礎提供了支持，也為其在實際應用中的推廣開辟了新的思路與方法。

This thesis provides a systematic review of recent advances in the application of membrane-type metamaterials for sound insulation and vibration control. In the acoustics section, a theoretical model is established to investigate two distinct mass shapes—arched masses and plate-type masses—while focusing on the asymmetric physical mechanisms and analyzing the effects of various parameter combinations on acoustic loss.
In the vibration section, the study reveals that, compared with structures using concentrated masses of equal weight, square frame-shaped masses are more effective in generating broad frequency ranges that lead to wave attenuation. A feasible mathematical model is subsequently proposed to predict the local resonant system of a tensioned elastic membrane with multiple arc masses attached to its surface. The model accurately estimates the first and second onset frequencies of the local resonant system. Notably, the proposed local resonant system can shift the effective bandgap frequency to below 300 Hz. By adjusting the geometric parameters of the arc mass (such as thickness, width, and position) or increasing the number of arc mass units, the model effectively predicts the onset frequencies of the bandgap, thus demonstrating its accuracy.
Finally, we propose a novel membrane-type metamaterial plate comprising two masses of unequal weight (M1 and M2). Using finite-element analysis (FEA), the dispersion curves and effective mass density distribution of the material are obtained, forming the basis for an in-depth examination of its flexural wave propagation characteristics. By adjusting the position of mass M1, the modal behavior of the local structure is successfully tuned, thereby enabling controllable adjustment of the bandgap location. Theoretical predictions are validated through vibration experiments, with results showing strong agreement with FEA outcomes. This confirms the potential of this metamaterial plate for multi-frequency vibration attenuation.
These findings not only provide theoretical support for acoustic and vibration metamaterials but also offer new perspectives and methods for their practical implementation.

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