| 摘要: | 本文建立理論分析方法，探討板結構受質量效應影響的振動特徵和暫態波傳行為，包含任意外加質量分佈的平板共振頻率與模態形狀差異，以及撓曲波通過質量陣列的傳遞軌跡與能量變化，藉此設計質量透鏡。
理論模型首先推導平板上附加質量陣列的自由振動解析解，以Gorman疊加法求出共振頻率和模態形狀等振動特徵後，藉由模態展開法獲得暫態波傳理論解。振動特徵與暫態波傳的理論分析結果透過有限元素模擬軟體相互比對驗證，理論解析之共振頻率、模態形狀和暫態位移、應變等各種物理量皆十分準確，確定本研究所提出的理論方法可正確有效地分析平板結構附加任意質量的頻域與時域動態行為。基於此理論模型，探討質量陣列的排列分佈對於平板振動特徵及暫態波傳的影響，藉由附加質量陣列改變板結構動態行為的概念，開發平板撓曲波適用之波傳軌跡分析方法，整理撓曲波的群速度與附加質量間的相對關係，藉此控制波速差異改變波傳方向，以便形成特定需求的波傳軌跡，建立其對應的質量陣列。
本文最後也藉此設計方法，依據質量透鏡的波傳目的，計算出可形成特定效果的質量陣列內容，其中包含聚焦、發散與控制波傳方向等，成功實現控制撓曲波能量的目的，對於能量回收、減震等需求將可提供明顯助益。
;This thesis establishes a theoretical analysis method to investigate the vibration characteristics and transient wave propagation behavior of plate structures under the influence of mass effects, including the differences in resonant frequencies and mode shapes of plates with arbitrarily added mass distributions, as well as the transmission paths and energy changes of flexural waves passing through mass arrays, thereby achieving the effect of a mass lens.
The theoretical model first derives an analytical solution for the free vibration of a plate with an attached mass array. After obtaining the vibration characteristics such as resonant frequency and mode shape using the Gorman superposition method, the transient wave propagation theoretical solution is obtained through normal mode method. The theoretical analysis results of vibration characteristics and transient wave propagation are verified by comparison with finite element simulation software. The theoretical analysis of resonant frequency, mode shape, transient displacement, strain, and other physical quantities is highly accurate, confirming that the theoretical method proposed in this study can accurately and effectively analyze the frequency domain and time domain dynamic behavior of plate structures with arbitrarily added mass.
Based on this theoretical model, the influence of the arrangement and distribution of the mass array on the vibration characteristics and transient wave propagation of the plate is investigated. By changing the dynamic behavior of the plate structure through the attached mass array, a wave propagation path analysis method applicable to plate flexural waves is developed. The relationship between the group velocity of flexural waves and the added mass is summarized to control the wave velocity difference to change the wave propagation direction, thereby forming a specific required wave propagation path, and establishing its corresponding mass array.
Finally, based on this design method, the content of the mass array that can form a specific effect, including focusing, divergence, and control of wave propagation direction, is calculated, successfully achieving the purpose of controlling the energy of flexural waves, which can provide significant benefits for energy recovery and vibration reduction. |
