無閥流體驅動現象廣泛存在於工程系統中與生物體內，且為其中工作流體輸送之重要助力、甚或主力。本文中我們考慮以一由兩條硬管連結兩個可延展流體儲存槽所組成之封閉無閥流體迴路，並為其建構了一套分段線性之總括參數數學模型，以期釐清擠壓致動器衝擊效應對無閥流體驅動動態響應的影響，這是長久以來被忽略的重要課題。同時，漸近分析與數值計算結果指出，擠壓頻率以及其他系統參數對於致動器與受壓槽間的交互作用具有重要的影響，進而使得系統動態行為甚為豐富多樣。具體而言，在本文中我們除了利用漸進方法計
算致動器與受壓槽間各種不同的交互作用模式轉換之臨界頻率外，也針對前述數學模型進行有系統的數值參數探討，從而歸納出系統動態響應之可能類型，以及各類型響應所對應之系統參數範圍。不同類型的動態響應，對於系統平均流量將有截然不同的影響；也對平均壓力產生趨勢上的改變。同時，藉由追蹤若干特徵相位角 ( 例如在一擠壓週期中，致動器與受壓槽脫離或碰撞時的相位角 ) 隨擠壓頻率變動之趨勢，我們也明確地指認各類型系統動態響應的關連性與演進過程。同時，系統的穩定性也透過線性穩定度分析法進行探討與歸納。整體而言，我們透過一簡要物理模型，成功解釋擠壓致動器與受壓槽間的交互作用對系統動態響應影響甚鉅，在工程設計實務上，必須謹慎考慮此衝擊效應以達成不同的工程目的。在基礎理論研究方面，也對於無閥流體系統的根本機制探索有更進一步的貢獻。

Valveless pumping assists in fluid transport in various biomedical and engineering systems. Here we focus on one factor that has often been overlooked in previous studies of valveless pumping, namely the impact that a compression actuator exerts upon the pliant part of the system when they collide. In particular, a fluid-filled closed-loop system is considered, which consists of two distensible reservoirs connected by two rigid tubes, with one of the reservoirs compressed by an actuator at a prescribed frequency. A lumped-parameter model with constant coefficients accounting for mass and momentum balance in the system is constructed. Based upon such a model, a mean flow in the fluid loop can only be produced by system asymmetry and the nonlinear effects associated with actuator impact. Through asymptotic and numerical solutions of the model, a systematic parameter study is carried out, thereby revealing the rich and complex system dynamics that strongly depends upon the driving frequency of the actuator and other geometrical and material properties of the system.
In particular, a number of critical frequencies that characterize the interactions between the actuator and the system are calculated asymptotically. Guided by such critical frequencies, the numerical results are categorized into different types of dynamical responses, and the parameter regions for their existence are systematically determined. Moreover, the transition of different system responses are observed through critical phase (which corresponding to the moment when different system responses occur) tracking.

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