Dynamics of collapsible tubes connected in series

Collapsible tubes arise in various physiological and engineering systems, such as blood vessels, respiratory airways, and flexible pipelines, where flow-induced instabilities significantly affect performance and function. Understanding their dynamics is essential for predicting and controlling self-excited oscillations in such compliant systems. This study investigates the non-linear fluid-structure interaction dynamics of two collapsible tubes connected in series and subjected to flow-induced oscillations. Experimental observations reveal various dynamical behaviors, including single- and multi-frequency periodic and aperiodic oscillations across varying Reynolds numbers. The oscillatory regime is strongly influenced by downstream resistance (Rd) and external pressure (Pext). A reduced-order mathematical model is developed and numerically solved to replicate the observed dynamics qualitatively. A comprehensive bifurcation analysis of the model reveals a rich sequence of transitions, including supercritical Hopf, torus (Neimark–Sacker), and homoclinic bifurcations, leading to diverse oscillatory regimes such as period-1 oscillations, quasiperiodic motion, multi-frequency oscillations, and chaotic responses (as evidenced by the positive Lyapunov exponent). The increase in Rd narrows the oscillatory regime, enhances oscillation amplitudes, and lowers the dominant frequency. At the same time, reduced Pext similarly compresses the range of oscillatory behavior, lowers the dominant frequency, and eliminates chaotic responses. The theoretical predictions show good qualitative agreement with the experimental findings, demonstrating the robustness of the model in capturing the key features of the non-linear behavior of the system.