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Chaotic oscillations in a simple collapsible-tube model.

¹Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK.

Journal of Biomechanical Engineering

|February 1, 1992

Summary

Flow instabilities in collapsible tubes can cause self-excited oscillations. Numerical simulations reveal large amplitude oscillations with relaxation structures and complex behaviors, matching experimental findings.

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Area of Science:

Fluid dynamics
Mechanical vibrations
Nonlinear dynamics

Background:

Externally pressurized collapsible tubes are prone to flow instabilities.
Self-excited oscillations can arise from the interaction between internal flow and tube walls.
Previous models predicted steady flows and multiple oscillation modes.

Purpose of the Study:

To numerically investigate a one-dimensional model of collapsible tube flow.
To analyze the behavior of large amplitude oscillations.
To explore nonlinear interactions between different oscillation modes.

Main Methods:

Numerical investigation of a one-dimensional model.
Analysis of steady flow and oscillation modes.
Examination of large amplitude oscillations and nonlinear interactions.

Main Results:

Large amplitude oscillations exhibit a relaxation structure.
Nonlinear interactions lead to quasiperiodic and aperiodic behaviors.
Numerical predictions align well with experimental observations.

Conclusions:

The one-dimensional model effectively captures complex flow dynamics in collapsible tubes.
Nonlinear interactions are crucial for understanding emergent oscillatory behaviors.
The study validates numerical predictions against experimental data.

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