[Paper Review] Fast, large amplitude vibrations of compliant cylindrical shells carrying a fluid

Pawel Zimoch, Eliott Tixier+3 more|arXiv (Cornell University)|Oct 15, 2012

Vibration and Dynamic Analysis1 references3 citations

TL;DR

This study investigates fast, large-amplitude vibrations in compliant cylindrical shells (made of vinylpolysiloxane or latex) carrying internal air flow, demonstrating the first three circumferential modes of instability. When air flow exceeds a critical threshold, the shells undergo self-excited oscillations: the first mode exhibits side-to-side 'garden hose' motion at ~15 Hz, the second mode shows inward buckling with frequencies of 200–700 Hz directly proportional to flow rate, and the third mode features three flapping segments vibrating at 600–1000 Hz.

ABSTRACT

In this fluid dynamics video, we demonstrate the first three circumferential modes of fast, large amplitude vibrations of compliant cylindrical shells carrying a fluid.

Motivation & Objective

• To experimentally investigate large-amplitude, high-frequency vibrations in compliant cylindrical shells under internal fluid flow.
• To identify and characterize the onset and behavior of distinct circumferential vibration modes in flexible shells.
• To determine the dependence of oscillation frequency on fluid flow rate and shell mechanical/geometry parameters.
• To explore the stability and robustness of different vibrational modes across a range of material and geometric configurations.

Proposed method

• Fabricated compliant cylindrical shells from vinylpolysiloxane (0.2–1.0 MPa elastic modulus) and latex with controlled dimensions (5–10 mm diameter, 5–50 mm length, 0.1–0.2 mm thickness).
• Clamped one end of each shell onto a rigid nozzle and passed air through at flow rates from 0.2 to 2.5 L/s to induce flow-induced instability.
• Used a Phantom v5.2 high-speed color camera to capture dynamic behavior, applying stroboscopic imaging to reconstruct phase-advanced frames for slow-motion visualization.
• Identified vibration modes by analyzing spatial and temporal patterns in the captured sequences, correlating mode shape with shell properties and flow rate.
• Measured oscillation frequencies and pressure drops across the nozzle to quantify dynamic response and instability thresholds.
• Correlated observed modes with theoretical circumferential normal modes of clamped cylindrical shells, validating experimental observations.

Experimental results

Research questions

• RQ1 What are the distinct circumferential vibration modes that emerge in compliant cylindrical shells under internal fluid flow?
• RQ2 How does the oscillation frequency of these modes scale with increasing air flow rate?
• RQ3 Which mode is most robust and observable across the widest range of shell parameters?
• RQ4 What is the relationship between shell mechanical properties (elastic modulus) and the onset of instability?
• RQ5 How do pressure drop changes correlate with the second mode’s inward buckling behavior?

Key findings

• The first mode, resembling a 'garden hose' motion, occurs at approximately 15 Hz and involves lateral side-to-side oscillation of the shell.
• The second mode features inward bending of the shell surface, causing a significant pressure drop increase and oscillating at 200–700 Hz, with frequency directly proportional to air flow rate.
• The second mode is the most robust and observable across the broadest range of shell geometries and material properties.
• The third mode exhibits three distinct flaps on the free end oscillating in and out, with frequencies ranging from 600–1000 Hz.
• In the second mode, the oscillation frequency varies widely between cycles, indicating dynamic instability despite a mean frequency trend.
• High-speed stroboscopic imaging enabled the creation of a slow-motion video by concatenating frames from different oscillation phases, enhancing visualization of transient dynamics.