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# Dynamic Model and Simulation of Flag Vibrations Modeled as a Membrane

[+] Author Affiliations
Gary Frey, Ben Carmichael, Joshua Kavanaugh, S. Nima Mahmoodi

The University of Alabama, Tuscaloosa, AL

Paper No. DSCC2014-5897, pp. V003T53A001; 8 pages
doi:10.1115/DSCC2014-5897
From:
• ASME 2014 Dynamic Systems and Control Conference
• Volume 3: Industrial Applications; Modeling for Oil and Gas, Control and Validation, Estimation, and Control of Automotive Systems; Multi-Agent and Networked Systems; Control System Design; Physical Human-Robot Interaction; Rehabilitation Robotics; Sensing and Actuation for Control; Biomedical Systems; Time Delay Systems and Stability; Unmanned Ground and Surface Robotics; Vehicle Motion Controls; Vibration Analysis and Isolation; Vibration and Control for Energy Harvesting; Wind Energy
• San Antonio, Texas, USA, October 22–24, 2014
• Conference Sponsors: Dynamic Systems and Control Division
• ISBN: 978-0-7918-4620-9
• Copyright © 2014 by ASME

## abstract

A flag is modeled as a membrane to investigate the two-dimensional characteristics of the vibration response to an uniform wind flow. Both the affecting tension and pressure functions for the wind flow with constant velocity are introduced and utilized in the modeling. In this case, the tension is caused by the weight of the flag. The pressure function is a function describing the pressure variations caused on the flag when in uniform flow. The pressure function is found by assuming that the air flow is relatively slow and that the flag is wide enough to minimize cross flow at the boundaries. An analysis of the downstream motion of the flag is necessary as well. Hamilton’s principle is employed to derive the partial differential equation of motion. The flag is oriented in the vertical direction to neglect the effect of the flag’s weight on the system’s response. Galerkin’s method is used to solve for the first four mode shapes of the system, and the system response is numerically solved. Simulations reveal a very reasonable model when the flag is modeled as a membrane.

Copyright © 2014 by ASME

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