Dynamic Model and Simulation of Flag Vibrations Modeled as a Membrane

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.