Frequency response of a cantilevered rectangular sheet under harmonic forced excitation in three-dimensional uniform flow

Abstract

Flexible thin manufactures (sheets) are used in numerous engineering applications. In their manufacturing processes, the sheets are subjected to a fluid flow, and external disturbances can induce vibrations. The vibrations cause severe damage to the sheets. Therefore, an in-depth understanding of the vibration characteristics and excitation mechanism of a sheet in a fluid flow is essential. In this study, the vibration characteristics and excitation mechanism of a sheet under a harmonic forced excitation are investigated by both theoretical calculations and experiments. In the experiments, a harmonic displacement excitation is inputted at the leading edge of a sheet in a wind-tunnel by an exciter using the slider–crank mechanism. In the theoretical analysis, the sheet is modeled as a cantilevered beam, and the fluid force acting on the sheet surface is calculated using three-dimensional theory. The frequency response of the sheet in a uniform flow is investigated with changing the flow velocities and forcing frequencies inputted to the sheet. Finally, the work done by the fluid force acting on the sheet under the harmonic excitation is determined, and the excitation mechanism is discussed.It is found that the flow velocity considerably affects the sheet response. As the flow velocity increases, the amplitude of the second peak of the response becomes larger than that of the first peak. Moreover, the vibration mode of the second peak of the response transforms into a traveling-wave-type mode due to the modal coupling caused by the fluid force.