Vibration of thin, tensioned, helically wrapped plates

Free vibration analysis of a thin tensioned plate, wrapped around a cylindrical guide in a helical manner is presented. The system is a model of a thin, flexible web wrapped around a turn-bar. The equation of motion of the wrapped plate is derived by using the energy method and with the Kirchhoff–Love assumptions. The weak form of the equation of motion was obtained by the finite element method and the eigenvalue problem was solved numerically. The effects of parameters such as plate tension, guide radius, longitudinal and helical wrap angles, plate width, and the lengths of the non-wrapped segments were investigated. Eigenmodes with same mode numbers were observed in symmetric and anti-symmetric fashion about the center of the plate, for symmetrically wrapped plates. It was shown that the plate/shell boundary of the wrapped plate effectively acts like a support. For non-helically wrapped plates the free edges cause a frequency clustering of the lateral modes about the dominant longitudinal mode. The frequency clustering diminishes when helical wrap is introduced.