Free Vibration of Hyperbolic Cooling Towers

A modified finite difference technique is used to determine the natural frequencies and mode shapes of hyperbolic cooling tower shells. The influence of the meridional curvature and the boundary conditions on the vibration characteristics of the tower is investigated. In all cases, changes in frequency are found to be essentially due to changes in membrane energy. It is shown that, for a fixed-free shell, the increased meridional curvature leads to an increase in the natural frequency. The lack of axial restraint results in a large reduction in the membrane energy and consequently the natural frequency. For simply-supported shells, a critical meridional curvature at which the membrane energy effectively vanishes is shown to exist.