Free Vibrations of Hyperboloidal Shells of Revolution

Abstract

A bending theory of shells is used to determine natural frequencies and mode shapes of a hyperboloid of one sheet. Since these shells are commonly used for cooling towers, the character of the free vibration is of interest. The problem is formulated for a general shell of revolution of which the hyperboloid is considered as a special case. A generalization of the Holzer method is used to solve the eigenvalue problem, and the governing differential equations are integrated numerically with the aid of a technique for suppressing rapidly growing solutions.