THE SQUARE PRISM AS AN AEROELASTIC NON-LINEAR OSCILLATOR

Abstract

A quasi-steady analysis is made of the transverse galloping of a long prism of square section in a normal steady wind. Experimental stationary aerodynamic forces are used in the theory, which leads to an ordinary differential equation with small non-linearity for the displacement. This is solved by the first approximation method of Krylov and Bogoliubov, and it is found that some characteristics of non-linear oscillators unusual in a mechanical system are predicted, in particular the occurrence of oscillation hysteresis over a range of wind speeds. Quite accurate quantitative agreement between these predictions and wind tunnel measurements on an elastically mounted square prism is described.