Vibrations of Steel-Lined Concrete Chimneys

The mode shapes and the natural frequencies for the first four fundamental modes of vibration are calculated for tall reinforced concrete chimneys with independent steel liners. The results seem to indicate that for each mode of an unlined chimney there is a mode of near equal frequency for the same chimney with steel liner and that the mode shape of the concrete shell is nearly the same for both cases. The lined chimney, however, could have additional frequencies spaced between those frequencies described above depending primarily on the ratio of the length of the liner to that of the concrete shell. The modes are computed by using the Stodola numerical procedure and are based on the Bernoulli-Euler flexural theory. Shear deformations and rotary inertia effects are ignored. Graphs are presented to illustrate the variations of the modes with the major parameters of the problem.