Free vibration, stability and “non-classical modes” of cooling tower shells

Abstract

A ring and a shell finite element for the analysis of free vibration of shells of revolution and cooling tower shells are described. In the formulation of the ring element the effects of initial in-plane stresses are included so that both vibration and stability of the shells can be studied. For both elements, a variation of the shell thickness along the meridian is considered. The two elements are used to analyse a hyperboloid and a tower similar to those at Didcot Power Station. The results agree well with those obtained by other methods for the case when no singularities (such as legs) are introduced. It is found that no “non-classical” modes of vibration exist when the shell is completely rotationally symmetric without any singularities. The effects introduced by the legs of the cooling tower are studied by omitting parts of the shell near the base. It is shown that the natural frequencies are lower than for the complete shell, and that there are “non-classical” modes of vibration. It is shown that increasing the thickness in the lower part of the tower raises the natural frequencies, and that the self load stresses have only a marginal effect on the vibration and stability of the towers. It is also shown that lack of complete restraint at the base of a shell can greatly reduce the critical stress.