L. Cedolin, H.A. Mang, P. Torzicky:

"Dynamic Analysis of Cooling Towers Using a Frontal Based Frequently Solver";

Engineering Structures,2(1980), 3; S. 157 - 162.

Large hyperbolic cooling towers, often exceeding a height of 500 ft, represent a challenge to practioners and researchers in structural analysis. The main reason for this is the influence of dynamic phenomena such as wind and earthquakes on the structural integrity of cooling-tower shells which has only recently become better understood. A good account of these phenomena as well as of analysis techniques for determining the response of coolong-tower shells to wind and earthquake excitations, respectively, is given elsewhere. Basically, there are two methods to calculare the dynamic response of a structure - transient analysis and mode superposition analysis. A recent example applyin transient analysis tot he dynamic response of hyperbolic cooling towers to wind is the work of Steinmetz et al. The mode superposition method is usually preferred in earthquake response analyis. A major ingredient of this method is the solution of the eigenproblem which may be accomplsihed in various ways. Carter et al., for example, have computed frequencies and corresponding mode shapes of cooling towers with the help of the Holzer method. Hashish and Abu-Sitta have solved the same problem by means of the finite difference method. Abel at el. as well as Gould et al. have employed the finite element method using axisymmetric finite elements, for the solution of the eigenproblem and the evaluation of the earthquake response of cooling towers. The authors of reference 8 have taken the flexibility of the supports into account.In this paper, the same curved triangular finite element which has been employed for static and instability analysis of cooling towers, is used for the dynmic analysis of such shells. A particular feature of this element is the existence of a second set of nodal parameters - Lagrangian multipliers - required to establish algebraic constraint conditions for the purpose of enforcing interelement continuity. For an efficient solution of the eigenproblem, a novel scheme for static consideration of massless degrees of freedom is used, which exploits the 'element-oriented' character of the wave front algorithm for Gauss elimination. After describing the method, earthquake response analyses are carried out on a typical tower. A comparison is made with results reported elsewhere.

Keywords: cooling tower

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