Engineering Transactions, 48, 1, pp. 73–94, 2000

Objective Functions in Monocriterial and Multicriterial Optimizations Problems Against a Loss of Dynamic Stability

A. Foryś
Cracow University of Technology
Poland

J. Snamina
Cracow University of Technology
Poland

The paper concerns the specification and comparison of numerical examples of optimization of beams in the state of periodic parametric resonance with respect to different measures of the phenomena considered, i.e., with respect to different optimization criteria – some objective functions in monocriterion and multicriterial optimization. A formulation of monocriterion and multicriterial optimization problems for mechanical elements, subjected to a parametrically exciting force periodic in time, is given. In multicriterial optimization the scalar objective functions characterizing the parametric resonance are introduced. The paper deals with the problems of finding the control function – function of the shape (the area of cross-section of the beam) which maximizes or minimizes the objective functions under the constraint of constant volume. In some cases the optimization problems under conditions of parametric resonance reduce to the optimization problems with respect to natural frequency. The examples of parametric optimization against loss of stability are solved and analysed.
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