On an objective function in optimization problems with a loss of dynamic stability

The paper concerns optimization problems at the loss of dynamic stability. The transverse vibrations of a few periodically loaded rods for different boundary conditions are considered. The rods have variable cross-sections and are made of viscoelastic material. Parameters determining the shape of the rods are defined. The aim of the paper is to introduce an objective function which is a measure of dynamic instability region. Hitherto for similar systems the amplitude of the exciting force oscillating term was the objective function. It appears that the optimality of system depends upon the objective function. The problem of system optimization at a parametric resonance is a complicated one – a few objective functions must be taken into account. The paper indicates some problems. The considerations are limited to a one-degree-of-freedom problem which needs further analysis.