PERIODIC COMBINATION RESONANCE IN A NONLINEAR-SYSTEM OF NONPRISMATIC RODS

The parametric optimization of a plane system of non-prismatic viscoelastic rods subjected to conditions of combination resonance is considered. Because of couplings of the rods through periodically changing internal forces, the combination resonance has an autoparametric nature. In the equations of motion for non-prismatic rods, non-linear terms connected with damping and having a geometrical nature appear. The mathematical analysis of the equations was accomplished by using Tondl's method. In the optimization a few objective functions connected with amplitudes are taken into account. The paper deals with the analysis of the influence of some of the rod shape parameters upon the objective function. In the optimization the total mass of the system is constant. For optimal (minimal) values of the objective functions the optimal values of parameters connected with the shapes of the rods are obtained.