Internal resonance in a plane system of rods

The transverse vibrations of a plane system of rods is considered. The analysis of internal resonance in the system is a primary purpose of the paper. The internal resonance analyzed has an autoparametric nature. The couplings of the elements of the system through internal longitudinal forces, which are transverse forces at the ends of neighbouring rods, are taken into account. The amplitudes of the vibrations in the stationary states of internal resonance are investigated. Non-linear terms appear in the equations of motion. These terms are non-linear damping and non-linear inertia, and have a geometrical nature. The approximate method of calculation gives formulae for the vibration amplitudes of the rods. Plots of the amplitudes against frequency are presented. The stabilizing effect of masses placed at the articulated joints of the system is shown. The influences of the inertia and damping values on the character of the curves is considered. The results obtained are of a qualitative character.