Vibrations and dynamical stability of nonlinear system of rods to biharmonic excitations

In this paper, the method of internal resonances in a system of rods under vertical kinematic biharmonic excitation is presented. The elements of the system are connected with articulated joints. The couplings of the elements of the system through internal longitudinal forces, which are parametrical, are taken into account. The analysis of such objects under kinematic excitation may have essential significance in the study of paraseismic phenomena. The fundamental problem is to choose the appropriate model of the described object (structures, buildings, mechanical devices and mechanisms). The model includes some important properties of the object in the particular situation. The autoparametric phenomena can play an essential role in the processes of destruction of described objects. The equations of motion are obtained from Lagrange's equations and the harmonic balance method is applied. Nonlinear terms appear in the equations of motion. These terms are nonlinear damping and nonlinear inertia and have a geometric nature. The amplitudes of the vibrations in the stationary states of internal resonance are investigated. Plots of the amplitudes against frequency are presented.