Influence of Parameters of Two Pendulums System With an Elastic Element on Regular and Chaotic Vibrations

In this work, a system with two degrees of freedom is studied, consisting of the two coupled pendulums, connected by the element characterized by linear elasticity of rigidity and linear damping. One of the pendulums is subjected to harmonic horizontal excitation. The equations of motion within the studied system are derived as Lagrange’s equations. For small vibrations it was assumed that displacement of the spring element is horizontal only. Exemplary results of the energy transfer, for different parameter values of the system are presented. Numerically, it was indicated that near the internal and external resonance, except different kinds of periodic vibrations, chaotic vibration may also occur. For characterizing an irregular chaotic response, the Poincare maps and maximal exponents of Lyapunov have been constructed.