ASYMPTOTIC RESPONSE OF A 2 DOF ELASTOPLASTIC SYSTEM UNDER HARMONIC EXCITATION - INTERNAL RESONANCE CASE

The study of a two DOF elastoplastic system is formulated in a suitabl e phase space, velocity and force, in which an originally multi-valued restoring force is represented by a proper function. The asymptotic r esponse can thus be studied using the Poincare map concept and avoidin g approximate analytical techniques. On account of the peculiarity of this hysteretic system, which has a well-defined yielding point, its d ynamic is studied in a reduced dimension phase space using an efficien t numerical algorithm. It is shown that the asymptotic response is alw ays periodic with the period of the driven frequency and is always sta ble. Thus the response of the oscillator is described by its frequency response curves at various intensities of the excitation. The results presented refer to a system with two linear frequencies in a ratio of 1 : 3. The response is highly complex with numerous peaks correspondi ng to higher harmonics. The effect of coupling in conditions of intern al resonance is a strong modification of the frequency response curves and of the oscillation shape of the structure.