Resonant and coupled response of hysteretic two-degree-of-freedom systems using harmonic balance method

The response of two-degree-of-freedom chain systems with elements which have hysteretic restoring force, is studied under sinusoidal imposed motion. The hysteretic behavior of the elements are described by the Masing model. Since attention is focused on the periodic response, the multi-component harmonic balance method is used to evaluate the solution. This method, combined with a path-following algorithm, is a robust tool capable of accurately describing the frequency response curves, which are particularly complex in some frequency range due to the strong non-linearities and non-linear modal coupling. The influence of hysteretic law parameters is investigated, and, in particular, the ratio between the two natural frequencies. It is shown that the coupling is very notable not only for the system in internal resonance condition 1:3, but also for the system with a ratio between the two natural frequencies in a large range around 3. The frequency response curves exhibit generally a number of resonance peaks greater than the number of degrees-of-freedom. The description of the oscillation shape at resonances is likely to furnish a complete picture of the response of the systems. © 2002 Elsevier Science Ltd. All rights reserved.