Use of the Harmonic Balance Method to Analyse Systems with Nonlinear Resonators

Resumo

The mitigation of mechanical vibrations in specific applications and frequency ranges can be effectively achieved using resonators, as demonstrated by locally resonant metamaterials. A key challenge in this approach lies in accurately predicting system behaviour during the modelling stage, which requires the appropriate selection of analysis methods. This choice depends on the system’s characteristics and aims to balance accuracy with computational efficiency. Focusing on a finite system of linear oscillators coupled with nonlinear resonators, the present study initiates an investigation into the suitability of the Harmonic Balance method to meet these objectives. To assess the method’s capabilities, the influence of excitation amplitude on the system’s response is examined. Additionally, the stability of the responses is evaluated using Hill’s method.