Non-linear dynamics of asymmetric structures under 2:2:1 resonance

The non-linear dynamic behavior of a novel model of a single-story asymmetric structure under earthquake and harmonic excitations and near two-to-one internal resonance is investigated. The non-linearities of the proposed model, ignored in conventional linear models, are caused by non-linear inertial coupling between translational and torsional degrees of freedom defined in the directions of a non-inertial rotational system of reference, attached to the center of mass of the floor. The multiple scales method is used to achieve approximately linear solutions for the originally non-linear equations near a two-to-one ratio of external and internal resonant conditions. The suitability of the proposed model is justified by the similarity between the simulated response of the non-linear model and the experimental results. The numerical results of time history and frequency domain analyses illustrate the difference between the non-linear and linear models. Energy transfer from a lower natural frequency excited mode to a higher one due to non-linear interaction in the novel model is shown. The effects of amplitude, frequency detuning parameters, uncoupled lateral and torsional frequencies, and damping ratio on the responses are inspected and some non-linear phenomena such as hysteresis, jumping, hardening, and softening are observed. ► We present a novel model for ground excited motions of asymmetric structure. ► The suitability of the proposed model is justified by the experimental results. ► 2:1 internal and external resonance between perpendicular natural modes happens. ► Transfer energy, jump, hysteretic and Hopf bifurcation are observed. ► Effects of lateral and torsional damping and stiffness on modal response are inspected.