A Nonlinear Oscillator Model to Generate Lateral Walking Force on a Rigid Flat Surface

Abstract

This study proposes a single degree of freedom nonlinear oscillator to model the lateral movement of the body center of mass of a pedestrian walking on a flat rigid surface. Experimentally recorded ground reaction force of a dozen of pedestrians in the lateral direction is used to develop the model. In detail, the hardening and softening effects are observed in the stiffness curve as well as higher odd harmonics are present in the frequency spectrum of the lateral force signals. The proposed oscillator is a modification of the Rayleigh and the Van der Pol oscillators with additional nonlinear softening and hardening terms. To obtain an approximation of the limit cycle of the oscillator and its stability, two methods are studied: the energy balance method and the Lindstedt–Poincare perturbation technique. The experimental force signals of pedestrians at four different walking speeds are used for the identification of the values of the model parameters. The results obtained from the proposed model show a good agreement with the experimental ones.