Numerical study on the response scenarios in a vibro-impact single-degree-of-freedom oscillator with two unilateral dissipative and deformable constraints

Abstract

In this paper, some of the scenarios that can occur in the numerical nonlinear non-smooth response of a vibro-impact single-degree-of-freedom system, symmetrically constrained by deformable and dissipative bumpers, were identified and described. The different scenarios, obtained varying selected dimensionless parameters, were investigated identifying homogeneous frequency intervals, characterized by similar features in terms of number and types of limit cycles, and resorting to phase portraits, basins of attraction and Fourier spectra. Despite the relative simplicity of the model, which however takes into account impact, clearance and unilaterality of the constraints, decreasing the dimensionless gap δ0, from δ0=1 to δ0=0, gradually more complex and varied scenarios, characterized by different types of secondary resonances (with right or left hysteresis or of non-regular type), cascades in the low frequency range, periodic, quasi-periodic or chaotic solutions were observed. The occurrence of primary and secondary grazing was also highlighted.