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Dynamical investigation of a multirhythmic vibroimpact self-sustained system with enhanced memory damping regime according to correlated noise excitation
Phys. Rev. E 114, 054214 – Published 12 November, 2026
DOI: https://doi.org/10.1103/xfdr-m6j4
Abstract
Investigating the dynamics of vibroimpact self-sustaining systems is of immense scientific interest, because systems that undergo vibroimpact interactions can be found in various engineering contexts. Repercussions and associated noise are prevalent in mechanical engineering. Conversely, in a self-sustaining system including viscoelastic material, the damping component is influenced not only by the current time and position, but also by previous states. The memory property of viscoelastic materials is determined by an exponential relaxation function and noise. Based on this viewpoint, this study investigates a self-sustained birhythmic vibroimpact oscillator with improved memory damping subjected to correlated noise. In the beginning, the nonsmooth transformation is implemented to eliminate the discontinuity in the vibroimpact oscillator. The detailed feature space analysis reveals that the correlation time and vibroimpact coefficient can effectively control the oscillator's rhythmic characteristics. To identify the maximal birhythmic zone in parameter space, select an approximate restitution coefficient and correlated noise intensity. In a stochastic environment, decreased noise intensity reduces the essential quantity of the vibroimpact coefficient and control parameters required for birhythmicity. The Rayleigh oscillator is a traditional nonlinear dynamics paradigm, and varying the nonlinear Rayleigh parameters together with vibroimpact coefficients enables control of the nonlinear dynamic multirhythmic system. The reported results demonstrate how the strength of correlated noise, correlation time, restitution coefficient, and system characteristics influence the transition from one potential well to another, and Monte Carlo simulation is used to confirm the stochastic generalized method's effectiveness. Furthermore, for this self-sustaining system, the method of recurrence plots is employed for numerical time series analysis, and the impacts of the restitution coefficient and noise correlation time on recurrence quantification have been demonstrated.
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