Bifurcation phenomena and statistical regularities in dynamics of forced impacting oscillator

Sergii Skurativskyi,Jan Awrejcewicz,Grzegorz Kudra,Krzysztof Witkowski

doi:10.1007/s11071-019-05286-x

Sergii Skurativskyi, Jan Awrejcewicz + Show 2 more

Open Access

https://doi.org/10.1007/s11071-019-05286-x

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Journal: Nonlinear Dynamics	Publication Date: Oct 19, 2019
Citations: 13	License type: open-access

Affiliation: Lodz University of Technology

Abstract

The paper is devoted to the study of harmonically forced impacting oscillator. The physical model for oscillator is a cart on a guide connected to the support with springs and excited by the stepper motor. The support also is provided with limiter of motion. The mathematical model for this system is defined with the second-order piecewise smooth differential equation. Model’s nonlinearity is connected with the incorporation of dry friction and generalized Hertz contact law. Analyzing the classical Poincare sections and inter-impact sequences obtained experimentally and numerically, the bifurcations and statistical properties of periodic, multi-periodic, and chaotic regimes were examined. The development of impact-adding regime as a new nonlinear phenomenon when the forcing frequency varies was observed.

Highlights

A large number of artificial devices and natural systems contain oscillating elements, dynamics of which essentially affect [1,2] the parent system
There are observed jumps between the extensions of the branches corresponding to the long inter-impact intervals
Bifurcation diagrams consist of Poincare maps defined in standard way, i.e., they are based on sampling the position of the cart every period of external forcing (Fig. 3a) and inter-impact intervals (Fig. 3b)

Summary

Introduction

A large number of artificial devices and natural systems contain oscillating elements, dynamics of which essentially affect [1,2] the parent system. Springs and dash-pots as structural elements are used To model their dynamics, the smooth mathematical models are applied, for studies of which the powerful analytical and numerical tools have been developed. Incorporation of dry friction and impact rheologic elements into vibration systems allows one to describe a wider range of physical processes. The attractors inherent in the smooth models can be endowed by new properties Such models can demonstrate special types of evolution including border-collision bifurcations [10,15,16,17,18] and chattering phenomena [19].

Experimental stand and mathematical model

Experimental and preliminary simulation results

The system behavior at low frequencies

Concluding remarks

Compliance with ethical standards