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# Interaction between coexisting orbits in impact oscillators

[+] Author and Article Information
Narasimha Suda

Department of Physical Sciences Indian Institute of Science Education and Research Kolkata Mohanpur campus 741246, India
ssuda555@gmail.com

Soumitro Banerjee

Department of Physical Sciences Indian Institute of Science Education and Research Kolkata Mohanpur campus 741246, India
soumitro@iiserkol.ac.in

1Corresponding author.

ASME doi:10.1115/1.4036712 History: Received December 01, 2016; Revised May 01, 2017

## Abstract

Impact oscillators exhibit an abrupt onset of chaos close to grazing due to the square root singularity in their discrete-time maps. In practical applications, this large-amplitude chaotic vibration needs to be avoided. It has been shown that this can be achieved if the ratio of the natural frequency of the oscillator and the forcing frequency is an even integer. But in practice it is difficult to set a parameter at such a precise value. We show that in systems with square root singularity (pre-stressed impacting surface), there exists a range of $\omega_0$ around the theoretical value over which the chaotic orbit does not occur, and that this is due to an interplay between the main attractor and coexisting orbits. We show that this range of forcing frequency has exponential dependence on the amount of pre-stress as well as on the stiffness ratio of the springs.

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