The effect of fractional damping and time-delayed feedback on the stochastic resonance of asymmetric SD oscillator

Qiubao Wang,Yuejuan Yang,Hao Wu

doi:10.1007/s11071-021-07105-8

Qiubao Wang, Yuejuan Yang + Show 1 more

Open Access

https://doi.org/10.1007/s11071-021-07105-8

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Abstract

This paper proposes the stiffness nonlinearities and asymmetric SD (smooth and discontinuous) oscillator under time-delayed feedback control with the fractional derivative damping. With the effect of displacement and velocity feedback, the oscillator can be adjusted to the desired vibration state, and then the stochastic resonance (SR) is achieved. This article discusses the contribution of various system parameters and time-delayed feedback to SR, especially which induced by fractional order. It should be noted that this paper provides effective guidance for fault diagnosis and weak signal detection, energy harvesting, vibration isolation and vibration reduction.

Highlights

Fault diagnosis, signal detection and vibration control have been active fields of research over the past decades
In order to construct a filter based on SD oscillator for fault diagnosis and signal detection, the stochastic resonance (SR) of the nonlinear stiffness SD oscillator subjected to time delay feedback, asymmetric parameters and fractional damping is studied under the influence of harmonic forcing and Gaussian white noise
285 In this paper, fractional order damping and time-delay feedback are given to control the vibration of asymmetric SD oscillators with stiffness nonlinearities

Summary

Introduction

Signal detection and vibration control have been active fields of research over the past decades. The phenomena of snap-through buckling in engineering was re vealed by Thompson and Hunt [50], who put forward that the SD oscillator was developed based on the shallow arch model It is necessary for the engineering practice needs to study on nonlinear dynamics of oscillator under nonlinear stiffness time-delay feedback control [39]. In order to construct a filter based on SD oscillator for fault diagnosis and signal detection, the SR of the nonlinear stiffness SD oscillator subjected to time delay feedback, asymmetric parameters and fractional damping is studied under the influence of harmonic forcing and Gaussian white noise.

Delay-fractional derivative-controlled stochastic resonance

Signal-to-noise ratio

Weak signal detection

Vibration energy harvesting

Conclusions and discussions