Vibrational and stochastic resonances in driven nonlinear systems: part 2

Abstract

Nonlinearity is ubiquitous in both natural and engineering systems. The resultant dynamics has emerged as a multidisciplinary field that has been very extensively investigated, due partly to the potential occurrence of nonlinear phenomena in all branches of sciences, engineering and medicine. Driving nonlinear systems with external excitations can yield a plethora of intriguing and important phenomena—one of the most prominent being that of resonance. In the presence of additional harmonic or stochastic excitation, two exotic forms of resonance can arise: vibrational resonance or stochastic resonance, respectively. Several promising state-of-the-art technologies that were not covered in part 2 of this theme issue are discussed here. They include inter alia the improvement of image quality, the design of machines and devices that exert vibrations on materials, the harvesting of energy from various forms of ambient vibration and control of aerodynamic instabilities. They form an important part of the theme issue as a whole, which is dedicated to an overview of vibrational and stochastic resonances in driven nonlinear systems. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 2)’.

Stochastic parametric excitation of convective heat transfer

“…Consider the case of high-frequency modulation of parameters, where σ ξ(t) = σ Ω cos Ωt in equation system (3.1), Ω |L jk | [14][15][16]. Not only the deterministic vibrational fluid dynamics is a versatile and well-developed subject area [14][15][16][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47] but also in the field of nonlinear dynamics the phenomenon of stochastic resonance found its deterministic counterpart-the vibrational resonance [48][49][50], which was also studied in fluid dynamical systems [47].…”

Frequency modulated signal standing out by stochastic resonance effect

“…Noise can help amplify the signal. This phenomenon is known as stochastic resonance (SR) [4,7,10,16]. The SR effect presents the response to the weak input signal, in a non-linear system.…”

Delay-Induced Vibrational Resonance in Rayleigh-Plesset Bubble Oscillator

“…Among the various forms of nonlinear resonance occurring in mechanical, electrical and biological systems, stochastic and vibrational resonance phenomena are of particular interest and importance. They are strongly connected because dual-frequency forcing is required in each case for their occurrence [9,47,85,86]. Stochastic resonance is induced by noise driving [24,28]; while vibrational resonance is a deterministic phenomenon that occurs when there is cooperation between lowfrequency and high-frequency harmonic forces driving a nonlinear system [1,12,49,65].…”