Topic
Nonlinear resonance
About: Nonlinear resonance is a research topic. Over the lifetime, 2633 publications have been published within this topic receiving 43350 citations.
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01 Jan 1950
TL;DR: In this article, the authors studied the stability of nonlinear oscillations with nonlinear restoring forces free oscillations and nonlinear self-sustained oscillations using the Hill's equation.
Abstract: Linear vibrations free vibrations of undamped systems with nonlinear restoring forces free oscillations with damping and the geometry of integral curves forced oscillations of systems with nonlinear restoring force self-sustained oscillations Hill's equation and its application to the study of the stability of nonlinear oscillations.
704 citations
TL;DR: In this paper, the authors reviewed the overall progress in nonlinear ultrasonic technique with the brief introduction of basic principle in the application of each nonlinear Ultrasonic phenomenon, including higher harmonic generation, subharmonic generation, nonlinear resonance, or mixed frequency response.
Abstract: The nondestructive assessment of the damage that occurs in components during service plays a key role for condition monitoring and residual life estimation of in-service components/structures. Ultrasound has been widely utilized for this; however most of these conventional methods using ultrasonic characteristics in the linear elastic region are only sensitive to gross defects but much less sensitive to micro-damage. Recently, the nonlinear ultrasonic technique, which uses nonlinear ultrasonic behavior such as higher-harmonic generation, subharmonic generation, nonlinear resonance, or mixed frequency response, has been studied as a positive method for overcoming this limitation. In this paper, overall progress in this technique is reviewed with the brief introduction of basic principle in the application of each nonlinear ultrasonic phenomenon.
581 citations
31 Jul 1996
TL;DR: The method of non-smooth temporal transformations (NSTTs) nonlinear localization in Discrete Oscillators (DOS) has been used for NNMs in continuous systems as discussed by the authors.
Abstract: NNMs in Discrete Oscillators: Qualitative Results Stability and Bifurcations of NNMs Resonances of Discrete Systems Close to NNMs The Method of Non-Smooth Temporal Transformations (NSTTs) Nonlinear Localization in Discrete Systems NNMs in Continuous Systems Nonlinear Localization in Systems of Coupled Beams Nonlinear Localization in Other Continuous Systems.
540 citations
536 citations
TL;DR: In this paper, the authors experimentally demonstrate the occurrence of optical Bloch oscillations in a waveguide array with linearly growing effective index of the individual guides and observe a periodic transverse motion of the field and complete recovery of the initial excitation.
Abstract: We experimentally demonstrate the occurrence of optical Bloch oscillations in a waveguide array with linearly growing effective index of the individual guides. We monitored the output profiles for varying propagation lengths and observed a periodic transverse motion of the field and a complete recovery of the initial excitation. The action of the focusing nonlinearity leads to a loss of recovery, symmetry breaking, and power-induced beam spreading.
504 citations