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Random Excitation of a Non-Linear System with Hysteresis

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A non-linear system is considered which is subjected to a random excitation whose restoring force exhibits hysteresis.

The investigation is performed by taking as a model an electrical circuit (a resonant parallel circuit) but the results could be extended by analogy to the case of a mechanical system. The simple hysteresis model proposed by Hayashi has been used in the case of sinusoidal excitation; this model allows one to write a differential equation which admits of an integrable Fokker-Planck equation. Various statistical quantities are evaluated and are compared with the results given by another method. The principal conclusions are as follows: the evidence with regards to the non-linear oscillator without hysteresis is that the response is always very feeble; in the case where the excitation consists of a sinusoidal signal and Gaussian white noise, the evidence is that the ratio of the useful part of l the response to that of the noise is improved.
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Document Type: Research Article

Publication date: January 1, 1966

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  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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