Journal ArticleDOI
Multiple solutions generated by statistical linearization and their physical significance
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In this paper, the first and second moments of the displacement response were analyzed using the statistical linearization (SL) procedure and the results of an SL analysis were quantitatively compared with the behaviour of digitally simulated sample functions of the response.Abstract:
Three cases are examined where the statistical linearization (SL) procedure can yield multiple solutions for the first and second moments of the response. The first is an oscillator with a hardening non-linear stiffness excited by a narrow-band random excitation, the second is an oscillator with two potential wells excited by wide-band random excitation, and the third is an oscillator where the non-linear features present in the first two problems are combined. The results of an SL analysis are quantitatively compared with the behaviour of digitally simulated sample functions of the displacement response. In all cases a definite correspondence is found between the occurrence of multiple solutions generated by the SL method and the appearance of noticeable jumps in sample functions of the response. In some cases a quantitative agreement exists between the first and second moment values of the multiple solutions and the magnitude of “local” moments of the response.read more
Citations
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Nonlinear vibrations of suspended cables—Part III: Random excitation and interaction with fluid flow
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Dissertation
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Qualitative and quantitative characteristics of parametric ship rolling in random waves in the light of physical model experiments
TL;DR: In this article, an extensive series of experiments on the parametrically excited rolling motion of a partially restrained post-panamax containership in longitudinal irregular long crested waves has been performed at Osaka University.
References
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Journal ArticleDOI
Response of Hard‐Spring Oscillator to Narrow‐Band Excitation
TL;DR: In this article, the response of an oscillator with a nonlinear stiffness of the hard-spring type to narrow band Gaussian random noise is analyzed theoretically by using the method of quasi linearization.
Journal ArticleDOI
Phase plane for narrow band random excitation of a Duffing oscillator
H.G. Davies,D. Nandlall +1 more
TL;DR: In this article, the response of a Duffing oscillator to very narrow band random excitation has been investigated, and it is shown that multiple values of the response can occur at some frequencies for very narrow excitation bandwidths, but these reduce to a single value as the bandwidth is increased.
Journal ArticleDOI
Non-linear resonance in strings under narrow band random excitation, part i: planar response and stability
K. Richard,G.V. Anand +1 more
TL;DR: In this article, a non-linear planar response of a string to planar narrow band random excitation is investigated and a response equation for the mean square deflection σ2 is obtained under a single mode approximation by using the equivalent linearization technique.
Journal ArticleDOI
Narrow-Band Excitation of a Nonlinear Oscillator
W. C. Lennox,Y. C. Kuak +1 more
TL;DR: In this article, a nonlinear oscillator characterized by a hardening-type restoring force is excited by stationary narrow-band noise, and an expression for the probability of the occurrence of jumps is derived.
Journal ArticleDOI
Stochastic response and stability of the Duffing oscillator under narrowband excitation
TL;DR: In this article, the Duffing equation under narrowband Gaussian excitation is studied and almost sure asymptotic stability analysis is used to discuss the realizability of multivalued steady states.