Free vibration analysis of a structural system with a pair of irrational nonlinearities
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TLDR
In this article, an alternative method of deriving accurate and simple analytical approximate solutions to a structural dynamical system governed by a pair of strong irrational restoring forces is presented, where a rational approximation of the nonlinear restoring force function is applied to achieve a convergent truncation.About:
This article is published in Applied Mathematical Modelling.The article was published on 2017-05-01 and is currently open access. It has received 5 citations till now. The article focuses on the topics: Restoring force & Harmonic balance.read more
Citations
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Suppressing homoclinic chaos for a weak periodically excited non-smooth oscillator
TL;DR: In this paper, some new effective methods for suppressing homoclinic chaos in a weak periodically excited non-smooth oscillator are studied, and the main idea is to modify slightly the Melnikov function such that the zeros are eliminated.
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Global dynamics for a class of new bistable nonlinear oscillators with bilateral elastic collisions
TL;DR: In this paper, a new bistable nonlinear oscillator with bilateral elastic constraints and a three-piecewise nonlinear restoring force is established to study the perturbation of viscous damping and an external harmonic excitation.
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Approximate expressions for solutions to two kinds of transcendental equations with applications
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Global dynamics for a class of tristable system with negative stiffness
TL;DR: In this article , the subharmonic bifurcation and chaos of a class of tristable systems with negative stiffness are studied, and the thresholds for homoclinic-heteroclinics chaos and sub-harmonic resonance are derived by using non-smooth Melnikov method.
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Homoclinic-Heteroclinic Bifurcations and Chaos in a Coupled SD Oscillator Subjected to Gaussian Colored Noise
TL;DR: In this paper , the chaos threshold of a coupled smooth and discontinuous (SD) oscillator with Gaussian colored noise was investigated analytically using piecewise linearization to fit the transcendental function.
References
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Potential benefits of a non-linear stiffness in an energy harvesting device
TL;DR: In this article, the benefits of using a non-linear stiffness in an energy harvesting device comprising a mass-spring-damper system are investigated based on the principle of conservation of energy.
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Enhanced Vibrational Energy Harvesting Using Non-linear Stochastic Resonance
TL;DR: In this paper, the authors demonstrate that by adding periodic forcing to a vibrationally excited energy harvesting mechanism, the power available from the device is apparently enhanced over a mechanism without periodic forcing.
Journal ArticleDOI
Archetypal oscillator for smooth and discontinuous dynamics
Qingjie Cao,Marian Wiercigroch,Ekaterina Pavlovskaia,Celso Grebogi,J. Michael T. Thompson,J. Michael T. Thompson +5 more
TL;DR: An archetypal system to investigate transitions from smooth to discontinuous dynamics and has coexisting attractors and also a chaotic saddle which becomes a chaotic attractor when a smoothness parameter drops to zero.
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An analytical approximate technique for a class of strongly non-linear oscillators
Baisheng Wu,W. P. Sun,C.W. Lim +2 more
TL;DR: In this article, an analytical approximate technique for large amplitude oscillations of a class of conservative single degree-of-freedom systems with odd non-linearity is proposed, which incorporates salient features of both Newton's method and the harmonic balance method.
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Internal Resonance Energy Harvesting
Li-Qun Chen,Wen-An Jiang +1 more
TL;DR: In this paper, an electromagnetic device with snap-through nonlinearity is proposed as an archetype of an internal resonance energy harvester, based on the equations governing the vibration measured from a stable equilibrium position, the method of multiple scales is applied to derive the amplitude-frequency response relationships of the displacement and the power in the first primary resonances with the two-to-one internal resonance.