Resonant response functions for nonlinear oscillators with polynomial type nonlinearities

Xin, Zhenfang; Neild, Simon A; Wagg, DJ; Zuo, Zhengxing

doi:10.1016/j.jsv.2012.09.022

Cited by 12 publications

(12 citation statements)

References 24 publications

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“…Following the procedure in Neild and Wagg 2011, or using the general solution for polynomial nonlinearities reported in Xin et al 2013, the amplitude of the oscillation can be related to the input excitation by…”

Section: Analytical Modelmentioning

confidence: 99%

Optimum resistive loads for vibration-based electromagnetic energy harvesters with a stiffening nonlinearity

Cammarano

Neild

Burrow

et al. 2014

Journal of Intelligent Material Systems and Structures

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The exploitation of nonlinear behavior in vibration-based energy harvesters has received much attention over the last decade. One key motivation is that the presence of nonlinearities can potentially increase the bandwidth over which the excitation is amplified and therefore the efficiency of the device. In the literature, references to resonating energy harvesters featuring nonlinear oscillators are common. In the majority of the reported studies, the harvester powers purely resistive loads. Given the complex behavior of nonlinear energy harvesters, it is difficult to identify the optimum load for this kind of device. In this paper the aim is to find the optimal load for a nonlinear energy harvester in the case of purely resistive loads. This work considers the analysis of a nonlinear energy harvester with hardening compliance and electromagnetic transduction under the assumption of negligible inductance. It also introduces a methodology based on numerical continuation which can be used to find the optimum load for a fixed sinusoidal excitation.

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Section: Analytical Modelmentioning

confidence: 99%

Optimum resistive loads for vibration-based electromagnetic energy harvesters with a stiffening nonlinearity

Cammarano

Neild

Burrow

et al. 2014

Journal of Intelligent Material Systems and Structures

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“…Following the approach of [20], but using a complex exponential rather than trigonometric representation, we then writë…”

Section: Stability Of the Backbone Curvesmentioning

confidence: 99%

“…The stability of the zero-solution can then be assessed by considering the eigenvalues of the matrix of derivatives of f , f U1 , about the equilibrium solution U 1 = 0, see [20], calculated from…”

Section: Stability Of the Backbone Curvesmentioning

confidence: 99%

Bifurcations of backbone curves for systems of coupled nonlinear two mass oscillator

et al. 2014

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This paper considers the dynamic response of coupled, forced and lightly damped nonlinear oscillators with two degree-of-freedom. For these systems, backbone curves define the resonant peaks in the frequency-displacement plane and give valuable information on the prediction of the frequency response of the system. Previously, it has been shown that bifurcations can occur in the backbone curves. In this paper we present an analytical method enabling the identification of the conditions under which such bifurcations occur. The method, based on second order nonlinear normal forms, is also able to provide information on the nature of the bifurcations and how they affect the characteristics of the response.This approach is applied to a two-degree-of-freedom mass, spring, damper system with cubic hardening springs. We use the second-order normal form method to transform the system coordinates and identify which parameter values will lead to resonant interactions and bifurcations of the backbone curves. Furthermore, the relationship between the backbone curves and the complex dynamics of the forced system is shown.

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“…Nonlinear oscillator models represent a wide class of dynamic systems in many areas of physics and engineering [1][2][3]. For example, the classic Duffing model for mechanical systems [4,5], the delayed-reaction model for sensors and actuators [6], the time-varying mass model for crane and bridge cables [7], the M-shaped bent-beam model [8], and the coupled linear-nonlinear oscillator model [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

A fast continuation scheme for accurate tracing of nonlinear oscillator frequency response functions

Chen

Dunne

2016

Journal of Sound and Vibration

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A new algorithm is proposed to combine the split-frequency harmonic balance method (SF-HBM) with arc-length continuation (ALC) for accurate tracing of the frequency response of oscillators with non-expansible nonlinearities. ALC is incorporated into the SF-HBM in a two-stage procedure: Stage I involves finding a reasonably accurate response frequency and solution using a relatively large number of low-frequency harmonics. This step is achieved using the SF-HBM in conjunction with ALC. Stage II uses the SF-HBM to obtain a very accurate solution at the frequency obtained in Stage I. To guarantee rapid path tracing, the frequency axis is appropriately subdivided. This gives high chance of success in finding a globally optimum set of harmonic coefficients. When approaching a turning point however, arc-lengths are adaptively reduced to obtain a very accurate solution. The combined procedure is tested on three hardening stiffness examples: a Duffing model; an oscillator with non-expansible stiffness and single harmonic forcing; and an oscillator with nonexpansible stiffness and multiple-harmonic forcing. The results show that for non-expansible nonlinearities and multiple-harmonic forcing, the proposed algorithm is capable of tracingout frequency response functions with high accuracy and efficiency.

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Resonant response functions for nonlinear oscillators with polynomial type nonlinearities

Cited by 12 publications

References 24 publications

Optimum resistive loads for vibration-based electromagnetic energy harvesters with a stiffening nonlinearity

Optimum resistive loads for vibration-based electromagnetic energy harvesters with a stiffening nonlinearity

Bifurcations of backbone curves for systems of coupled nonlinear two mass oscillator

A fast continuation scheme for accurate tracing of nonlinear oscillator frequency response functions

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