A generalized frequency detuning method for multidegree-of-freedom oscillators with nonlinear stiffness

Neild, Simon A; Wagg, DJ

doi:10.1007/s11071-013-0818-7

Cited by 16 publications

(25 citation statements)

References 19 publications

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“…the mechanical damping is the only loss mechanism in the system), the nonlinear elastic force can be of the same order of magnitude as the linear elastic force. However this does not affect the computation of the primary response (see Neild and Wagg 2013). To confirm this, an error analysis is presented in Section 3.5.…”

Section: Analytical Modelmentioning

confidence: 75%

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: 75%

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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“…Furthermore, the technique may be extended to include harmonic responses and may be computed to a higher-order of accuracy [23]; however, for the response range considered here, a good level of accuracy is achieved without these extensions.…”

Section: Backbone Curves Of An Example Systemmentioning

confidence: 99%

Interpreting the forced responses of a two-degree-of-freedom nonlinear oscillator using backbone curves

Hill

Cammarano

Neild

et al. 2015

Journal of Sound and Vibration

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a b s t r a c tIn this paper the backbone curves of a two-degree-of-freedom nonlinear oscillator are used to interpret its behaviour when subjected to external forcing. The backbone curves describe the loci of dynamic responses of a system when unforced and undamped, and are represented in the frequency-amplitude projection. In this study we provide an analytical method for relating the backbone curves, found using the second-order normal form technique, to the forced responses. This is achieved using an energy-based analysis to predict the resonant crossing points between the forced responses and the backbone curves. This approach is applied to an example system subjected to two different forcing cases: one in which the forcing is applied directly to an underlying linear mode and the other subjected to forcing in both linear modes. Additionally, a method for assessing the accuracy of the prediction of the resonant crossing points is then introduced, and these predictions are then compared to responses found using numerical continuation.

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“…The left column shows the two distinct backbone curves corresponding to solutions S1 and S2, see Eqs. (16) and (17). For this case κ < 4κ 2 and so no further real solutions exist.…”

Section: Backbone Curvesmentioning

confidence: 80%

“…Here the method is presented in its most general formulation; however detailed discussions are given in [16,17]. This approach can give valuable insight into the physics of the observed behaviour, as will be seen in Section 3.…”

Section: Methodsmentioning

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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A generalized frequency detuning method for multidegree-of-freedom oscillators with nonlinear stiffness

Cited by 16 publications

References 19 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

Interpreting the forced responses of a two-degree-of-freedom nonlinear oscillator using backbone curves

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

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