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Three different dissipation models have been used to identify the increase of damping with the vibration amplitude for a rubber rectangular plate. For this purpose, a square rubber plate made of silicone with fixed edges has been ...
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Three different dissipation models have been used to identify the increase of damping with the vibration amplitude for a rubber rectangular plate. For this purpose, a square rubber plate made of silicone with fixed edges has been tested and its linear and nonlinear responses have been measured by laser Doppler vibrometers. First, a reduced-order model, using energy based approach and global discretization, has been constructed, taking into account geometric imperfections; the linear viscous damping at each excitation level in the nonlinear regime has been identified from the experimental data. This numerical model with linear viscous damping has been widely validated and constitutes the basis for comparison with subsequent damping identifications. Then, three different single degree of freedom models have been fitted to the same experimental data; each model has a different damping description. Specifically, the models are based on a modified Duffing oscillators with linear, quadratic and cubic stiffness and: (i) a linear viscous damping; (ii) a nonlinear viscoelastic dissipation described by the loss factor; (iii) a standard linear solid viscoelastic model with nonlinear springs. The dissipation identified by the different models is discussed and confirms the major nonlinear nature of damping as a function of the vibration amplitude.
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The nonlinear modes of a non-conservative nonlinear system are sometimes referred to as damped nonlinear normal modes (dNNMs). Because of the non-conservative characteristics, the dNNMs are no longer periodic. To compute non-perio...
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The nonlinear modes of a non-conservative nonlinear system are sometimes referred to as damped nonlinear normal modes (dNNMs). Because of the non-conservative characteristics, the dNNMs are no longer periodic. To compute non-periodic dNNMs using classic methods for periodic problems, two concepts have been developed in the last two decades: complex nonlinear mode (CNM) and extended periodic motion concept (EPMC). A critical assessment of these two concepts applied to different types of non-conservative nonlinearities and industrial full-scale structures has not been thoroughly investigated yet. Furthermore, there exist two emerging techniques which aim at predicting the resonant solutions of a nonlinear forced response using the dNNMs: extended energy balance method (E-EBM) and nonlinear modal synthesis (NMS). A detailed assessment between these two techniques has been rarely attempted in the literature. Therefore, in this work, a comprehensive comparison between CNM and EPMC is provided through two illustrative systems and one engineering application. The EPMC with an alternative damping assumption is also derived and compared with the original EPMC and CNM. The advantages and limitations of the CNM and EPMC are critically discussed. In addition, the resonant solutions are predicted based on the dNNMs using both E-EBM and NMS. The accuracies of the predicted resonances are also discussed in detail.
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This paper investigates the nonlinear mass and damping effects of nonlinear electromagnetic shunt damping (N-EMSD) for vibration isolation performance enhancement of a permanent magnets (PMs) based nonlinear vibration isolator (NV...
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This paper investigates the nonlinear mass and damping effects of nonlinear electromagnetic shunt damping (N-EMSD) for vibration isolation performance enhancement of a permanent magnets (PMs) based nonlinear vibration isolator (NVI). An electromagnetic structure composing of two coils and two PMs is designed to realize equivalent nonlinear damping and mass. The nonlinear mechanic-electromagnetic coupling coefficient is analyzed and modeled. The voltage frequency of the circuit is twice the displacement frequency that is totally different with that of the linear electromagnetic shunt damping (L-EMSD). The amplitude frequency response function of the NVI with N-EMSD is theoretically derived via the harmonic balance method (HBM) and the stability is judged with Jacobian matrix. Then the equivalent nonlinear damping and nonlinear mass of the N-EMSD is derived. The numerical predictions agree with the experimental results, which demonstrate that the use of inductance in shunt circuit can change the equivalent nonlinear mass and the "jump" frequency of the NVI. Large value of inductance deteriorates the vibration isolation performance and the optimal inductance is slightly smaller than zero. Furthermore, N-EMSD can realize nonlinear damping to achieve wide band vibration isolation of the NVI. The optimal negative resistance is discussed.
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In this study model identification of the nonlinear dynamics of a micro-speaker is carried out hy purely electrical measurements, avoiding any explicit vibration measurements. It is shown that a dynamic model of the micro-speaker,...
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In this study model identification of the nonlinear dynamics of a micro-speaker is carried out hy purely electrical measurements, avoiding any explicit vibration measurements. It is shown that a dynamic model of the micro-speaker, which takes into account the nonlinear damping characteristic of the device, can be identified by measuring the response between the voltage input and the current flowing into the coil. An analytical formulation of the quasi-linear model of the micro-speaker is first derived and an optimisation method is then used to identify a polynomial function which describes the mechanical damping behaviour of the micro-speaker. The analytical results of the quasi-linear model are compared with numerical results. This study potentially opens up the possibility of efficiently implementing nonlinear echo cancellers.
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The nonlinear damping resulting from surface energy loss in suspended beam micro and nanoresonators is investigated theoretically. Surface energy loss is known to be a relevant and in some cases a dominant damping mechanism in mic...
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The nonlinear damping resulting from surface energy loss in suspended beam micro and nanoresonators is investigated theoretically. Surface energy loss is known to be a relevant and in some cases a dominant damping mechanism in micro and nanoresonators. So far, it was only investigated in the linear (low amplitude) regime. In this work we consider the beam as made of an anelastic material and introduce the beam stretching effect in the elastic model of transversally vibrating beams clamped at both ends. This model results in a nonlinear contribution to the damping. Analytical expressions for the resulting amplitude dependent quality factor and the nonlinear damping parameter in a reduced order model are derived. Large nonlinear damping is predicted when the amplitude of transversal vibration is comparable to the beam thickness, which can be relevant to the beam dynamics. (C) 2019 Elsevier Ltd. All rights reserved.
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Linear electromagnetic shunt damping (L-EMSD) has been investigated deeply for vibration control in previous studies. This paper proposes nonlinear electromagnetic shunt damping (N-EMSD) for vibration isolation enhancement of line...
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Linear electromagnetic shunt damping (L-EMSD) has been investigated deeply for vibration control in previous studies. This paper proposes nonlinear electromagnetic shunt damping (N-EMSD) for vibration isolation enhancement of linear vibration isolators (LVIs), which has not been discussed in existing literature. N-EMSD composes of a pair of the permanent magnets (PMs) and a pair of the coils, where the two coils are wound in opposite direction and connected in series. The nonlinear electromagnetic coupling coefficient is derived. The coupling governing equations of a LVI with N-EMSD are established and the amplitude-frequency relationship is theoretically derived using the harmonic balance method (HBM). Both the simulations and experiments are carried out to verify the nonlinear damping characteristic of N-EMSD. The results demonstrate that the LVI with N-EMSD can effectively reduce the vibration in the resonance region without affecting the vibration isolation performance in the isolation region compared with the traditional L-EMSD. It is also found in both simulation and experiment for the two coils configuration that the frequency of the induced voltage is twice the frequency of the displacement. Furthermore, the transmissibility of the LVI with N-EMSD reduces with the increase of the input amplitude in the resonance region, which demonstrates the nonlinearity of N-EMSD. The natural frequency slightly decreases with the decrease of the peak transmissibility. This paper extends the electromagnetic shunt damping (EMSD) technique from linear to nonlinear fields and provides a guideline to design nonlinear damping. (C) 2020 Elsevier Ltd. All rights reserved.
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Traditional linear electromagnetic shunt damping (L-EMSD) has been studied deeply, however, the vibration isolation performance becomes worse with the increase of linear damping in the isolation region. To overcome the limitation ...
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Traditional linear electromagnetic shunt damping (L-EMSD) has been studied deeply, however, the vibration isolation performance becomes worse with the increase of linear damping in the isolation region. To overcome the limitation of L-EMSD, this paper proposes two types of nonlinear electromagnetic shunt damping (N-EMSD) to develop nonlinear damping for the broadband vibration isolation of linear vibration isolators (LVIs). Both the two types of N-EMSD consist of two permanent magnets (PMs) and coils, however, the ways to connect to the external shunt circuits and the configurations between the PMs and coils are different. Nonlinear electromagnetic coupling coefficients are analyzed theoretically. The theoretical transmissibility of the LVI with N-EMSD is derived via the harmonic balance method (HBM). Numerical simulations and experiments are conducted to verify nonlinear damping performance of N-EMSD. The results demonstrate that compared to L-EMSD the proposed N-EMSD have similar vibration suppression performance in the resonance region, but are more effective in the isolation region.
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By using the functional type cone expansion and compression fixed-point theorem in cones, some new and general results on the existence of positive solution for twin singular boundary value problems with damping term are obtained....
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By using the functional type cone expansion and compression fixed-point theorem in cones, some new and general results on the existence of positive solution for twin singular boundary value problems with damping term are obtained. An example is given to illustrate our results.
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The paper presents analysis of nonlinear response of a classical mechanical oscillator placed within a magnetic field and driven by a harmonic force. With an appropriate choice of control parameters, the system vibrates chaoticall...
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The paper presents analysis of nonlinear response of a classical mechanical oscillator placed within a magnetic field and driven by a harmonic force. With an appropriate choice of control parameters, the system vibrates chaotically between different equilibrium positions. To prove this result, Lyapunov exponents have been calculated using the algorithm proposed by Rangarajan G., Habib S. and Ryne R. [18]. Moreover, the appropriate time series, phase portrait, Poincaré cross-section and power spectrum are given to support the conclusion.
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We have performed a statistical analysis of upper band and lower band chorus emissions observed by the Geotail spacecraft. Chorus elements are generated near the magnetic equator (or the high-latitude minimum-B pockets in the oute...
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We have performed a statistical analysis of upper band and lower band chorus emissions observed by the Geotail spacecraft. Chorus elements are generated near the magnetic equator (or the high-latitude minimum-B pockets in the outer magnetosphere) as discrete emissions covering a frequency range of 0.1–0.65 f_(ce0), where f_(ce0) is the cyclotron frequency in the generation region, with wave vectors parallel to the ambient magnetic field. As the emissions propagate away from the generation region, it is possible that they undergo the nonlinear damping at half the local cyclotron frequency 0.5 f_(ce) because of the quasi-parallel propagation. The nonlinear damping can separate the emissions into the upper band and lower band chorus emissions. We have found that the lower cutoff of the upper band emissions coincides with 0.5 f_(ce), while the upper cutoff of the lower band emissions represents 0.5 f_(ce0). When 0.5 f_(ce) exceeds 0.65 f_(ce0), the chorus emission is observed as a lower band-only emission.
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