Using nonlinear jumps to estimate cubic stiffness nonlinearity: An experimental study

Tang, Bin; Brennan, M.J.; Lopes, Vicente; Silva, Samuel da; Ramlan, Roszaidi

doi:10.1177/0954406215606746

Cited by 25 publications

(22 citation statements)

References 18 publications

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“…An approach related to this method in which the backbone curve is estimated from the jump-down frequencies has been recently reported by some of the authors of this paper [24]. A nonlinear vibration absorber, used in the thesis by Hsu [25], is tested in a particular configuration with an electrodynamic shaker, such that the dynamics of the shaker are largely decoupled from the dynamics of the absorber.…”

Section: Introductionmentioning

confidence: 99%

Experimental characterization of a nonlinear vibration absorber using free vibration

Tang

Brennan

Gatti

et al. 2016

Journal of Sound and Vibration

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a b s t r a c tKnowledge of the nonlinear characteristics of a vibration absorber is important if its performance is to be predicted accurately when connected to a host structure. This can be achieved theoretically, but experimental validation is necessary to verify the modelling procedure and assumptions. This paper describes the characterization of such an absorber using a novel experimental procedure. The estimation method is based on a free vibration test, which is appropriate for a lightly damped device. The nonlinear absorber is attached to shaker which is operated such that the shaker works in its mass-controlled regime, which means that the shaker dynamics, which are also included in the measurement, are considerably simplified, which facilitates a simple estimation of the absorber properties. From the free vibration time history, the instantaneous amplitude and instantaneous damped natural frequency are estimated using the Hilbert transform. The stiffness and damping of the nonlinear vibration absorber are then estimated from these quantities. The results are compared with an analytical solution for the free vibration of the nonlinear system with cubic stiffness and viscous damping, which is also derived in the paper using an alternative approach to the conventional perturbation methods. To further verify the approach, the results are compared with a method in which the internal forces are balanced at each measured instant in time.

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Section: Introductionmentioning

confidence: 99%

Experimental characterization of a nonlinear vibration absorber using free vibration

Tang

Brennan

Gatti

et al. 2016

Journal of Sound and Vibration

Self Cite

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“…It is easier to keep this signal constant over a range of frequency, using the power amplifier in the electrical current mode, than to keep the force applied constant close to the resonance frequency of the system. The same strategy was used in Tang et al (2016) [21]. All signals were measured using 1024 Hz as sampling rate, being that 4096 samples were collected.…”

Section: Methodsmentioning

confidence: 99%

Damage detection in an uncertain nonlinear beam based on stochastic Volterra series: An experimental application

Villani

Silva

Cunha

et al. 2019

Mechanical Systems and Signal Processing

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Damage detection in an uncertain nonlinear beam based on stochastic Volterra series: an experimental application. Mechanical Systems and Signal Processing, Elsevier, 2019, 128, pp.obtained by the deterministic version of the Volterra series, showing the advantage of the stochastic model use when we consider the experimental data variation with the capability to detect the presence of the damage with statistical confidence. Besides, the nonlinear metric used presented a higher sensitivity to the occurrence of the damage compared with the linear one, justifying the application of a nonlinear metric when the system exhibits intrinsically nonlinear behavior.

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“…It has been the subject of experimental study to identify cubic stiffness non-linearity of single degree-offreedom Duffing system Tang et al (2015). The aim of this experimental setup is to study the vibration of a preloaded beam.…”

Section: Methodsmentioning

confidence: 99%

“…The experimental setup has a screw in the top of the beam to apply an axial preload force. The preload was adjusted by trial and error until just before the buckling load of the beam Tang et al (2015). This was done to obtain a stronger nonlinear effect since the linear stiffness is reduced by applying the preload Kovacic and Brennan (2011).…”

Section: Methodsmentioning

confidence: 99%

Updating of a Nonlinear Finite Element Model Using Discrete-Time Volterra Series

Bussetta

Silva

2017

Lat. Am. j. solids struct.

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In this study, the discrete-time Volterra series are used to update parameters in a nonlinear finite element model. The main idea of the Volterra series is to describe the discrete-time output of a nonlinear system using multidimensional convolutions between the Volterra kernels represented in a Kautz orthogonal basis and the excitations. A metric based on the residue between the experimental and the numerical Volterra kernels is used to identify the parameters of the numerical model. First, the identification of the linear parameters is performed using a metric based only on the first order Volterra kernels. Then the nonlinear parameters are identified through a metric based on the higher-order kernels. The originality of this nonlinear updating method stems from the decoupling of linear and nonlinear parameters and the use of global nonlinear model. In order to put in light the applicability of this technique, this work focus on the identification of the parameters in a nonlinear finite element model of a beam that was preloaded by compression mechanism. This work shows that the updated numerical model was able to represent the behaviour observed in the experimental measurements.Keywords Discrete-time Volterra series, Kautz filters, model updating, nonlinear finite element model, nonlinear identification, sensitivity. Updating of a Nonlinear Finite Element Model Using Discrete-Time Volterra Series 1 INTRODUCTIONIn many cases, the dynamical behaviour is needed to design a mechanical system. Moreover, the knowledge of the dynamical behaviour of a structure is important to control its integrity and to predict its service life. In the practical systems, nonlinear effects due to large displacements, gaps, jumps, discontinuities, etc. are very common (e.g. Worden and Tomlinson (2001)). The nonlinear finite element method is a very powerful tool to study the nonlinear vibrations. Nevertheless, it is not easy to identify the parameters of the nonlinear model due to the uncertainties in the modelling of the experimental system (e.g. the mechanical properties, the boundary conditions). Despite of the important number of investigations, the nonlinear model updating techniques are not mature as the classical linear ones.A bibliography review on the state of the art nonlinear system identification techniques in structure dynamics is presented by Noël and Kerschen (2017). Furthermore, a bibliography review of the nonlinear updating methods is exposed by Bussetta et al. (2017). Generally, the updating methods are based on the minimisation of an objective function or a metric that represents the difference between the numerical results and the experimental data. This objective function can use data in the frequency domain or in the time domain. The Volterra series can be used to defined this objective function (e.g. Wu and Kareem (2014); Guo et al. (2013)). In the paper of Shiki et al. (2012) the authors made a numerical comparison of a nonlinear model updating technique based on Volterra series and proper orthogonal ...

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Using nonlinear jumps to estimate cubic stiffness nonlinearity: An experimental study

Cited by 25 publications

References 18 publications

Experimental characterization of a nonlinear vibration absorber using free vibration

Experimental characterization of a nonlinear vibration absorber using free vibration

Damage detection in an uncertain nonlinear beam based on stochastic Volterra series: An experimental application

Updating of a Nonlinear Finite Element Model Using Discrete-Time Volterra Series

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