Methodology for model updating of mechanical components with local nonlinearities

Kurt, Mehmet; Eriten, Melih; McFarland, D. Michael; Bergman, Lawrence A.; Vakakis, Alexander F.

doi:10.1016/j.jsv.2015.07.012

Cited by 38 publications

(15 citation statements)

References 30 publications

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“…The cubic nonlinear term encountered in the above equation is known to generate localized nonlinear modes in structural systems with geometric nonlinearities [62,63], systems with nonlinear absorbers or energy sinks [64], and granular dimer chains [65,66]. Localization and motion confinement are observed when vibrational energy tends to be confined to one particular area of a structure or continuous media.…”

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confidence: 99%

Mechanistic Insights into Human Brain Impact Dynamics through Modal Analysis

et al. 2018

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Although concussion is one of the greatest health challenges today, our physical understanding of the cause of injury is limited. In this Letter, we simulated football head impacts in a finite element model and extracted the most dominant modal behavior of the brain's deformation. We showed that the brain's deformation is most sensitive in low frequency regimes close to 30 Hz, and discovered that for most subconcussive head impacts, the dynamics of brain deformation is dominated by a single global mode. In this Letter, we show the existence of localized modes and multimodal behavior in the brain as a hyperviscoelastic medium. This dynamical phenomenon leads to strain concentration patterns, particularly in deep brain regions, which is consistent with reported concussion pathology. DOI: 10.1103/PhysRevLett.120.138101 Traumatic brain injury (TBI) is a major cause of death and disability in the United States, contributing to about 30% of all injury-related deaths [1,2]. Every year, millions of Americans are diagnosed with TBI [3,4], 80% of which are categorized as mild [2]. Undiagnosed cases, due to either lack of clinical expertise or underreporting, might be twice as high [5][6][7][8]. Given that mild TBI (MTBI), or concussion, has become a serious health concern in society, the burden of understanding and preventing it has become ever more indisputable for clinicians and physicists alike.Efforts to model the brain's physics date back to the 1940s when Holbourn proposed the head as a mechanical system and explored the relation between the input to this system (in the form of head motion) to the output (in the form of relative brain displacement) [9,10]. Kornhauser proposed isodisplacement curves in a second-order springmass system representing relative brain displacement as a measure for classifying injury [11]. Others have also showed that, in different loading regimes, injury could be more sensitive to peak acceleration or maximum change in velocity or a combination of both [12,13]. Since then, many scientists have investigated the brain's response in severe scenarios of TBI with skull flexure [14,15], and more recently in mild scenarios with mostly inertial loading on the brain [16][17][18]. In particular, for helmeted sports, much of previous research has focused on brain deformation while assuming a rigid skull. In time, with the advances in imaging techniques, axonal injury, which requires excessive regional stretching of axons [19,20], has become one of the leading hypotheses behind the mechanism of concussions. Confirming this hypothesis, strain in the brain and specifically strain in the periventricular region of the brain-with the highest density of axon fibers-have been shown to correlate best with acute concussion and longterm neurological deficits [21][22][23][24]. However, dynamical behavior of the brain during rapid head motions with various amplitudes, durations, and directions, as well as the reason for higher susceptibility of these deep regions of the brain to strain are still largely unknow...

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Mechanistic Insights into Human Brain Impact Dynamics through Modal Analysis

et al. 2018

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“…In fact, backbone curves govern the evolution of the system's resonance frequencies for increasing vibration amplitudes, which represent a great deal of useful information that can be used to understand the system's dynamics. They can also be exploited to estimate and update model parameters as suggested in [Worden & Tomlinson, 2001;Dick et al, 2006;Hill et al, 2016;Sracic et al, 2012;Kurt et al, 2015;Peter et al, 2015]. This paper is organized as follows.…”

Section: Experimental Tracking Of Limit-point Bifurcations and Backbomentioning

confidence: 99%

Experimental Tracking of Limit-Point Bifurcations and Backbone Curves Using Control-Based Continuation

Renson

Barton

Neild

2017

Int. J. Bifurcation Chaos

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Control-based continuation (CBC) is a means of applying numerical continuation directly to a physical experiment for bifurcation analysis without the use of a mathematical model. CBC enables the detection and tracking of bifurcations directly, without the need for a post-processing stage as is often the case for more traditional experimental approaches. In this paper, we use CBC to directly locate limit-point bifurcations of a periodically forced oscillator and track them as forcing parameters are varied. Backbone curves, which capture the overall frequency-amplitude dependence of the system's forced response, are also traced out directly. The proposed method is demonstrated on a single-degree-of-freedom mechanical system with a nonlinear stiffness characteristic. Results are presented for two configurations of the nonlinearity -one where it exhibits a hardening stiffness characteristic and one where it exhibits softening-hardening.

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“…• advanced signal processing for updating gray-box models [1,2,4,8,9], • neural network based methods [10,11],…”

Section: Introductionmentioning

confidence: 99%

Recovery of Differential Equations from Impulse Response Time Series Data for Model Identification and Feature Extraction

2019

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Time recordings of impulse-type oscillation responses are short and highly transient. These characteristics may complicate the usage of classical spectral signal processing techniques for (a) describing the dynamics and (b) deriving discriminative features from the data. However, common model identification and validation techniques mostly rely on steady-state recordings, characteristic spectral properties and non-transient behavior. In this work, a recent method, which allows reconstructing differential equations from time series data, is extended for higher degrees of automation. With special focus on short and strongly damped oscillations, an optimization procedure is proposed that fine-tunes the reconstructed dynamical models with respect to model simplicity and error reduction. This framework is analyzed with particular focus on the amount of information available to the reconstruction, noise contamination and nonlinearities contained in the time series input. Using the example of a mechanical oscillator, we illustrate how the optimized reconstruction method can be used to identify a suitable model and how to extract features from uni-variate and multivariate time series recordings in an engineering-compliant environment. Moreover, the determined minimal models allow for identifying the qualitative nature of the underlying dynamical systems as well as testing for the degree and strength of nonlinearity. The reconstructed differential equations would then be potentially available for classical numerical studies, such as bifurcation analysis. These results represent a physically interpretable enhancement of data-driven modeling approaches in structural dynamics.

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Methodology for model updating of mechanical components with local nonlinearities

Cited by 38 publications

References 30 publications

Mechanistic Insights into Human Brain Impact Dynamics through Modal Analysis

Mechanistic Insights into Human Brain Impact Dynamics through Modal Analysis

Experimental Tracking of Limit-Point Bifurcations and Backbone Curves Using Control-Based Continuation

Recovery of Differential Equations from Impulse Response Time Series Data for Model Identification and Feature Extraction

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