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Abstract Frequency-domain analysis of brain tissue motion has received increased focus in recent years as an approach to describing the response of the brain to impact or vibration sources in the built environment. While researchers in many experimental and numerical studies have sought to identify natural resonant frequencies of the brain, sparse description of the associated vibration modes limits comparison of results between studies. We performed a modal analysis to extract the natural frequencies and associated mode shapes of a finite element (FE) model of the head. The vibration modes were characterized using two-dimensional (2D) plate deformation notation in the basic medical planes. Many of the vibration modes characterized are similar to those found in previous numerical and experimental studies. We propose this characterization method as an approach to increase compatibility of results between studies of brain vibration behavior.
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Resonant modal interactions in micro/nano-mechanical structures
Abstract This paper considers nonlinear interactions between vibration modes with a focus on recent studies relevant to micro- and nanoscale mechanical resonators. Due to their inherently small damping and high susceptibility to nonlinearity, these devices have brought to light new phenomena and offer the potential for novel applications. Nonlinear interactions between vibration modes are well known to have the potential for generating a “zoo” of complicated bifurcation patterns and a wide variety of dynamic behaviors, including chaos. Here, we focus on more regular, robust, and predictable aspects of their dynamics, since these are most relevant to applications. The investigation is based on relatively simple two-mode models that are able to capture and predict a wide range of transient and sustained dynamical behaviors. The paper emphasizes modeling and analysis that has been done in support of recent experimental investigations and describes in full detail the analysis and attendant insights obtained from the models that are briefly described in the experimental papers. Standard analytical tools are employed, but the questions posed and the conclusions drawn are novel, as motivated by observations from experiments. The paper considers transient dynamics, response to harmonic forcing, and self-excited systems and describes phenomena such as extended coherence time during transient decay, zero dispersion response, and nonlinear frequency veering. The paper closes with some suggested directions for future studies in this area.
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- Award ID(s):
- 1662619
- PAR ID:
- 10296707
- Date Published:
- Journal Name:
- Nonlinear Dynamics
- Volume:
- 104
- Issue:
- 3
- ISSN:
- 0924-090X
- Page Range / eLocation ID:
- 1801 to 1828
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s11071-021-06405-3
