scholarly journals Nonlinear energy transfers and phase diagrams for geostrophically balanced rotating-stratified flows

2014 ◽  
Vol 89 (3) ◽  
Author(s):  
Corentin Herbert
Keyword(s):  
Phase Diagrams ◽  
Stratified Flows ◽  
Energy Transfers ◽  
Nonlinear Energy ◽  
Rotating Stratified Flows

Hybrid functions for nonlinear energy transfers at finite depths

2018 ◽  
Vol 4 (3) ◽  
pp. 187-198 ◽  
Author(s):  
G. Uma ◽  
V. Prabhakar ◽  
S. A. Sannasiraj
Keyword(s):  
Hybrid Functions ◽  
Energy Transfers ◽  
Nonlinear Energy

scholarly journals Nonlinear couplings and energy transfers in micro- and nano-mechanical resonators: intermodal coupling, internal resonance and synchronization

2018 ◽  
Vol 376 (2127) ◽  
pp. 20170141 ◽  
Author(s):  
Keivan Asadi ◽  
Jun Yu ◽  
Hanna Cho
Keyword(s):  
Internal Resonance ◽  
Development Stage ◽  
Vibrational Modes ◽  
Mechanical Resonators ◽  
The Past ◽  
Nonlinear Energy Transfer ◽  
Energy Transfers ◽  
Wide Range ◽  
Plate Type ◽  
Nonlinear Energy

Extensive development of micro/nano-electromechanical systems (MEMS/NEMS) has resulted in technologies that exhibit excellent performance over a wide range of applications in both applied (e.g. sensing, imaging, timing and signal processing) and fundamental sciences (e.g. quantum-level problems). Many of these outstanding applications benefit from resonance phenomena by employing micro/nanoscale mechanical resonators often fabricated into a beam-, membrane- or plate-type structure. During the early development stage, one of the vibrational modes (typically the fundamental mode) of a resonator is considered in the design and application. In the past decade, however, there has been a growing interest in using more than one vibrational mode for the enhanced functionality of MEMS/NEMS. In this paper, we review recent research efforts to investigate the nonlinear coupling and energy transfers between multiple modes in micro/nano-mechanical resonators, focusing especially on intermodal coupling, internal resonance and synchronization. This article is part of the theme issue ‘Nonlinear energy transfer in dynamical and acoustical systems’.

scholarly journals Targeted Energy Transfers for Suppressing Regenerative Machine Tool Vibrations

2016 ◽  
Vol 12 (1) ◽  
Author(s):  
Amir Nankali ◽  
Young S. Lee ◽  
Tamás Kalmár-Nagy
Keyword(s):  
Machine Tool ◽  
Passive Control ◽  
Stability Margin ◽  
Numerical Continuation ◽  
Continuation Methods ◽  
Transition Curve ◽  
Hopf Bifurcation Point ◽  
Energy Transfers ◽  
Tool Vibrations ◽  
Nonlinear Energy

We study the dynamics of targeted energy transfers in suppressing chatter instability in a single-degree-of-freedom (SDOF) machine tool system. The nonlinear regenerative (time-delayed) cutting force is a main source of machine tool vibrations (chatter). We introduce an ungrounded nonlinear energy sink (NES) coupled to the tool, by which energy transfers from the tool to the NES and efficient dissipation can be realized during chatter. Studying variations of a transition curve with respect to the NES parameters, we analytically show that the location of the Hopf bifurcation point is influenced only by the NES mass and damping coefficient. We demonstrate that application of a well-designed NES renders the subcritical limit cycle oscillations (LCOs) into supercritical ones, followed by Neimark–Sacker and saddle-node bifurcations, which help to increase the stability margin in machining. Numerical and asymptotic bifurcation analyses are performed and three suppression mechanisms are identified. The asymptotic stability analysis is performed to study the domains of attraction for these suppression mechanisms which exhibit good agreement with the bifurcations sets obtained from the numerical continuation methods. The results will help to design nonlinear energy sinks for passive control of regenerative instabilities in machining.

scholarly journals Nonlinear Infragravity–Wave Interactions on a Gently Sloping Laboratory Beach

2015 ◽  
Vol 45 (2) ◽  
pp. 589-605 ◽  
Author(s):  
A. T. M. de Bakker ◽  
T. H. C. Herbers ◽  
P. B. Smit ◽  
M. F. S. Tissier ◽  
B. G. Ruessink
Keyword(s):  
Surf Zone ◽  
Short Wave ◽  
Net Energy ◽  
Shape Transformation ◽  
Higher Harmonics ◽  
Energy Flows ◽  
Energy Transfers ◽  
Infragravity Wave ◽  
Nonlinear Energy ◽  
Triad Interactions

AbstractA high-resolution dataset of three irregular wave conditions collected on a gently sloping laboratory beach is analyzed to study nonlinear energy transfers involving infragravity frequencies. This study uses bispectral analysis to identify the dominant, nonlinear interactions and estimate energy transfers to investigate energy flows within the spectra. Energy flows are identified by dividing transfers into four types of triad interactions, with triads including one, two, or three infragravity–frequency components, and triad interactions solely between short-wave frequencies. In the shoaling zone, the energy transfers are generally from the spectral peak to its higher harmonics and to infragravity frequencies. While receiving net energy, infragravity waves participate in interactions that spread energy of the short-wave peaks to adjacent frequencies, thereby creating a broader energy spectrum. In the short-wave surf zone, infragravity–infragravity interactions develop, and close to shore, they dominate the interactions. Nonlinear energy fluxes are compared to gradients in total energy flux and are observed to balance nearly completely. Overall, energy losses at both infragravity and short-wave frequencies can largely be explained by a cascade of nonlinear energy transfers to high frequencies (say, f > 1.5 Hz) where the energy is presumably dissipated. Infragravity–infragravity interactions seem to induce higher harmonics that allow for shape transformation of the infragravity wave to asymmetric. The largest decrease in infragravity wave height occurs close to the shore, where infragravity–infragravity interactions dominate and where the infragravity wave is asymmetric, suggesting wave breaking to be the dominant mechanism of infragravity wave dissipation.

Resonance captures and targeted energy transfers in an inertially-coupled rotational nonlinear energy sink

2012 ◽  
Vol 69 (4) ◽  
pp. 1693-1704 ◽  
Author(s):  
G. Sigalov ◽  
O. V. Gendelman ◽  
M. A. AL-Shudeifat ◽  
L. I. Manevitch ◽  
A. F. Vakakis ◽  
...  
Keyword(s):  
Nonlinear Energy Sink ◽  
Energy Transfers ◽  
Energy Sink ◽  
Nonlinear Energy

scholarly journals The universal aspect ratio of vortices in rotating stratified flows: theory and simulation

2012 ◽  
Vol 706 ◽  
pp. 46-57 ◽  
Author(s):  
Pedram Hassanzadeh ◽  
Philip S. Marcus ◽  
Patrice Le Gal
Keyword(s):  
Aspect Ratio ◽  
Three Dimensional ◽  
Boussinesq Equations ◽  
Stratified Flows ◽  
Coriolis Parameter ◽  
Aspect Ratios ◽  
Ideal Gases ◽  
Horizontal Length ◽  
Background Density ◽  
Rotating Stratified Flows

AbstractWe derive a relationship for the vortex aspect ratio $\ensuremath{\alpha} $ (vertical half-thickness over horizontal length scale) for steady and slowly evolving vortices in rotating stratified fluids, as a function of the Brunt–Väisälä frequencies within the vortex ${N}_{c} $ and in the background fluid outside the vortex $\bar {N} $, the Coriolis parameter $f$ and the Rossby number $\mathit{Ro}$ of the vortex: ${\ensuremath{\alpha} }^{2} = \mathit{Ro}(1+ \mathit{Ro}){f}^{2} / ({ N}_{c}^{2} \ensuremath{-} {\bar {N} }^{2} )$. This relation is valid for cyclones and anticyclones in either the cyclostrophic or geostrophic regimes; it works with vortices in Boussinesq fluids or ideal gases, and the background density gradient need not be uniform. Our relation for $\ensuremath{\alpha} $ has many consequences for equilibrium vortices in rotating stratified flows. For example, cyclones must have ${ N}_{c}^{2} \gt {\bar {N} }^{2} $; weak anticyclones (with $\vert \mathit{Ro}\vert \lt 1$) must have ${ N}_{c}^{2} \lt {\bar {N} }^{2} $; and strong anticyclones must have ${ N}_{c}^{2} \gt {\bar {N} }^{2} $. We verify our relation for $\ensuremath{\alpha} $ with numerical simulations of the three-dimensional Boussinesq equations for a wide variety of vortices, including: vortices that are initially in (dissipationless) equilibrium and then evolve due to an imposed weak viscous dissipation or density radiation; anticyclones created by the geostrophic adjustment of a patch of locally mixed density; cyclones created by fluid suction from a small localized region; vortices created from the remnants of the violent breakups of columnar vortices; and weakly non-axisymmetric vortices. The values of the aspect ratios of our numerically computed vortices validate our relationship for $\ensuremath{\alpha} $, and generally they differ significantly from the values obtained from the much-cited conjecture that $\ensuremath{\alpha} = f/ \bar {N} $ in quasi-geostrophic vortices.

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