Negative Nonlinear Dissipation in Microelectromechanical Beams

2020 ◽  
Vol 29 (5) ◽  
pp. 954-959
Author(s):  
Nicholas Eric Bousse ◽  
James Marion Lehto Miller ◽  
Anne Louise Alter ◽  
Christopher Patrick Cameron ◽  
Hyun-Keun Kwon ◽  
...  
Keyword(s):  
Nonlinear Dissipation

scholarly journals Tuning nonlinear damping in graphene nanoresonators by parametric–direct internal resonance

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Ata Keşkekler ◽  
Oriel Shoshani ◽  
Martin Lee ◽  
Herre S. J. van der Zant ◽  
Peter G. Steeneken ◽  
...  
Keyword(s):  
Parametric Resonance ◽  
Internal Resonance ◽  
Microscopic Theory ◽  
Fold Increase ◽  
Nonlinear Damping ◽  
Supporting Evidence ◽  
Nonlinear Dissipation ◽  
Modal Interactions ◽  
Solid State Physics ◽  
Internal Resonances

AbstractMechanical sources of nonlinear damping play a central role in modern physics, from solid-state physics to thermodynamics. The microscopic theory of mechanical dissipation suggests that nonlinear damping of a resonant mode can be strongly enhanced when it is coupled to a vibration mode that is close to twice its resonance frequency. To date, no experimental evidence of this enhancement has been realized. In this letter, we experimentally show that nanoresonators driven into parametric-direct internal resonance provide supporting evidence for the microscopic theory of nonlinear dissipation. By regulating the drive level, we tune the parametric resonance of a graphene nanodrum over a range of 40–70 MHz to reach successive two-to-one internal resonances, leading to a nearly two-fold increase of the nonlinear damping. Our study opens up a route towards utilizing modal interactions and parametric resonance to realize resonators with engineered nonlinear dissipation over wide frequency range.

scholarly journals The GCM Response to Current Parameterizations of Nonorographic Gravity Wave Drag

2005 ◽  
Vol 62 (7) ◽  
pp. 2394-2413 ◽  
Author(s):  
Charles McLandress ◽  
John F. Scinocca
Keyword(s):  
Gravity Wave ◽  
General Circulation ◽  
Critical Level ◽  
Climate Modeling ◽  
Circulation Model ◽  
Wave Drag ◽  
Nonlinear Dissipation ◽  
Additional Experiment ◽  
Identical Response ◽  
Dissipation Mechanism

Abstract A comparison is undertaken of the response of a general circulation model (GCM) to the nonorographic gravity wave drag parameterizations of Hines, Warner and McIntyre, and Alexander and Dunkerton. The analysis is restricted to a comparison of each parameterization’s nonlinear dissipation mechanism since, in principle, this is the only component that differs between the schemes. This is achieved by developing a new, more general parameterization that can represent each of these dissipation mechanisms, while keeping all other aspects of the problem identical. The GCM simulations reveal differences in the climatological response to the three dissipation mechanisms. These differences are documented for both tropopause and surface launch elevations of the parameterized waves. The simulations also reveal systematic differences in the height at which momentum is deposited. This behavior is investigated further in a set of experiments designed to reduce these systematic differences, while leaving the details of the dissipation mechanisms unaltered. These sensitivity experiments demonstrate that it is possible to obtain nearly identical responses from all three mechanisms, which indicates that the GCM response is largely insensitive to the precise details of the dissipation mechanisms. This finding is supported by an additional experiment in which the nonlinear dissipation mechanisms are turned off and critical-level filtering is left to act as the only source of dissipation. In this experiment, critical-level filtering effectively replaces the nonlinear dissipation mechanism, producing a nearly identical response. The results of this study suggest that climate modeling efforts would potentially benefit more from the refinement of other aspects of the parameterization problem, such as the properties of the launch spectrum, than they have benefited from the refinement of dissipation mechanisms.

scholarly journals GENERAL DECAY OF SOLUTION FOR A POROUS-ELASTIC SYSTEM WITH WEAK NONLINEAR DISSIPATION

2018 ◽  
Vol 05 (01) ◽  
pp. 9-23
Author(s):  
SEBASTIAO M. S. CORDEIRO ◽  
MAURO L. SANTOS ◽  
CARLOS A. RAPOSO
Keyword(s):  
Elastic System ◽  
General Decay ◽  
Nonlinear Dissipation

scholarly journals Noise-induced transitions in a double-well oscillator with nonlinear dissipation

2016 ◽  
Vol 93 (5) ◽  
Author(s):  
Vladimir V. Semenov ◽  
Alexander B. Neiman ◽  
Tatyana E. Vadivasova ◽  
Vadim S. Anishchenko
Keyword(s):  
Nonlinear Dissipation

scholarly journals Effect of Nonlinear Dissipation on the Basin Boundaries of a Driven Two-Well Modified Rayleigh–Duffing Oscillator

2015 ◽  
Vol 25 (02) ◽  
pp. 1550024 ◽  
Author(s):  
C. H. Miwadinou ◽  
A. V. Monwanou ◽  
J. B. Chabi Orou
Keyword(s):  
Initial Conditions ◽  
Duffing Oscillator ◽  
Excitation Amplitude ◽  
Nonlinear Damping ◽  
Homoclinic Bifurcation ◽  
Nonlinear Dissipation ◽  
Transition To Chaos ◽  
Melnikov Criterion ◽  
Quadratic Nonlinearities ◽  
Basin Boundaries

This paper considers the effect of nonlinear dissipation on the basin boundaries of a driven two-well modified Rayleigh–Duffing oscillator where pure cubic, unpure cubic, pure quadratic and unpure quadratic nonlinearities are considered. By analyzing the potential, an analytic expression is found for the homoclinic orbit. The Melnikov criterion is used to examine a global homoclinic bifurcation and transition to chaos. Unpure quadratic parameter and parametric excitation amplitude effects are found on the critical Melnikov amplitude μ cr . Finally, the phase space of initial conditions is carefully examined in order to analyze the effect of the nonlinear damping, and particularly how the basin boundaries become fractalized.

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