Waves in elastic material

2021 ◽  
Author(s):  
Yiyi Whitchelo ◽  
Ingrid Olsen ◽  
Karsten Trulsen
Keyword(s):  
Elastic Material ◽  
Energy Transition ◽  
Nonlinear Effects ◽  
Open Water ◽  
Underlying Mechanism ◽  
Second Order ◽  
Wave Fields ◽  
Elastic Sheet ◽  
Temporal Properties ◽  
The Waves

<div>Sea ice covers about 7% of the Earth's surface and 12% of the world's oceans. The presence of global warming and an increase in human activities in the polar region has resulted in significant interest in the behaviour of waves and ice interaction. In this study, the experimental investigation of waves-ice interaction is presented in the form of propagating waves in elastic materials. This investigation aims to study wave propagation, and energy transition as waves enter from open water to a water region covered with an elastic sheet. As the waves propagate in the elastic material, the waves immediately attenuate, suggesting a loss in energy. This loss in energy cannot be explained in the classical sense (breaking etc.) as the elastic sheet's existence prevents the breaking in waves of large amplitudes. The underlying mechanism as waves adapt to the elastic region is crucial for understanding the possibility of build-up in wave energy within the elastic sheet.</div><div> </div><div>For the experiments, a JONSWAP spectrum was used to generate wave fields. Ultrasonic probes were used to measure the surface elevation of the elastic layer and the open water free surface, and these two were compared. The attenuation rates are investigated as a function of distance. The spatio-temporal properties of the wave fields are investigated using 2D FFT to obtain the wavenumber-frequency spectrum. We find significant second-order nonlinear effects as the waves propagate with an elastic cover. Especially the occurrence of second-order difference interactions, sometimes called the group line, was found to be conspicuous in some of the wave fields.</div>

Second Order Averaging Study of an Autoparametric System

1993 ◽  
Author(s):  
Bappaditya Banerjee ◽  
Anil K. Bajaj ◽  
Patricia Davies
Keyword(s):  
Dynamical Behavior ◽  
Period Doubling ◽  
Nonlinear Effects ◽  
Single Mode ◽  
Pitchfork Bifurcation ◽  
Second Order ◽  
System Response ◽  
Response Curves ◽  
Vibratory System ◽  
First Order

Abstract The autoparametric vibratory system consisting of a primary spring-mass-dashpot system coupled with a damped simple pendulum serves as an useful example of two degree-of-freedom nonlinear systems that exhibit complex dynamic behavior. It exhibits 1:2 internal resonance and amplitude modulated chaos under harmonic forcing conditions. First-order averaging studies of this system using AUTO and KAOS have yielded useful information about the amplitude dynamics of this system. Response curves of the system indicate saturation and the pitchfork bifurcation sets are found to be symmetric. The period-doubling route to chaotic solutions is observed. However questions about the range of the small parameter ε (a function of the forcing amplitude) for which the solutions are valid cannot be answered by a first-order study. Some observed dynamical behavior, like saturation, may not persist when higher-order nonlinear effects are taken into account. Second-order averaging of the system, using Mathematica (Maeder, 1991; Wolfram, 1991) is undertaken to address these questions. Loss of saturation is observed in the steady-state amplitude responses. The breaking of symmetry in the various bifurcation sets becomes apparent as a consequence of ε appearing in the averaged equations. The dynamics of the system is found to be very sensitive to damping, with extremely complicated behavior arising for low values of damping. For large ε second-order averaging predicts additional Pitchfork and Hopf bifurcation points in the single-mode response.

Gravitational waves: Some less discussed intriguing issues

2015 ◽  
Vol 24 (12) ◽  
pp. 1544023 ◽  
Author(s):  
C. Sivaram
Keyword(s):  
Gravitational Waves ◽  
Strong Field ◽  
Direct Detection ◽  
Recent Observation ◽  
High Redshift ◽  
Nonlinear Effects ◽  
Resonant Absorption ◽  
Compact Objects ◽  
The Waves ◽  
Very High

Attempts to detect gravitational waves is actively in progress with sophisticated devices like LIGO setup across continents. Despite being predicted almost 100 years ago, there has so far been no direct detection of these waves. In this work, we draw attention to some of the less discussed but subtle aspects arising, for example, from high orbital eccentricities, where emission near periastron could be millions of times more than that in the distant parts of the orbit. The strong field nonlinear effects close to the compact objects can substantially slow down and deflect the waves in the last (few) orbit(s) where much of the intensity is expected. Spin–orbit and other forces could be significant. There would also be plasma like resonant absorption (of kilohertz radiation) during the collapse. Recent observation of supermassive black holes at high redshift implies cluster collapse, where the gravitational wave intensity depends on very high powers of the mass. Any unambiguous claim of detection should perhaps consider several of these effects.

Nonlinear Wave Disturbance Around a Vertical Circular Column

2002 ◽  
Author(s):  
C. T. Stansberg ◽  
H. Braaten
Keyword(s):  
Linear Prediction ◽  
Harmonic Component ◽  
Nonlinear Effects ◽  
Second Order ◽  
Wave Disturbance ◽  
Difference Frequency ◽  
Irregular Waves ◽  
Order Effects ◽  
Sum Frequency ◽  
Circular Column

The wave disturbance close to vertical columns is analysed. In particular, the deviations from linear predictions are investigated, by experimental as well as by numerical methods. Thus a second-order numerical diffraction model is established by means of a diffraction analysis code (WAMIT) and compared to model tests with a single, fixed column with diameter 16m. Tests in regular, bi-chromatic as well as irregular waves are run. Significant nonlinear effects are observed, especially in steep waves, with the maximum elevation in front of the column increasing from 11.5m in a linear prediction to around 19m, in a 12s regular wave with 22m wave height. The main nonlinear effects in front of the column are identified as second-order sum-frequency and difference-frequency terms, plus a significant nonlinear increase in the first harmonic component. The WAMIT prediction of the second-order effects agrees fairly well with the measurements, although with some overprediction and underprediction, respectively, of the sum-frequency and difference-frequency (LF and mean set-up) terms in the steepest waves. For the underprediction of the first harmonic, however, a theory beyond second order is required.

scholarly journals Multi-spacecraft determination of wave characteristics near the proton gyrofrequency in high-altitude cusp

2005 ◽  
Vol 23 (3) ◽  
pp. 983-995 ◽  
Author(s):  
D. Sundkvist ◽  
A. Vaivads ◽  
M. André ◽  
J.-E. Wahlund ◽  
Y. Hobara ◽  
...  
Keyword(s):  
Magnetic Field ◽  
High Altitude ◽  
Nonlinear Effects ◽  
Linear Wave ◽  
Wave Growth ◽  
Ion Cyclotron Waves ◽  
Background Magnetic Field ◽  
Ion Cyclotron ◽  
The Waves ◽  
Proton Gyrofrequency

Abstract. We present a detailed study of waves with frequencies near the proton gyrofrequency in the high-altitude cusp for northward IMF as observed by the Cluster spacecraft. Waves in this regime can be important for energization of ions and electrons and for energy transfer between different plasma populations. These waves are present in the entire cusp with the highest amplitudes being associated with localized regions of downward precipitating ions, most probably originating from the reconnection site at the magnetopause. The Poynting flux carried by these waves is downward/upward at frequencies below/above the proton gyrofrequency, which is consistent with the waves being generated near the local proton gyrofrequency in an extended region along the flux tube. We suggest that the waves can be generated by the precipitating ions that show shell-like distributions. There is no clear polarization of the perpendicular wave components with respect to the background magnetic field, while the waves are polarized in a parallel-perpendicular plane. The coherence length is of the order of one ion-gyroradius in the direction perpendicular to the ambient magnetic field and a few times larger or more in the parallel direction. The perpendicular phase velocity was found to be of the order of 100km/s, an order of magnitude lower than the local Alfvén speed. The perpendicular wavelength is of the order of a few proton gyroradius or less. Based on our multi-spacecraft observations we conclude that the waves cannot be ion-whistlers, while we suggest that the waves can belong to the kinetic Alfvén branch below the proton gyrofrequency fcp and be described as non-potential ion-cyclotron waves (electromagnetic ion-Bernstein waves) above. Linear wave growth calculations using kinetic code show considerable wave growth of non-potential ion cyclotron waves at wavelengths agreeing with observations. Inhomogeneities in the plasma on the order of the ion-gyroradius suggests that inhomogeneous (drift) or nonlinear effects or both of these should be taken into account.

Does Interhemispheric Competition Mediate Motion-Induced Blindness? A Transcranial Magnetic Stimulation Study

Perception ◽  
10.1068/p5088 ◽  
2003 ◽  
Vol 32 (11) ◽  
pp. 1328-1338 ◽  
Author(s):  
Agnes P Funk ◽  
John D Pettigrew
Keyword(s):  
Transcranial Magnetic Stimulation ◽  
Binocular Rivalry ◽  
Magnetic Stimulation ◽  
Posterior Parietal Cortex ◽  
Right Hemisphere ◽  
Single Pulse ◽  
Underlying Mechanism ◽  
Temporal Properties ◽  
Interhemispheric Competition ◽  
Perceptual Rivalry

Motion-induced blindness (MIB) is a phenomenon, perhaps related to perceptual rivalry, where stationary targets disappear and reappear in a cyclic mode when viewed against a background (mask) of coherent, apparent 3-D motion. Since MIB has recently been shown to share similar temporal properties with binocular rivalry, we probed the appearance–disappearance cycle of MIB using unilateral, single-pulse transcranial magnetic stimulation (TMS)—a manipulation that has previously been shown to influence binocular rivalry. Effects were seen for both hemispheres when the timing of TMS was determined prospectively on the basis of a given subject's appearance–disappearance cycle, so that it occurred on average around 300 ms before the time of perceptual switch. Magnetic stimulation of either hemisphere shortened the time to switch from appearance to disappearance and vice versa. However, TMS of left posterior parietal cortex more selectively shortened the disappearance time of the targets if delivered in phase with the disappearance cycle, but lengthened it if TMS was delivered in the appearance phase after the perceptual switch. Opposite effects were seen in the right hemisphere, although less marked than the left-hemisphere effects. As well as sharing temporal characteristics with binocular rivalry, MIB therefore seems to share a similar underlying mechanism of interhemispheric modulation. Interhemispheric switching may thus provide a common temporal framework for uniting the diverse, multilevel phenomena of perceptual rivalry.

Analysis of second order nonlinear effects in strained silicon

2013 ◽  
Author(s):  
Pedro Damas ◽  
Xavier Le Roux ◽  
Eric Cassan ◽  
Nicolas Izard ◽  
Delphine Marris-Morini ◽  
...  
Keyword(s):  
Nonlinear Effects ◽  
Second Order ◽  
Strained Silicon

Analysis of second order nonlinear effects in strained silicon

2013 ◽  
Author(s):  
Pedro Damas ◽  
Xavier Le Roux ◽  
Eric Cassan ◽  
Delphine Marris-Morini ◽  
Nicolas Izard ◽  
...  
Keyword(s):  
Nonlinear Effects ◽  
Second Order ◽  
Strained Silicon
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