Nonlinear frequency shifts in acoustical resonators with varying cross sections

2009 ◽  
Vol 125 (3) ◽  
pp. 1310-1318 ◽  
Author(s):  
Mark F. Hamilton ◽  
Yurii A. Ilinskii ◽  
Evgenia A. Zabolotskaya
Keyword(s):  
Cross Sections ◽  
Nonlinear Frequency ◽  
Frequency Shifts

Linear and nonlinear frequency shifts in acoustical resonators with varying cross sections

2001 ◽  
Vol 110 (1) ◽  
pp. 109-119 ◽  
Author(s):  
Mark F. Hamilton ◽  
Yurii A. Ilinskii ◽  
Evgenia A. Zabolotskaya
Keyword(s):  
Cross Sections ◽  
Nonlinear Frequency ◽  
Frequency Shifts ◽  
Linear And Nonlinear

Stabilization of Explosive Instabilities by Nonlinear Frequency Shifts

1973 ◽  
Vol 30 (2) ◽  
pp. 49-51 ◽  
Author(s):  
V. N. Oraevskii ◽  
V. P. Pavlenko ◽  
H. Wilhelmsson ◽  
E. Ya. Kogan
Keyword(s):  
Nonlinear Frequency ◽  
Frequency Shifts

Effects of nonlinear frequency shifts on certain induced scattering processes

2002 ◽  
Vol 9 (11) ◽  
pp. 4520-4524 ◽  
Author(s):  
Peter H. Yoon ◽  
Rudi Gaelzer
Keyword(s):  
Nonlinear Frequency ◽  
Frequency Shifts

Nonlinear resonance frequency shifts in acoustical resonators with varying cross sections.

2008 ◽  
Vol 124 (4) ◽  
pp. 2491-2491 ◽  
Author(s):  
Yurii A. Ilinskii ◽  
Mark F. Hamilton ◽  
Evgenia A. Zabolotskaya
Keyword(s):  
Resonance Frequency ◽  
Cross Sections ◽  
Nonlinear Resonance ◽  
Frequency Shifts

Analysis and Experimental Estimation of Nonlinear Dispersion in a Periodic String

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Kevin L. Manktelow ◽  
Michael J. Leamy ◽  
Massimo Ruzzene
Keyword(s):  
Dispersion Curve ◽  
Wave Dispersion ◽  
Lumped Parameter Model ◽  
Nonlinear Frequency ◽  
Nonlinear Dispersion ◽  
Frequency Shifts ◽  
Wave Transport ◽  
Lumped Parameter ◽  
Dispersion Frequency ◽  
Nonlinear Frequency Response

Wave dispersion in a string carrying periodically distributed masses is investigated analytically and experimentally. The effect of the string's geometric nonlinearity on its wave propagation characteristics is analyzed through a lumped parameter model yielding coupled Duffing oscillators. Dispersion frequency shifts are predicted that correspond to the hardening behavior of the nonlinear chain and that relate well to the backbone of individual Duffing oscillators. Experiments conducted on a string of finite length illustrate the relation between measured resonances and the dispersion properties of the medium. Specifically, the locus of resonance peaks in the frequency/wavenumber domain outlines the dispersion curve and highlights the existence of a frequency bandgap. Moreover, amplitude-dependent resonance shifts induced by the string nonlinearity confirm the hardening characteristics of the dispersion curve. Analytical and experimental results provide a critical link between nonlinear dispersion frequency shifts and the backbone curves intrinsic to nonlinear frequency response functions. Moreover, the study confirms that amplitude-dependent wave properties for nonlinear periodic systems may be exploited for tunability of wave transport characteristics such as frequency bandgaps and wave speeds.

Transition from a coherent three wave system to turbulence with application to the fluid closure

2014 ◽  
Vol 81 (1) ◽  
Author(s):  
Jan Weiland ◽  
Chuan S. Liu ◽  
Anatoly Zagorodny
Keyword(s):  
Distribution Function ◽  
Wave Packet ◽  
Random Phase ◽  
Maxwellian Distribution ◽  
Wave System ◽  
Nonlinear Frequency ◽  
Frequency Shifts ◽  
Wave Dynamics ◽  
Phase Velocities ◽  
Maxwellian Distribution Function

AbstractWe start from a Mattor–Parker system and its generalization to include diffusion and derive the Random Phase equations. It is shown that the same type of fluid closure holds in the coherent and turbulent regimes. This is due to the fact that the Random Phase levels (1/I1 = 1/I2 + 1/I3), where Ij is the intensity of wave packet ‘j’, are attractors for the wave dynamics both in the coherent and incoherent cases. Focus here is on the wave dynamics with phase velocities varying due to nonlinear frequency shifts. Thus a Maxwellian distribution function is kept in all cases.

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