scholarly journals FEATURES OF NEAR-RESONANT TRIAD INTERACTIONS IN WAVES ON INTERMEDIATE DEPTH

2019 ◽  
Vol 47 (1) ◽  
pp. 138-144
Author(s):  
M.N. Shtremel
Keyword(s):  
Dispersion Relation ◽  
Relative Depth ◽  
Parameter Mismatch ◽  
Linear Dispersion ◽  
Intermediate Depth ◽  
Nonlinear Dispersion Relation ◽  
Frequency Mismatch ◽  
Spatial Periodicity ◽  
Common Opinion ◽  
Triad Interactions

The article is dedicated to studying of nonlinear triad interactions features. Full resonance in such interactions occurs either for triads of frequencies or wavenumbers. For the other parameter mismatch will occur. There is no common opinion whether there is wavenumber or frequency mismatch in waves propagating on intermediate depth. In this work it is shown that mismatch occurs for wavenumbers. Possibility of prediction of spatial periodicity of energy exchange between wave harmonics was also studied. It was found that beat length can be predicted with linear dispersion relation for the relative depth exceeding 0.05. For depths less than 0.05 beat length can be assessed with nonlinear dispersion relation which accounts for wave steepness.

Modification of a turbulent spectrum through the injection of a monochromatic wave Part 2. The dispersion relation

1977 ◽  
Vol 17 (1) ◽  
pp. 1-11
Author(s):  
Armando L. Brinca
Keyword(s):  
Growth Rate ◽  
Dispersion Relation ◽  
Frequency Shift ◽  
Dispersion Equation ◽  
Monochromatic Wave ◽  
Nonlinear Dispersion ◽  
Linear Dispersion ◽  
Real Frequency ◽  
Nonlinear Dispersion Relation ◽  
Turbulent Spectrum

Analysis of the influence of an injected monochromatic wave on a turbulent spectrum shows that the resulting nonlinear dispersion relation for the stochastic modes displays a real frequency shift and a corrected growth rate when contrasted with the classical quasi-linear dispersion equation.

scholarly journals Thermodynamical Extension of a Symplectic Numerical Scheme with Half Space and Time Shifts Demonstrated on Rheological Waves in Solids

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 155 ◽  
Author(s):  
Tamás Fülöp ◽  
Róbert Kovács ◽  
Mátyás Szücs ◽  
Mohammad Fawaier
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Dispersion Relation ◽  
Half Space ◽  
Numerical Stability ◽  
Numerical Scheme ◽  
Nonlinear Dispersion ◽  
Finite Element Software ◽  
Space And Time ◽  
Nonlinear Dispersion Relation

On the example of the Poynting–Thomson–Zener rheological model for solids, which exhibits both dissipation and wave propagation, with nonlinear dispersion relation, we introduce and investigate a finite difference numerical scheme. Our goal is to demonstrate its properties and to ease the computations in later applications for continuum thermodynamical problems. The key element is the positioning of the discretized quantities with shifts by half space and time steps with respect to each other. The arrangement is chosen according to the spacetime properties of the quantities and of the equations governing them. Numerical stability, dissipative error, and dispersive error are analyzed in detail. With the best settings found, the scheme is capable of making precise and fast predictions. Finally, the proposed scheme is compared to a commercial finite element software, COMSOL, which demonstrates essential differences even on the simplest—elastic—level of modeling.

scholarly journals Nonlinear Bloch waves and balance between hardening and softening dispersion

2018 ◽  
Vol 474 (2217) ◽  
pp. 20180173 ◽  
Author(s):  
M. I. Hussein ◽  
R. Khajehtourian
Keyword(s):  
Dispersion Relation ◽  
Cell Size ◽  
Unit Cell ◽  
Homogeneous Layer ◽  
Nonlinear Dispersion ◽  
Elastic Band ◽  
Bloch Waves ◽  
Unit Cell Size ◽  
Nonlinear Dispersion Relation ◽  
Hardening And Softening

The introduction of nonlinearity alters the dispersion of elastic waves in solid media. In this paper, we present an analytical formulation for the treatment of finite-strain Bloch waves in one-dimensional phononic crystals consisting of layers with alternating material properties. Considering longitudinal waves and ignoring lateral effects, the exact nonlinear dispersion relation in each homogeneous layer is first obtained and subsequently used within the transfer matrix method to derive an approximate nonlinear dispersion relation for the overall periodic medium. The result is an amplitude-dependent elastic band structure that upon verification by numerical simulations is accurate for up to an amplitude-to-unit-cell length ratio of one-eighth. The derived dispersion relation allows us to interpret the formation of spatial invariance in the wave profile as a balance between hardening and softening effects in the dispersion that emerge due to the nonlinearity and the periodicity, respectively. For example, for a wave amplitude of the order of one-eighth of the unit-cell size in a demonstrative structure, the two effects are practically in balance for wavelengths as small as roughly three times the unit-cell size.

scholarly journals Nonlinear dispersion relation in anharmonic periodic mass-spring and mass-in-mass systems

2019 ◽  
Vol 462 ◽  
pp. 114929 ◽  
Author(s):  
R. Zivieri ◽  
F. Garescì ◽  
B. Azzerboni ◽  
M. Chiappini ◽  
G. Finocchio
Keyword(s):  
Dispersion Relation ◽  
Nonlinear Dispersion ◽  
Nonlinear Dispersion Relation ◽  
Mass Spring
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