scholarly journals Elastic wave dispersion equation considering material and geometric nonlinearities

2021 ◽  
Author(s):  
xiangyang li ◽  
Na Li ◽  
Bin Zheng ◽  
Jianqiang Bao ◽  
Yan Wang ◽  
...  
Keyword(s):  
Geometric Nonlinearity ◽  
Fourier Spectrum ◽  
Wave Dispersion ◽  
Nonlinear Dispersion ◽  
Geometric Nonlinearities ◽  
Longitudinal Waves ◽  
One Dimensional ◽  
Nonlinear Dispersion Relation ◽  
Nonlinear Elastic ◽  
Relationship Of

Abstract In this letter, we describe the propagation of longitudinal waves in one-dimensional nonlinear elastic thin rods with material nonlinearity and geometric nonlinearity. Mathematical analysis is used to derive the analytical dispersion relationship of longitudinal waves; subsequently, the numerical Fourier spectrum method is used to solve the nonlinear wave equation directly and the results are used to verify the correctness of the derived nonlinear dispersion relation.

scholarly journals The Nonlinear Dispersion Relation and the Relationship of the Forming Soliton Area to the Evolution of Pulsars

1987 ◽  
Vol 125 ◽  
pp. 461-461 ◽  
Author(s):  
Mao Xinjie ◽  
Tong Yi
Keyword(s):  
Electric Field ◽  
Ground State ◽  
Nonlinear Effects ◽  
Electric Polarization ◽  
Nonlinear Dispersion ◽  
Hydrogen Atoms ◽  
Nonlinear Dispersion Relation ◽  
Relationship Of ◽  
The Relationship ◽  
The Universe

Based on Zakharov's equations, Karpman et al. claimed that there were solitons in the magnetosphere. According to the model proposed by Goldreich and Julin, there is a strong induced electric field in the magnetosphere. It seems that we should include the nonlinear effects of the electric field on the polarization of hydrogen atoms if there really are some hydrogen atoms spreading in the magnetosphere of the pulsar. Assuming the magnetosphere is symetric, therefore the electric polarization of hydrogen atoms is of the form P=χ(1)E +χχE3. We treat χ(1) and χ(2) as scalars because most hydrogen atoms in the universe are in the ground state and χ(3) is much smaller than χ(1).

scholarly journals One-Dimensional Vacuum Steady Seepage Model of Unsaturated Soil and Finite Difference Solution

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Feng Huang ◽  
Jianguo Lyu ◽  
Guihe Wang ◽  
Hongyan Liu
Keyword(s):  
Finite Difference ◽  
Unsaturated Soil ◽  
Vacuum Pressure ◽  
Vacuum Field ◽  
One Dimensional ◽  
Steady Seepage ◽  
Basic Equations ◽  
The One ◽  
Seepage Law ◽  
Relationship Of

Vacuum tube dewatering method and light well point method have been widely used in engineering dewatering and foundation treatment. However, there is little research on the calculation method of unsaturated seepage under the effect of vacuum pressure which is generated by the vacuum well. In view of this, the one-dimensional (1D) steady seepage law of unsaturated soil in vacuum field has been analyzed based on Darcy’s law, basic equations, and finite difference method. First, the gravity drainage ability is analyzed. The analysis presents that much unsaturated water can not be drained off only by gravity effect because of surface tension. Second, the unsaturated vacuum seepage equations are built up in conditions of flux boundary and waterhead boundary. Finally, two examples are analyzed based on the relationship of matric suction and permeability coefficient after boundary conditions are determined. The results show that vacuum pressure will significantly enhance the drainage ability of unsaturated water by improving the hydraulic gradient of unsaturated water.

Attenuation of longitudinal electro-acoustic waves in a plasma

1974 ◽  
Vol 11 (1) ◽  
pp. 37-49
Author(s):  
R. J. Papa ◽  
P. Lindstrom
Keyword(s):  
Dispersion Relation ◽  
Electric Field ◽  
Acoustic Waves ◽  
Collision Frequency ◽  
Wave Dispersion ◽  
Signal Frequency ◽  
Variable Theory ◽  
Longitudinal Waves ◽  
Confluent Hypergeometric Functions ◽  
Linearized Boltzmann Equation

There are several practical situations in partially ionized plasmas when both collisionless (Landau) damping and electron-neutral collisions contribute to the attenuation of longitudinal waves. The longitudinal-wave dispersion relation is derived from Maxwell's equations and the linearized Boltzmann equation, in which electron-neutral collisions are represented by a Bhatnagar–Gross–Krook model that conserves particles locally. (The dispersion relation predicts that, for a given signal frequency ώ), an infinite number of complex wavenumbers kn can exist. Using Fourier–Laplace transform techniques, an integral representation for the electric field of the longitudinal waves is readily derived. Then, using theorems from complex variable theory, a modal expansion of the electric field can be made in terms of an infinite sum of confluent hypergeometric functions, whose arguments are proportional to the complex wavenumbers kn. It is demonstrated numerically that the spatial integral of the square of the electric field amplitude decreases as the electron-neutral collision frequency increases. Also, the amount of energy contained in the first few (lowest) modes, and the coupling between the modes, is examined as a function of plasma frequency, signal frequency and collision frequency.

scholarly journals Estimation for Two-Dimensional Nonsymmetric Coherently Distributed Source in L-Shaped Arrays

2018 ◽  
Vol 2018 ◽  
pp. 1-16
Author(s):  
Tao Wu ◽  
Zhenghong Deng ◽  
Qingyue Gu ◽  
Jiwei Xu
Keyword(s):  
Expectation Maximization ◽  
Two Dimensional ◽  
Signal Distribution ◽  
Distributed Source ◽  
One Dimensional ◽  
Least Squares Estimators ◽  
Iterative Calculation ◽  
Symmetric Source ◽  
Relationship Of ◽  
The Relationship

We explore the estimation of a two-dimensional (2D) nonsymmetric coherently distributed (CD) source using L-shaped arrays. Compared with a symmetric source, the modeling and estimation of a nonsymmetric source are more practical. A nonsymmetric CD source is established through modeling the deterministic angular signal distribution function as a summation of Gaussian probability density functions. Parameter estimation of the nonsymmetric distributed source is proposed under an expectation maximization (EM) framework. The proposed EM iterative calculation contains three steps in each cycle. Firstly, the nominal azimuth angles and nominal elevation angles of Gaussian components in the nonsymmetric source are obtained from the relationship of rotational invariance matrices. Then, angular spreads can be solved through one-dimensional (1D) searching based on nominal angles. Finally, the powers of Gaussian components are obtained by solving least-squares estimators. Simulations are conducted to verify the effectiveness of the nonsymmetric CD model and estimation technique.

scholarly journals Analytic Representation of the Optimal Flow for Gravity Irrigation

Water ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 2710 ◽  
Author(s):  
Carlos Fuentes ◽  
Carlos Chávez
Keyword(s):  
Linear Relationship ◽  
Analytic Representation ◽  
Hydrodynamic Characteristics ◽  
One Dimensional ◽  
Coupled Equations ◽  
Irrigation Flow ◽  
Coefficient Of Uniformity ◽  
Relationship Of ◽  
Strip Length ◽  
Infiltration Parameters

The aim of this study is the deduction of an analytic representation of the optimal irrigation flow depending on the border length, hydrodynamic properties, and soil moisture constants, with high values of the coefficient of uniformity. In order not to be limited to the simplified models, the linear relationship of the numerical simulation with the hydrodynamic model, formed by the coupled equations of Barré de Saint-Venant and Richards, was established. Sample records for 10 soil types of contrasting texture were used and were applied to three water depths. On the other hand, the analytical representation of the linear relationship using the Parlange theory of infiltration proposed for integrating the differential equation of one-dimensional vertical infiltration was established. The obtained formula for calculating the optimal unitary discharge is a function of the border strip length, the net depth, the characteristic infiltration parameters (capillary forces, sorptivity, and gravitational forces), the saturated hydraulic conductivity, and a shape parameter of the hydrodynamic characteristics. The good accordance between the numerical and analytical results allows us to recommend the formula for the design of gravity irrigation.

scholarly journals Study of Abnormal Group Velocities in Flexural Metamaterials

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Hong Woo Park ◽  
Joo Hwan Oh
Keyword(s):  
Group Velocity ◽  
Periodic Structure ◽  
Three Dimensional ◽  
Wave Dispersion ◽  
Abnormal Behavior ◽  
Flexural Wave ◽  
Negative Group ◽  
One Dimensional ◽  
Optical Branch ◽  
Negative Group Velocity

Abstract Generally, it has been known that the optical branch of a simple one-dimensional periodic structure has a negative group velocity at the first Brillouin zone due to the band-folding effect. However, the optical branch of the flexural wave in one-dimensional periodic structure doesn’t always have negative group velocity. The problem is that the condition whether the group velocity of the flexural optical branch is negative, positive or positive-negative has not been studied yet. In consequence, who try to achieve negative group velocity has suffered from trial-error process without an analytic guideline. In this paper, the analytic investigation for this abnormal behavior is carried out. In particular, we discovered that the group velocity of the optical branch in flexural metamaterials is determined by a simple condition expressed in terms of a stiffness ratio and inertia ratio of the metamaterial. To derive the analytic condition, an extended mass-spring system is used to calculate the wave dispersion relationship in flexural metamaterials. For the validation, various numerical simulations are carried out, including a dispersion curve calculation and three-dimensional wave simulation. The results studied in this paper are expected to provide new guidelines in designing flexural metamaterials to have desired wave dispersion curves.

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.

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