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dispersion equation of magnetoelastic shear waves in irregular monoclinic layer

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Applied Mathematics and Mechanics(English Edition) 2011年第5期32卷 571-586页

作者： A.CHATTOPADHYAY S.GUPTA S.A.SAHU A.K.SINGH Department of Applied Mathematics Indian School of Mines

This paper studies the propagation of horizontally polarized shear waves in an internal magnetoelastic monoclinic stratum with irregularity in lower interface. The stratum is sandwiched between two magnetoelastic monoclinic semi-infinite media. dispersion equation is obtained in a closed form. In the absence of magnetic field and irregularity of the medium, the dispersion equation agrees with the equation of classical case in three layered media. The effects of magnetic field and size of irregularity on the phase velocity are depicted by means of graphs.

关键词： shear wave magnetoelastic monoclinic irregularity dispersion equation perturbation

G-type dispersion equation under suppressed rigid boundary:analytic approach

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Applied Mathematics and Mechanics(English Edition) 2016年第4期37卷 501-512页

作者： S.K.VISHWAKARMA Runzhang XU College of Automation Harbin Engineering University Department of Mathematics Birla Institute of Technology and Science (BITS)Pilani Hyderabad Campus College of Science Harbin Engineering University

This paper studies dispersion of a G-type earthquake wave under the influence of a suppressed rigid boundary. Inside the Earth, the density and rigidity of the crustal layer and the mantle of the Earth vary exponentially and periodically along the depth. The displacements of the wave are found in the individual medium followed by a dispersion equation using a suitable analytic approach and a boundary condition. The prominent effect of inhomogeneity contained in the media, the rigid boundary plane, and the initial stress on the phase and group velocities is shown graphically.

关键词： G-type wave analytic approach dispersion equation group velocity rigid boundary

dispersion equation in Non-uniform Optical Waveguide

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Semiconductor Photonics and Technology 1996年第2期2卷 90-98页

作者： ZHANG Jinwei(Jinan University, Guangzhou 510632,CHN)

We study the WKB dispersion equation in non-uniform optical *** are three methods given in this paper:(1) method of Airy function;(2)method of connection formula;and(3) method of phase *** last we make some remarks.

关键词： Optical Waveguide dispersion equation WKB Approximate Method

dispersion equation of a double shell-fluid coupled system

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Chinese Journal of Acoustics 1996年第4期15卷 350-357页

作者： ZHAO Xiang XU Jianxue and JIANG Jun(Research Institute for Nonlinear Dynamics, Xi’an Jiantong University Xi’an 710049)

The dispersion behaviour of a double shell-fluid system, which consists of two thin concentric cylindrical elastic shells coupled by the entrained annular fluid, is a fundamental for investigation of its vibroacoustical characteristics. Based on Flugge's infinite shell equations,the sound wave equation for the fluid field and boundary conditions at the fluidstructure interfaces, the dispersion equationfor the system is deduced and a corresponding numerical example is given in the paper.

关键词： Double shell Annular flow Coupled system dispersion equation

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关于色散方程的一类二阶恒稳显格式

高等学校计算数学学报 2001年第3期23卷 255-260页

作者：陈海光张大凯贵州大学数学系上海201418 上海师范大学奉贤校区机电学院贵阳550025

A kind of absolutely stable explicit difference schemes with two parameters for the dispersion equation u t=au xxx are proposed by this paper here. The truncation errors of the schemes are first order in time and second order in space. And the schemes are absolutely stable, simple and easy to calculate. For the present, they are the perfect three level explicit difference schems which have good accuracy, stability and calculation simplity. The numerical examples have examined the result of theoretical analysis.

关键词： dispersion equation explicit difference scheme absolutely stability.

Acoustics of a viscoelastic medium with encapsulated bubbles

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Journal of Hydrodynamics 2021年第1期33卷 55-62页

作者： Damir A.Gubaidullin Yuri V.Fedorov Laboratory of Continuum Mechanics Institute of Mechanics and EngineeringFRC Kazan Scientific CenterRussian Academy of SciencesKazanRussia

In this paper,a modified Rayleigh-Lamb equation is derived that takes into account the radial vibrations of a gas bubble coated with a viscoelastic shell and located in an elastic *** small oscillations of inclusion,the problem of heat exchange between a gas,a liquid phase,a viscoelastic shell,and an elastic medium is *** energy integral is *** the case of small disturbances,the dispersion relation is found from the Rayleigh-Lamb equations,energy,and the known wave equation for the bubbly *** analytical expression of the equilibrium speed of sound is written out and its dependence on the size of the viscoelastic shell and the disturbance frequency is *** example of a mixture of polydimethylsiloxane with air bubbles coated with a rubber shell illustrates the influence of the elasticity of the carrier medium and the shell of the bubbles on the dependence of the phase velocity and attenuation coefficient on the perturbation *** a mixture of water with air bubbles coated with a rubber shell,the influence of the dependences of the shear modulus and viscosity of butyl rubber on the frequency of disturbances at different temperature on the dispersion curves is shown.A comparison of the theory with experimental data is given.

关键词： Acoustic wave gas bubbles viscoelastic medium and shell shear modulus dispersion equation

Linear theory of a dielectric-loaded rectangular Cerenkov maser with a sheet electron beam

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Chinese Physics B 2012年第10期21卷 245-250页

作者：陈晔赵鼎刘文鑫王勇万晓声 Key Laboratory of High Power Microwave Sources and Technologies Institute of ElectronicsChinese Academy of Sciences Graduate University of Chinese Academy of Sciences

A three-dimensional model of a dielectric-loaded rectangular Cerenkov maser with a sheet electron beam for the beam-wave interaction is *** on this model,the hybrid-mode dispersion equation is derived with the Borgnis potential function by using the field-matching *** approximate solution is obtained under the assumption of a dilute electron *** using the Ansoft high frequency structural simulator（HFSS） code,the electromagnetic field distribution in the interaction structure is *** numerical calculations,the effects of beam thickness,beam and dielectric-layer gap distance,beam voltage,and current density on the resonant growth rate are analysed in detail.

关键词： rectangular Cerenkov maser beam-wave interaction hybrid-mode dispersion equation Borgnis potential function

Theoretical dispersion curves for borehole real-valued wave modes in vertically transverse isotropic formations

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Petroleum Science 2022年第6期19卷 2649-2662页

作者： Fu-Qiang Zeng Chao Li Hubei Subsurface Multi-scale Imaging Key Laboratory Institute of Geophysics and GeomaticsChina University of GeosciencesWuhan430074HubeiChina State Key Laboratory of Acoustics Institute of AcousticsChinese Academy of SciencesBeijing100190China Beijing Engineering and Technology Research Center for Deep Drilling Exploration and Measurement Beijing100190China

The dispersion curves of real-valued modes in a fluid-filled borehole are widely used in acoustic well *** accurate dispersion curves are the precondition of theoretical analysis and inversion ***,these curves can be obtained by solving the conventional dispersion equation for isotropic formations and most vertically transverse isotropy(VTI)***,if the real-valued solutions exist when the radial wavenumbers for the formation quasi-P and quasi-S equals to each other,the existed methods based on the conventional dispersion equation could lead to incorrect results for some VTI *** studies have focused on the influence of these real-valued solutions on dispersion curve *** remove these real-valued solutions,we have proposed a modified dispersion equation and its corresponding solving *** solving the dispersion equation,the Scholte wave velocity of VTI formation at high frequency is used as the initial *** two synthetic examples including fast and slow VTI formations validate that these real-valued solutions do not contribute to the wavefield,and the new dispersion curve extraction method is suitable for all kinds of VTI ***,the method can provide reliable dispersion curves for both theoretical analysis and anisotropic parameters inversion in VTI formations.

关键词： dispersion equation Scholte wave velocity Acoustic properties Transverse isotropy Thomsen anisotropic parameters inversion

THE STABILITY OF VISCOUS LIQUID JETS IN A SWIRLING GAS

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Acta Mechanica Sinica 1998年第3期14卷 226-233页

作者：易世君解茂昭陈白欣 Chengdu Electromechanical College Chengdu 610031China Department of Power Engineering Dalian University of TechnologyDalian 116023China

Based on the linear analysis of stability, a dispersion equation is deduced which delineates the evolution of a general 3-dimensional disturbance on the free surface of an incompressible viscous liquid jet injected into a gas with swirl. Here, the dimensionless parameter J(e) is again introduced, in the meantime, another dimensionless-parameter E called as circulation is also introduced to represent the relative swirling intensity. With respect to the spatial growing disturbance mode, the numerical results obtained from solving the dispersion equation reveal the following facts. First, at the same value of E, in pace-with the changing of J(e), the variation of disturbance and the critical disturbance mode still keep the same characters. Second, the present results are the same as that of S.P. Lin when J(e) > 1; but in the range of J(e) < 1, it's no more the case, the swirl decreases the axisymmetric disturbance, yet increases the asymmetric disturbance, furthermore the swirl may make the character of the most unstable disturbance mode changed (axisymmetric or asymmetric); the above action of the swirl becomes much Stronger when J(e) << 1.

关键词： jet stability dispersion equation swirling gas