Two-Dimensional Theory

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A M Sergeev - One of the best experts on this subject based on the ideXlab platform.

  • Two-Dimensional Theory of Cherenkov radiation from short laser pulses in a magnetized plasma.
    Physical review. E Statistical nonlinear and soft matter physics, 2004
    Co-Authors: M I Bakunov, S B Bodrov, A V Maslov, A M Sergeev
    Abstract:

    The Cherenkov wakes excited by intense laser drivers in a perpendicularly magnetized plasma are a potential source of high-power terahertz radiation. We present a Two-Dimensional (2D) Theory of the emission of magnetized wakes excited by a short laser pulse. The 2D model reveals the important role of the transverse size of the laser pulse missed in previous simple one-dimensional estimations of the radiation. We derived expressions for the radiated fields and for the angular/frequency distribution of the radiated energy. Beats in the radiation pattern behind the moving pulse are predicted and explained. For the interpretation of existing experimental results, the time dependence of the energy flux parallel and perpendicular to the laser path is examined.

Ji Wang - One of the best experts on this subject based on the ideXlab platform.

  • A Two-Dimensional Theory for the analysis of surface acoustic waves in finite elastic solids
    Journal of Sound and Vibration, 2006
    Co-Authors: Ji Wang, Ken-ya Hashimoto
    Abstract:

    The analysis of surface acoustic waves in elastic solids started from a semi-infinite isotropic elastic body with solutions and techniques dated back to Lord Rayleigh. These solutions have explained the surface acoustic wave phenomena and guided its engineering applications in many fields. Research work followed have been using the same semi-infinite model with solution techniques for approximate and exact results in both analytical and numerical manners for many application problems involving finite elastic solids. On the other hand, we have noticed that various Two-Dimensional theories, notably plate Theory by Mindlin, have been derived to study the bulk wave propagation in finite elastic solids like plates and bars with satisfactory results. The lack of such a Two-Dimensional Theory has made the analysis of surface acoustic wave propagation in various waveguides primitive and difficult because the precise solutions cannot be obtained through any analytical effort and numerical solutions are also difficult to obtain because of the complicated nature of problems. To meet the need of a simplified analytical method for surface acoustic waves in finite elastic solids, we start the derivation from the well-known three-dimensional solutions of semi-infinite elastic solids. Using exact solutions as the basis for the Two-Dimensional expansion, we found that the usual procedure of dimension reduction works perfectly in this case because the unknown wavenumber is eventually removed in the expansion process, and the depth of the solid is considered through integration constants that are exponentially decaying functions of the wavenumber, which is to be specified. In addition, we also found the Two-Dimensional equations give the exact phase velocity without corrections of any kind in the limiting case in which the solid is semi-infinite. With these equations, Two-Dimensional solutions of mechanical displacements and phase velocity can be obtained analytically from four coupled differential equations that are similar to Mindlin plate equations. We demonstrated the applications of the Two-Dimensional Theory with the analysis of surface waves in isotropic elastic rectangular strips. The velocity and displacement results offer a chance to understand surface acoustic waves in finite solids and the presence of overtone modes and transition zones.

  • A Two-Dimensional analysis of surface acoustic waves in finite solids with the consideration of electrodes
    International Journal of Applied Electromagnetics and Mechanics, 2005
    Co-Authors: Ji Wang, Jingbo Lin, Yongping Wan, Zheng Zhong
    Abstract:

    The analysis of surface acoustic wave propagation in finite elastic solids is of essential importance in the study of the propagation nature and practical applications, and tremendous efforts have been made lately in employing both analytical and numerical methods for accurate solutions of the phase velocity and displacements. To overcome current difficulties in the physical model and computational intensity, a Two-Dimensional Theory similar to Mindlin and Lee plate theories has been established for the surface acoustic wave propagating in finite elastic solids. A systematic simplification of the three-dimensional equations resulted in a Two-Dimensional Theory with accuracy and potential to solve surface acoustic wave problems in solids in a more efficient manner. For practical applications, the presence of a thin film over the substrate is studied with the Two-Dimensional Theory with systematic modification, and straight-crested solutions with different film thickness are obtained.

  • A Two-Dimensional Theory for Surface Acoustic Wave Propagation in Finite Piezoelectric Solids
    Journal of Intelligent Material Systems and Structures, 2005
    Co-Authors: Ji Wang, Jingbo Lin
    Abstract:

    Surface acoustic waves (Rayleigh waves) are analyzed for semi-infinite anisotropic solids only for essential propagation characteristics like the velocity and decaying parameters, which are important in engineering applications. The limitations of these results are obvious because devices are usually built on a finite piezoelectric substrate with propagation properties different from the analytical model with which the parameters are derived. For an accurate analysis of the dominant mode of surface acoustic wave propagation in plate-like finite piezoelectric solids, a Two-Dimensional Theory has been developed based on the exponential expansion of displacements and electrical potential in the thickness direction, effectively creating a Theory similar to popular plate theories of Mindlin, Lee, and others.

  • A Two-Dimensional Theory for the analysis of surface acoustic waves in finite anisotropic solids
    IEEE Symposium on Ultrasonics 2003, 1
    Co-Authors: Ji Wang, Ken-ya Hashimoto
    Abstract:

    A Two-Dimensional Theory for surface acoustic waves (SAW) analysis in finite solids is developed for anisotropic materials through the introduction of complex exponentially decaying parameters and expansion functions with the combination of trigonometric and exponential functions. Following the usual procedure for dimension reduction with three components in the basis function and complete coupling of three mechanical displacements due to anisotropy, we now have nine Two-Dimensional equations for the surface acoustic wave propagation in a finite anisotropic solid, resembling the higher-order Mindlin plate equations for bulk acoustic waves. We also found that these equations give the identical velocity in limiting case where the depth of the solid is infinite. With these equations and corresponding decaying parameters that are material specific and can be extracted through the half-space solutions, we calculated the phase velocity of straight-crested surface acoustic waves in a finite anisotropic strip to demonstrate the applications of these Two-Dimensional equations and the solution technique. Similar to plate theories, this Two-Dimensional Theory can be used in the surface acoustic wave device modeling for both analytical and numerical solutions with the advantage of simplifying the physical model and reducing the computational difficulty, thus posing great potential in aiding the increasingly complicated but important modeling and analytical efforts.

Jingbo Lin - One of the best experts on this subject based on the ideXlab platform.

  • A Two-Dimensional analysis of surface acoustic waves in finite solids with the consideration of electrodes
    International Journal of Applied Electromagnetics and Mechanics, 2005
    Co-Authors: Ji Wang, Jingbo Lin, Yongping Wan, Zheng Zhong
    Abstract:

    The analysis of surface acoustic wave propagation in finite elastic solids is of essential importance in the study of the propagation nature and practical applications, and tremendous efforts have been made lately in employing both analytical and numerical methods for accurate solutions of the phase velocity and displacements. To overcome current difficulties in the physical model and computational intensity, a Two-Dimensional Theory similar to Mindlin and Lee plate theories has been established for the surface acoustic wave propagating in finite elastic solids. A systematic simplification of the three-dimensional equations resulted in a Two-Dimensional Theory with accuracy and potential to solve surface acoustic wave problems in solids in a more efficient manner. For practical applications, the presence of a thin film over the substrate is studied with the Two-Dimensional Theory with systematic modification, and straight-crested solutions with different film thickness are obtained.

  • A Two-Dimensional Theory for Surface Acoustic Wave Propagation in Finite Piezoelectric Solids
    Journal of Intelligent Material Systems and Structures, 2005
    Co-Authors: Ji Wang, Jingbo Lin
    Abstract:

    Surface acoustic waves (Rayleigh waves) are analyzed for semi-infinite anisotropic solids only for essential propagation characteristics like the velocity and decaying parameters, which are important in engineering applications. The limitations of these results are obvious because devices are usually built on a finite piezoelectric substrate with propagation properties different from the analytical model with which the parameters are derived. For an accurate analysis of the dominant mode of surface acoustic wave propagation in plate-like finite piezoelectric solids, a Two-Dimensional Theory has been developed based on the exponential expansion of displacements and electrical potential in the thickness direction, effectively creating a Theory similar to popular plate theories of Mindlin, Lee, and others.

Dan White - One of the best experts on this subject based on the ideXlab platform.

  • Magnetoelasticity of highly deformable thin films: Theory and simulation
    International Journal of Non-Linear Mechanics, 2012
    Co-Authors: Matthew Barham, David Steigmann, Dan White
    Abstract:

    A non-linear Two-Dimensional Theory is developed for thin magnetoelastic films capable of large deformations. This is derived directly from the three-dimensional Theory. Significant simplifications emerge in the descent from three dimensions to two, permitting the self-field generated by the body to be computed a posteriori. The model is specialized to isotropic elastomers and numerical solutions are obtained to equilibrium boundary-value problems in which the membrane is subjected to lateral pressure and an applied magnetic field.

M I Bakunov - One of the best experts on this subject based on the ideXlab platform.

  • Two-Dimensional Theory of Cherenkov radiation from short laser pulses in a magnetized plasma.
    Physical review. E Statistical nonlinear and soft matter physics, 2004
    Co-Authors: M I Bakunov, S B Bodrov, A V Maslov, A M Sergeev
    Abstract:

    The Cherenkov wakes excited by intense laser drivers in a perpendicularly magnetized plasma are a potential source of high-power terahertz radiation. We present a Two-Dimensional (2D) Theory of the emission of magnetized wakes excited by a short laser pulse. The 2D model reveals the important role of the transverse size of the laser pulse missed in previous simple one-dimensional estimations of the radiation. We derived expressions for the radiated fields and for the angular/frequency distribution of the radiated energy. Beats in the radiation pattern behind the moving pulse are predicted and explained. For the interpretation of existing experimental results, the time dependence of the energy flux parallel and perpendicular to the laser path is examined.