Papers by Keyword: Dispersion Relation

Abstract: Dispersion relation for the p-wave sound speed and attenuation has been described by several models based on continuum or scattering theory. As an alternative approach, this study proposes a model describing relation for the p-wave in case of elastic grain scatterers existing in background fluid medium. Dispersion relations are shown as a function of different grain size distribution and Rayleigh parameter . For quantitative analysis of the proposed model, experiments are performed using water-saturated glass beads. Two sets of experiments employing unimodal and bimodal grain size distributions are performed and used for comparison with the current proposed model.

Abstract: This work is concerned with the dispersion characteristics of Love waves propagating in a layered structure consisting of an anisotropic elastic layer and a piezoelectric half-space. The layer processes one symmetric plane, while the half-space is transversely isotropic. The explicit dispersion equation is derived. As an example, an inclined orthotropic material is chosen as an elastic layer to reveal the effect of material anisotropy on the dispersion behaviors. The numerical results show that the phase velocity is strongly influenced by the anisotropic degree.

Abstract: A novel approach is presented to solve the propagation of Lamb wave in a pre-stressed plate with finite thickness, where the commonly used Helmholtz decomposition method fails to find the solution. By using the proposed approach, some important relations of Lamb wave such as the dispersion relation can be obtained and analyzed in closed form, and the effects of initial stress are discussed in details. The method presented herein can be developed further to study the mechanical behaviors of other surface wave acoustic devices.

Abstract: There are many benchmark problems in computational aeroacoustics (CAA) and acoustic mode in the annular duct with uniform mean flow is a problem of this kind. The energy relation of the duct mode is deduced from the governing equation, Euler equations in this paper. If the sound power level, angular frequency, azimuthal mode number and radial mode number are given, the acoustic mode in the annular duct can be expressed explicitly by the deduced results. The simulation of two different cases shows the propagation of a single acoustic mode in annular duct pictorially.

Abstract: Back in 1990, D. S. Stewart and the first author contributed significantly to understanding the one-dimensional stability of detonation waves [1]. For this purpose, the reactive Euler’s equation with the one-component reaction term was linearized around the steady state of the well-known ZND (Zeldovich-Doering-von Neumann) model. The key aspect of this paper was to derive the linearized radiation condition (named after A. Sommerfeld). They numerically found multiple eigenvalues for pairs of the temporal frequency and temporal attenuation rate (TAR). Of course, the propagating-wave mode having the least value of the TAR (in the sense of its absolute value) was selected. The successful numerical implementation of the far-field radiation condition is a must when it comes to incorporating a large surrounding space into a problem of finite extent. To one of the sure examples in this category belong the problems involving detonation waves, where high-energy-rate processes take place in spatially confined spaces while the surrounding space should be taken into account for reasons of energy loss (or leaky waves in the language of optics). In another fascinating area of science is nano-photonics, where energy transport should be handled in highly confined regions of space, yet being surrounded by unbounded (dielectric) media. The total energy release in nano-photonics is certainly much smaller than that involved in detonation. However, the energy per unit nanometer-scale volume is not negligibly small in nano-photonics. Over the years, the first author has been successful in implementing both theory and numerical methods to find a multitude of eigenvalues in optics [2]. In this case, the governing Maxwell’s equations are already in a linearized form, being in a sense similar to the linearized Euler equations. In addition, the noble metals such as gold and silver are instrumental in enhancing local electric-field intensities, for which the science of plasmonics is being vigorously investigated in nano-photonics. Even the Bloch’s hydrodynamic equation describing the collective motion of the electrons is akin to the Navier-Stokes equations [3]. Meanwhile, assuming a real-valued frequency has been an old tradition in optics, partly because the real-valued photon’s energy is proportional to frequency and normally the continuous-wave (cw) approximation holds true. In a radical departure from this optical scientists’ tradition, we have recently attempted to deal with complex-valued frequencies in examining the wave propagations around nanoparticles [4, 5]. In consequence, the stability of multiple propagating waves was successfully determined for selecting most realizable wave mode. Further interesting points of the interplay between the two seemingly disparate branches of science (fluid dynamics and photonics) will be expounded in this talk.

Abstract: The propagation behavior of Love waves in a functionally graded material layered half-space with initial stress is taken into account. The Wentzel-Kramers-Brillouin (WKB) asymptotic technique is adopted for the theoretical derivations. The analytical solutions are obtained for the dispersion relations and the distributions of mechanical displacement and stress along thickness direction in the layered structure. Firstly, these solutions are used to study effects of the initial stress on the dispersion relations and phase velocities, then influences of the initial stress on the distributions of mechanical displacement and shear stresses along thickness direction are discussed in detail. Numerical results obtained indicate that the phase velocity of Love wave increases with the increase of the magnitude of the initial tensile stress, while decreases with the increase of the magnitude of the initial compression stress. The effects on the dispersion relations of the Love wave propagation are negligible as the magnitudes of the initial stress are less than 100MPa. Some other results are shown for distributions of field quantities along thickness direction. The results obtained are not only meaningful for the design of functionally graded structures with high performance but also effective for the evaluation of residual stress distribution in the layered structures.

Abstract: The propagation of shear horizontal (SH) wave is studied in a tri-material composed of a piezomagnetic layer and two semi-infinite piezoelectric half-spaces. These materials are hexagonal (6mm) crystals. A dispersion relation is exactly derived. The numerical results show the existence of the SH wave and its dispersion characteristics. These may be useful for the applications of piezoelectric-piezomagnetic media in the microwave technology.