Wave propagation on coated cylindrical shells

Guided wave is a type of wave propagation in which the waves are guided in plates, rods, pipes or elongated structures such as rails and I-beams. In order to extract the guided wave velocities and wavestructures, for waveguides of arbitrary cross section, a theoretical framework is developed. Here, a semi-analytical finite element (SAFE) method is used for the calculation of the wave propagation characteristics in elastic waveguides immersed in vacuum. The method couples an approximate displacement field over the cross-section of the waveguide and assumes time harmonic representation of the propagating waves along the length of the guide. The Hamilton’s principle and the finite element discretization lead to a discrete weak form of the energy balance equation. The wave propagation problem reduces to a system of algebraic equations, from which the dispersive equation can be obtained. The solution, which depends on both time t and propagation coordinate z, i.e. e i(ξz − ωt) results in a two-parameter eigensystem. By specifying a real axial wavenumber ξ, the eigenproblem permits real frequencies of propagating modes to be determined. Giving instead real frequency ω, both real and complex axial wavenumbers can be extracted, where real values pertain to propagating modes and the complex ones to the evanescent modes. The method allows us to model a generic cross-section of solid waveguide and it is well suited for computing the phase velocity, the group velocity and the wavestructure or cross-sectional mode shape.

PROPAGATING WAVES AND END MODES IN PRETWISTED BEAMS

In a previous paper, by Lee, Liu and Ballato (IEEE Ultr. Symp. pp. 869-72, 1999), the 3D equations of linear piezoelectricity with quasi-electrostatic approximation were extended to include losses attributed to the mechanical damping in solid and the resistance in current conduction. These equations were employed to investigate the plane wave propagation in an unbounded solid and forced thickness vibration of an infinite piezoelectric plate. In this paper, these equations are employed to obtain solutions of plane harmonic wave of arbitrary direction in an infinite and dissipative piezoelectric plate with general crystal symmetry, in a manner similar to that of Syngellakis and Lee (J. Appl. Phys., vol. 73, no. 11, pp. 7152-61, 1993). Dispersion curves are computed and plotted for real frequencies and complex wave numbers. Effects of energy loss on the wave propagation are examined in detail for AT-cut quartz as well as barium titanate ceramic plate.

On identification of a wave number for Helmholtz equation

A study is presented for boundary value problems arising from the wave diffraction theory and involving variable impedance conditions. Two different geometrical situations are considered: the diffraction by a strip and by a half-plane. In the first case, both situations of real and complex wave numbers are analyzed, and in the second case only the complex wave number case is considered. At the end, conditions are founded for the well-posedness of the problems in Bessel potential space settings. These conditions depend on the wave numbers and the impedance properties.

The impedance boundary-value problem of diffraction by a strip

Eddy-current inverse techniques using single-frequency currents have been applied with limited success to the reconstruction of crack width and thickness profiles primarily for one-dimensional and axisymmetric geometries. Because of the diffusive nature of the induced low-frequency eddy currents, the reconstruction process differs from high-frequency wave propagation methods. On the physical basis that both diffusive and wave phenomena can be described by the same Green's function with either a complex or real wave number, an integral formulation for the low-frequency magnetic vector potential is presented. By employing an iterative Born approximation algorithm and the method of moments, a reconstruction method for the conductivity profile in a metallic specimen is developed. To make this formulation amenable to complex geometries, finite-element analysis techniques are utilized to compute the integral kernel. The inversion process is tested with synthetic data generated by the numerical solution of a generic embedded flaw in a full-space and a surface-breaking defect.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In his remarks on the comments by Yokoyama (see ibid., vol.43, no.5, p.541-42, 1995) and the reply by King and Sandler (see ibid., vol.43, no.5, p.542-44, 1995) regarding our paper (see ibid., vol.42, no.3, p.382-9, 1994) J. R. Wait (see ibid., vol.44, no.2, p.271-72, 1996) makes a number of statements that require correction. These are considered in turn, but since they all center about the definition of the Sommerfeld numerical distance, this is introduced first. In a paper by Norton (1937), which is later quoted and applied by Wait, a formula is given for the generalized numerical distance for the height z and radial distance /spl rho/ due to a vertical dipole at the height d in the air (region 2, real wave number k/sub z/) over a conducting or dielectric region 1 (complex wave number k/sub 1/). It is important to emphasize that the purpose of this response is not to belittle the important pioneer work of Norton, Wait, and others. Interest a half century ago was in communication over the surface of the Earth and sea with (z+d)/sup 2//spl Lt//spl rho//sup 2/. In this range, their formulas are accurate. However, recent progress which eliminates the restriction (z+d)/sup 2//spl Lt//spl rho//sup 2/ or k/sub 2//spl rho//spl Gt/1 should not be ignored by blindly using restricted formulas where they do not apply.

This study investigates tropical cyclone energy dispersion under horizontally sheared flows using a nonlinear barotropic model. In addition to common patterns, unusual features of Rossby wave trains are also found in flows with constant vorticity and vorticity gradients. In terms of the direction of the energy dispersion, the wave train can rotate clockwise and elongate southwestward under anticyclonic circulation (ASH), which contributes to the reenhancement of the tropical cyclone (TC). The wave train even splits into two obvious wavelike trains in flows with a southward vorticity gradient (WSH). Energy dispersed from TCs varies over time, and variations in the intensity of the wave train components typically occur in two stages. Wave‐activity flux diagnosis and ray tracing calculations are extended to the frame that moves along with the TC to reveal the concrete progress of wave propagation. The direction of the wave‐activity flux is primarily determined by the combination of the basic flow and the TC velocity. Along the flux, the distribution of pseudomomentum effectively illustrates the development of wave trains, particularly the rotation and split of wave propagation. Ray tracing involves the quantitative tracing of wave features along rays, which effectively coincide with the wave train regimes. Flows of a constant shear (parabolic meridional variation) produce linear (nonlinear) wave number variations. For the split wave trains, the real and complex wave number waves move along divergent trajectories and are responsible for different energy dispersion ducts.

We present the existence and uniqueness theorem for the solutions of the boundary value problems (BVPs) of the Helmholtz equation with a real or complex constant wave number k. The essence of the theorem is employed to develop a new method of suppressing all resonant modes produced by Helmholtz BVPs at high frequencies.

Electrostatic wave noise in the neutral sheet in the earth's geomagnetic tail

This paper presents a numerical approach based on spectral methods for the computation of guided ultrasonic wave modes in stressed elastic plates and rods. The approach is applicable to Lamb modes in anisotropic plates and longitudinal modes in isotropic rods under uniform stress. The proposed approach computes the modeshapes and the full complex dispersion spectrum (real frequency, complex wavenumber), accommodating both propagating (real wavenumber) and non-propagating (complex wavenumber) modes. Numerical results are presented for plates composed of fiber-reinforced graphite/epoxy (GREP) and plates and rods composed of Hecla 17 steel. The results are used to investigate and compare the effect of stress on the dispersion curves for plates and rods, while demonstrating the computational efficiency of spectral methods. The convergence rate is demonstrated, showing spectral convergence.

We study the fundamental modes of radiation hydrodynamic linear waves that arise from one-dimensional small-amplitude initial fluctuations with wave number k in a radiating and scattering grey medium by taking into account the gravitational effects. The equation of radiative acoustics is derived from three hydrodynamic equations, Poisson’s equation, and two moment equations of radiation, by assuming a spherical symmetry for the matter and radiation and by using the Eddington approximation. We solve the dispersion relation as a quintic function of angular frequency ω, the wave number k being a real parameter. Numerical results reveal that wave patterns of five solutions are distinguished into three types: the radiation-dominated, type 1, and type 2 matter-dominated cases. In the case of no gravitaional effects (Kaneko et al., 2005), the following wave modes appear: radiation wave, conservative radiation wave, entropy wave, Newtonian-cooling wave, opacity-damped and cooling-damped waves, constant-volume and constant-pressure diffusions, adiabatic sound wave, cooling-damped and drag-force-damped isothermal sound waves, isentropic radiation-acoustic wave, and gap mode. Meanwhile, the gravitaional effects being taken into account, the growing gravo-diffusion mode newly arises from the constant-pressure diffusion at the point that k agrees with Jeans’ wave number specified by the isothermal sound speed. This mode changes to the growing radiation-acoustic gravity mode near the point that k becomes Jeans’ wave number specified by the isentropic radiation-acoustic speed. In step with a transition between them, the isentropic radiation-acoustic wave splits into the damping radiation-acoustic gravity mode and constant-volume diffusion. The constant-volume diffusion emerges twice if the gravitational effects are taken into account. Since analytic solutions are derived for all wave modes, we discuss their physical significance. The critical conditions are given which distinguish between radiation-dominated and type 1 matter-dominated cases, and between type 1 and type 2 matter-dominated cases. Waves in a self-gravitating scattering grey medium are also analyzed, which provides us some hints for the effects of energy and momentum exchange between matter and radiation.

Effect of heterogeneity on the axisymmetric vibrations of cylindrical shells

An algebraic description of basic discrete symmetries (space reversal P, time reversal T, and their combination PT) is studied. Discrete subgroups of orthogonal groups of multidimensional spaces over the fields of real and complex numbers are considered in terms of fundamental automorphisms of Clifford algebras. In accordance with a division ring structure, a complete classification of automorphism groups is established for the Clifford algebras over the field of real numbers. The correspondence between eight double coverings (Dąbrowski groups) of the orthogonal group and eight types of the real Clifford algebras is defined with the use of isomorphisms between the automorphism groups and finite groups. Over the field of complex numbers there is a correspondence between two nonisomorphic double coverings of the complex orthogonal group and two types of complex Clifford algebras. It is shown that these correspondences associate with a well-known Atiyah–Bott–Shapiro periodicity. Generalized Brauer–Wall groups are introduced on the extended sets of the Clifford algebras. The structure of the inequality between the two Clifford–Lipschitz groups with mutually opposite signatures is elucidated. The physically important case of the two different double coverings of the Lorentz groups is considered in details.