Cylindrical Wave Field Research Articles

Interaction between inclined pile groups subjected to harmonic vibrations

Vertical and inclined piles are used in seismic areas where they could be subjected to oblique harmonic vibration loads. The effect of closely spaced battered piles on the pile–soil–pile interaction has not yet been fully recognized. A simple analytical method, based on the elasto-dynamic theory by Novak and his associates, is used in the present study to characterize vertical and inclined isolated cylindrical piles subjected to inclined harmonic vibrations. The free field movement of the ground in the vicinity of the piles is determined using an approximate approach based on the interference of the cylindrical wave field originating along each pile shaft and spreading radially outward. In calculating the interaction factor between two battered piles, an analysis has been carried out to demonstrate the effect of the presence of a neighboring pile (receiver) while the first pile (source) is loaded. In this situation, it has been found that the movement of the source pile head is decreased when a receiver pile is present. Also, the effects of the pile–pile distance, the group geometry, the length of the piles, and the inclined angle for each or all of the piles have been studied and the corresponding results will be presented.

The cylindrical wave field of wave energy converters

Knowledge of the wave field modification by a wave energy converter (WEC) is important to device and wave farm design. Cylindrical solutions to the linear wave field have long been used to analytically compute wave forces on circular-cylindrical geometries and have been the means of an important multi-body interaction theory. The cylindrical solutions are valid for an arbitrary geometry, but previous methods for computing the necessary coefficients were cumbersome. Herein, we present a new method for computing the cylindrical wave-field coefficients for an arbitrary geometry from a known circular-cylindrical section of the wave field. The method employs the Fourier transform and the orthogonality property of the depth dependence. The necessary circular-cylindrical section of the wave field is computed with the industry-standard boundary-element-method solver, WAMIT. Coefficients are computed for the radiated and scattered wave fields of four WECs, a heaving point absorber, a surging point absorber, a terminator, and an attenuator. The resulting cylindrical wave fields are compared over a large domain to wave fields computed completely by WAMIT and are found to be very accurate. The asymptotic representation of the cylindrical wave field is also considered and its range of accuracy is shown to depend the number of partial waves used to accurately represent the cylindrical wave field. Analytical solutions to the WEC wave field enable the use of interaction theories that accelerate WEC array computation and the integration with wave models that include additional physics.

Bifurcation of Nonlinear Conservation Laws from the Classical Energy Conservation Law for Internal Gravity Waves in Cylindrical Wave Field

New conservation laws bifurcating from the classical form of conservation laws are constructed to the nonlinear Boussinesq model describing internal Kelvin waves propagating in a cylindrical wave field of an uniformly stratified water affected by the earth’s rotation. The obtained conservation laws are different from the well known energy conservation law for internal waves and they are associated with symmetries of the Boussinesq model. Particularly, it is shown that application of Lie group analysis provide three infinite sets of nontrivial integral conservation laws depending on two arbitrary functions, namely a (t, θ ), b (t, r ) and an arbitrary function c (t, θ, r ) which is given implicitly as a nontrivial solution of a partial differential equation involving a (t, θ ) and b (t, r ).

Focusing and scattering of the cylindrical-wave field by a finite Veselago lens

Scattering of the field of a cylindrical wave by a Veselago lens of a finite dimension is analyzed on the basis of rigorous calculations at various refractive indexes |nr| 1 of the metamaterial of the lens. It is shown that the features of geometric-optics ray patterns (including patterns obtained with allowance for field rereflections by the lens faces) for such a lens are due to the presence of a caustic with one cusp point and two end points. The effects of the geometric dimensions, the refractive index, and the position of a cylindrical-wave source on the field in focusing regions and on the scattering pattern are studied.

Stability of microwave heating of ceramic materials in a cylindrical cavity

Microwave heating of ceramic materials in a cylindrical wave field is analyzed by numerical simulation. The issues of temperature uniformity and stability inside the sample undergoing microwave heating are addressed. The heating regimes leading to development of global and localized thermal instabilities are illustrated. The role of the temperature dependence of the material's microwave dielectric properties in the formation of instabilities is demonstrated. The tuning and matching of a cylindrical cavity containing the sample is analyzed within a simple model for the microwave and millimetre-wave frequency ranges.

Nonspecular reflections from a curved interface

If an incident wavefield hits a curved interface that possesses certain inflection points, there may exist “nonspecular” events in the reflected field that cannot be explained by real ray theory. The magnitude of such events can reach the order of the specular ones and can be expressed in terms of specular reflections at certain points on the analytic continuation of the interface. In fact, specular reflected “complex rays,” connecting complex reflection points with the observation point, are used to explain such events. Previous results obtained for acoustic calculations, involving an incident plane wave and a perfectly soft reflector, are extended to arbitrary velocity and density contrasts, as well as to an incident far‐field cylindrical wavefield. Moreover, the agreement between analytic results and independent computations using a finite‐differences scheme is shown. It confirms the existence of nonspecular reflections. The interpreter of a seismic section should, therefore, be aware of not attributing a subsurface interface to a nonspecular reflection, e.g., at a flank of a saltdome.

Spall observations and mechanisms in alluvium

Spall, as identified by minus 1 g dwells on vertical accelerometers followed by impulsive rejoin signals, has been observed in ground motion data recorded in alluvium. These data resulted from explosions ranging from fully contained to surface burst configurations. The variability of the loading environments and the observational data support the conclusion that the phenomena result from multiple mechanisms. The data show that relatively low accelerations (<20 g) accompany the process, but owing to the long dwell times involved, resulting displacements may be large. Five spall models are discussed and shown to operate in some aspect of the data base. These mechanisms include (1) simple tensile reflection from the free surface, (2) Rayleigh/shear waves from surface sources, (3) spherical and cylindrical wave field divergence, (4) positive and negative phase airblast effects on porous materials, and (5) material properties of porous particulate matter.

Mode-III crack kinking under stress-wave loading

A horizontally polarized step-stress wave is incident on a semi-infinite crack in an elastic solid. At the instant that the crack tip is struck, the crack starts to propagate in the forward direction, but under an angle κπ with the plane of the original crack. In this paper a self-similar solution is obtained for the particle velocity of the diffracted cylindrical wave field. The use of Chaplygin's transformation reduces the problem to the solution of Laplace's equation in a semi-infinite strip containing a slit. The Schwarz-Christoffel transformation is employed to map the semi-infinite strip on a half-plane. An analytic function in the half-plane which satisfies appropriate conditions along the real axis, can subsequently be constructed. The Mode-III stress-intensity factor at the tip of the kinked crack has been computed for angles of incidence varying from normal to grazing incidence, for angles of crack kinking defined by -0.5⩽κ⩽0.5, and for arbitrary subsonic crack tip speeds.