scholarly journals Modeling strong motions produced by earthquakes with two-dimensional numerical codes

1988 ◽  
Vol 78 (1) ◽  
pp. 109-121
Author(s):  
Donald V. Helmberger ◽  
John E. Vidale
Keyword(s):  
Wave Equation ◽  
Asymptotic Form ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Cylindrical Coordinates ◽  
Dimensional Theory ◽  
Dimensional Solution ◽  
Source Excitation ◽  
Dislocation Sources

Abstract We present a scheme for generating synthetic point-source seismograms for shear dislocation sources using line source (two-dimensional) theory. It is based on expanding the complete three-dimensional solution of the wave equation expressed in cylindrical coordinates in an asymptotic form which provides for the separation of the motions into SH and P-SV systems. We evaluate the equations of motion with the aid of the Cagniard-de Hoop technique and derive close-formed expressions appropriate for finite-difference source excitation.

Theory of Laminated Plates

1971 ◽  
Vol 38 (1) ◽  
pp. 231-238 ◽  
Author(s):  
C. T. Sun
Keyword(s):  
Equations Of Motion ◽  
Three Dimensional ◽  
Continuum Theory ◽  
Laminated Plates ◽  
Harmonic Waves ◽  
Two Dimensional ◽  
Laminated Plate ◽  
Governing Equations ◽  
Dimensional Theory ◽  
Rotatory Inertia

A two-dimensional theory for laminated plates is deduced from the three-dimensional continuum theory for a laminated medium. Plate-stress equations of motion, plate-stress-strain relations, boundary conditions, and plate-displacement equations of motion are presented. The governing equations are employed to study the propagation of harmonic waves in a laminated plate. Dispersion curves are presented and compared with those obtained according to the three-dimensional continuum theory and the exact analysis. An approximate solution for flexural motions obtained by neglecting the gross and local rotatory inertia terms is also discussed.

Membrane theory

2017 ◽  
Author(s):  
David J. Steigmann
Keyword(s):  
Three Dimensional ◽  
Thin Sheets ◽  
Two Dimensional ◽  
Leading Order ◽  
Membrane Theory ◽  
Dimensional Theory ◽  
Small Thickness

This chapter develops two-dimensional membrane theory as a leading order small-thickness approximation to the three-dimensional theory for thin sheets. Applications to axisymmetric equilibria are developed in detail, and applied to describe the phenomenon of bulge propagation in cylinders.

Study on soliton solutions of the longitudinal wave equation and magneto-electro-elastic circular rod dynamical model

2021 ◽  
Vol 35 (13) ◽  
pp. 2150168
Author(s):  
Adel Darwish ◽  
Aly R. Seadawy ◽  
Hamdy M. Ahmed ◽  
A. L. Elbably ◽  
Mohammed F. Shehab ◽  
...  
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Longitudinal Wave ◽  
Physical Interpretation ◽  
Elliptic Function ◽  
Function Method ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Jacobi Elliptic Function ◽  
Two Dimensional

In this paper, we use the improved modified extended tanh-function method to obtain exact solutions for the nonlinear longitudinal wave equation in magneto-electro-elastic circular rod. With the aid of this method, we get many exact solutions like bright and singular solitons, rational, singular periodic, hyperbolic, Jacobi elliptic function and exponential solutions. Moreover, the two-dimensional and the three-dimensional graphs of some solutions are plotted for knowing the physical interpretation.

Contact Temperature in Dry Bearings. Three Dimensional Theory and Verification

1981 ◽  
Vol 103 (2) ◽  
pp. 243-251 ◽  
Author(s):  
A. Floquet ◽  
D. Play
Keyword(s):  
Fourier Transform ◽  
Boundary Conditions ◽  
Experimental Verification ◽  
Three Dimensional ◽  
Contact Temperature ◽  
3D Analysis ◽  
New Work ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
Infra Red

Boundary conditions were arbitrarily specified in an earlier two dimensional (2D) analysis of contact temperature. In this new work a general three dimensional (3D) Fourier transform solution is obtained from which for specific cases, the boundary conditions can be estimated. Further, experimental verification of 3D analysis was performed using infra-red technique.

scholarly journals Visualization of CD2 interaction with LFA-3 and determination of the two-dimensional dissociation constant for adhesion receptors in a contact area.

1996 ◽  
Vol 132 (3) ◽  
pp. 465-474 ◽  
Author(s):  
M L Dustin ◽  
L M Ferguson ◽  
P Y Chan ◽  
T A Springer ◽  
D E Golan
Keyword(s):  
Contact Area ◽  
Dissociation Constants ◽  
Three Dimensional ◽  
Lateral Diffusion ◽  
Solution Phase ◽  
Phospholipid Bilayer ◽  
Cell Contact ◽  
Two Dimensional ◽  
Adhesion Receptors ◽  
Dimensional Solution

Many adhesion receptors have high three-dimensional dissociation constants (Kd) for counter-receptors compared to the KdS of receptors for soluble extracellular ligands such as cytokines and hormones. Interaction of the T lymphocyte adhesion receptor CD2 with its counter-receptor, LFA-3, has a high solution-phase Kd (16 microM at 37 degrees C), yet the CD2/LFA-3 interaction serves as an effective adhesion mechanism. We have studied the interaction of CD2 with LFA-3 in the contact area between Jurkat T lymphoblasts and planar phospholipid bilayers containing purified, fluorescently labeled LFA-3. Redistribution and lateral mobility of LFA-3 were measured in contact areas as functions of the initial LFA-3 surface density and of time after contact of the cells with the bilayers. LFA-3 accumulated at sites of contact with a half-time of approximately 15 min, consistent with the previously determined kinetics of adhesion strengthening. The two-dimensional Kd for the CD2/LFA-3 interaction was 21 molecules/microns 2, which is lower than the surface densities of CD2 on T cells and LFA-3 on most target or stimulator cells. Thus, formation of CD2/LFA-3 complexes should be highly favored in physiological interactions. Comparison of the two-dimensional (membrane-bound) and three-dimensional (solution-phase) KdS suggest that cell-cell contact favors CD2/LFA-3 interaction to a greater extent than that predicted by the three-dimensional Kd and the intermembrane distance at the site of contact. LFA-3 molecules in the contact site were capable of lateral diffusion in the plane of the phospholipid bilayer and did not appear to be irreversibly trapped in the contact area, consistent with a rapid off-rate. These data provide insights into the function of low affinity interactions in adhesion.

A THREE-DIMENSIONAL AZIMUTHAL WIDE-ANGLE MODEL FOR THE PARABOLIC WAVE EQUATION

1999 ◽  
Vol 07 (04) ◽  
pp. 269-286 ◽  
Author(s):  
CHIFANG CHEN ◽  
YING-TSONG LIN ◽  
DING LEE
Keyword(s):  
Wave Equation ◽  
Prediction Models ◽  
Three Dimensional ◽  
3D Models ◽  
Theoretical Development ◽  
Wide Angle ◽  
Two Dimensional ◽  
Narrow Angle ◽  
Propagation Prediction ◽  
Dimensional Range

In predicting wave propagations in either direction, the size of the angle of propagation plays an important role; thus, the concept of wide-angle is introduced. Most existing acoustic propagation prediction models do have the capability of treating the wide-angle but the treatment, in practice, is vertical. This is desirable for solving two-dimensional (range and depth) problems. In extending the two-dimensional treatment to 3 dimensions, even though the wide-angle capability is maintained in most 3D models, it is still vertical. Owing to the need of a wide-angle capability in the azimuth direction, this paper formulates an azimuthal wide-angle wave equation whose theoretical development is presented. An illustrative example is included to demonstrate the need for such azimuthal wide-angle capability. Also, a comparison is shown between results using narrow-angle and wide-angle equations separately.

FREQUENCY DOMAIN RECONSTRUCTION FOR PHOTO- AND THERMOACOUSTIC TOMOGRAPHY WITH LINE DETECTORS

2009 ◽  
Vol 19 (02) ◽  
pp. 283-306 ◽  
Author(s):  
MARKUS HALTMEIER
Keyword(s):  
Wave Equation ◽  
Frequency Domain ◽  
Boundary Data ◽  
Three Dimensional ◽  
Photoacoustic Tomography ◽  
Two Dimensional ◽  
Reconstruction Problem ◽  
Acoustic Data ◽  
Dimensional Wave ◽  
Frequency Domain Reconstruction

This paper is concerned with a version of photoacoustic tomography, that uses line shaped detectors (instead of point-like ones) for the recording of acoustic data. The three-dimensional image reconstruction problem is reduced to a series of two-dimensional ones. First, the initial data of the two-dimensional wave equation is recovered from boundary data, and second, the classical two-dimensional Radon transform is inverted. We discuss uniqueness and stability of reconstruction, and compare frequency domain reconstruction formulas for various geometries.

Forced Wave Propagation in Elastic Cables With Small Curvature

1995 ◽  
Author(s):  
M. Behbahani-Nejad ◽  
N. C. Perkins
Keyword(s):  
Nonlinear Response ◽  
Asymptotic Form ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Harmonic Excitation ◽  
Forced Response ◽  
Transverse Waves ◽  
Propagating Waves ◽  
Distinct Frequency ◽  
Elastic Cables

Abstract This study presents an investigation of the coupled longitudinal-transverse waves that propagate along an elastic cable. The coupling considered derives from the equilibrium curvature (sag) of the cable. A mathematical model is presented that describes the three-dimensional nonlinear response of a long elastic cable. An asymptotic form of this model is derived for the linear response of cables having small equilibrium curvature. Linear in-plane response is described by coupled longitudinal-transverse partial differential equations of motion, which are comprehensively evaluated herein. The spectral relation governing propagating waves is derived using transform methods. In the spectral relation, three qualitatively distinct frequency regimes exist that are separated by two cut-off frequencies. This relation is employed in deriving a Green’s function which is then used to construct solutions for in-plane response under arbitrarily distributed harmonic excitation. Analysis of forced response reveals the existence of two types of periodic waves which propagate through the cable, one characterizing extension-compressive deformations (rod-type) and the other characterizing transverse deformations (string-type). These waves may propagate or attenuate depending on wave frequency. The propagation and attenuation of both wave types are highlighted through solutions for an infinite cable subjected to a concentrated harmonic excitation source.

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