SH-wave generation by dislocation sources—A numerical study

1979 ◽  
Vol 69 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Robert B. Herrmann
Keyword(s):  
Real Axis ◽  
Numerical Study ◽  
Numerical Technique ◽  
Far Field ◽  
Sh Wave ◽  
The Real ◽  
Relative Contribution ◽  
Time Histories ◽  
Point Dislocation ◽  
Dislocation Sources

abstract A numerical technique is presented for attaining the SH-wave contribution to tangential displacements due to point dislocation sources in a plane layered Earth. The method uses contour integration in the complex k-plane and includes the contribution of branch line integrals along the real and imaginary axes of the k-plane as well as poles along the real axis. Examples are provided to illustrate the effect of neglecting the P-SV contribution to tangential displacements, the effect of improper truncation in estimating far-field time histories, as well as the relative contribution of the various singularities in the complex k-plane to the solution.

A numerical study of P-, SV-, and SH-wave generation in a plane layered medium

1980 ◽  
Vol 70 (4) ◽  
pp. 1015-1036 ◽  
Author(s):  
C. Y. Wang ◽  
R. B. Herrmann
Keyword(s):  
Elastic Medium ◽  
Numerical Study ◽  
Theoretical Ground ◽  
Matrix Operations ◽  
Surface Displacements ◽  
Motion Time ◽  
Starting Point ◽  
Time Histories ◽  
Simple Matrix ◽  
Dislocation Sources

abstract A solution for the surface displacements due to buried dislocation sources in a multi-layered elastic medium is found using the Haskell (1964) paper as a starting point and more importantly, for notation. Through the introduction of some simple matrix operations, the Haskell (1964) solution is made simultaneously more compact and computationally stable. Time histories are computed for a perfectly elastic medium by performing classical contour integration in the complex wavenumber plane. A new aspect in the evaluation of those contours is introduced because of the recognition of nonzero singularity contributions of the Hankel and modified Bessel functions at k = 0. Theoretical ground motion time histories are presented to show the usefulness of the formulation. The overall objective of this paper is to incorporate the modifications made since 1964 to the Haskell (1964) paper in an easily understandable, step-by-step development.

A numerical study about the influence of channel-scale secondary circulation on mixing processes at Kama/Vishera confluence

2020 ◽  
Author(s):  
Tatyana Lyubimova ◽  
Anatoly Lepikhin ◽  
Yanina Parshakova ◽  
Carlo Gualtieri ◽  
Bernard Roux ◽  
...  
Keyword(s):  
Turbulent Diffusion ◽  
Stokes Equations ◽  
Single Channel ◽  
Numerical Study ◽  
Rectangular Channel ◽  
Taylor Dispersion ◽  
Secondary Circulation ◽  
Far Field ◽  
The Real ◽  
The Government

<p>Confluences are common components of all riverine systems, and are characterized by converging flow streamlines and mixing of separate flows, which can take some significant distance to be complete. Whilst turbulent diffusion and Taylor dispersion are expected to affect mixing in any open channel flow, the analysis of mixing at river confluences should also consider some peculiar processes, which could be divided between near-field processes and far-field processes. The former, which have been well studied, are those operating at the junction itself and lead to rapid mixing only if some form of asymmetry (geometry, discordance, momentum, density difference) between the tributaries exists. The latter are advective processes, such as secondary circulation, that can enhance mixing to degrees greater than those associated with turbulent diffusion or Taylor dispersion combined. These processes, which have received less attention, were investigated using a three-dimensional computation of the Reynolds averaged Navier-Stokes equations combined with a Reynolds stress turbulence model for the confluence of the Kama river and Vishera rivers in the Russian Urals. To test the hypothesis that far-field mixing can be both enhanced and reduced by the type of secondary circulation that develops, numerical simulations on an idealized configuration (rectangular channel with no curvature) and on the real configuration with the natural planform and/or bathymetry were carried out to isolate the relative impacts of real planform and bathymetry on secondary circulation and mixing for different combinations of momentum/discharge ratio. Results show that if the rivers are represented as an idealized junction, the initial vortices that form due to channel-scale pressure gradients decline rapidly with distance downstream. Mixing is slow and incomplete at more than 10 multiples of channel width downstream from the junction corner. On the other side, if the real configuration is introduced, rates of mixing increase dramatically. This is related to both increase intensity of secondary circulation at the junction and the formation of a single channel-scale vortex downstream of the junction. The latter appears to be aided by curvature of the post-junction channel. This effect is strongest when the discharge of the tributary that has the same direction of curvature as the post junction channel is greatest.</p><p>The study was performed under financial support of the Government of Perm Krai (grant C 26/788) and Russian Foundation for Basic Research (grant 19-41-590013).</p>

scholarly journals Numerical Study of the Seismic Response of an Instrumented Building with Underground Stories

2021 ◽  
Vol 11 (7) ◽  
pp. 3190
Author(s):  
Edmundo Schanze ◽  
Gilberto Leiva ◽  
Miguel Gómez ◽  
Alvaro Lopez
Keyword(s):  
Seismic Response ◽  
Soil Structure ◽  
Numerical Study ◽  
Time History ◽  
Building Design ◽  
Average Height ◽  
The Real ◽  
Vibration Data ◽  
Finite Element Software ◽  
Stiffness Reduction

Engineering practitioners do not usually include soil–structure interactions in building design; rather, it is common to model and design foundations as embedded joints with joint–based reactions. In some cases, foundation structures are modeled as rigid bodies, embedding the first story into lower vertical elements. Given that the effects of underground floors on the seismic response are not generally included in current building design provisions, it has been little explored in the literature. This work compares and analyzes models to study the effects of different underground stories modeling approaches using earthquake vibration data recorded for the 16–story Alcazar building office in downtown Viña del Mar (Chile). The modeling expands beyond an embedded first story structure to soil with equivalent springs, representing soil–structure interaction (SSI), with varying rigid soil homogeneity. The building was modeled in a finite element software considering only dead load as a static load case because the structure remained in the framing stage when the monitoring system was operating. The instruments registered 72 aftershocks from the 2010 Maule Earthquake, and this study focused on 11 aftershocks of different hypocenters and magnitudes to collect representative information. The comparisons between empirical records and models in this study showed a better fit between the model and the real vibration data for the models that do consider the SSI using horizontal springs attached to the retaining walls of the underground stories. In addition, it was observed that applying a stiffness reduction factor of 0.7 to all elements in deformation verification models for average–height buildings was suitable to analyze the behavior under small earthquakes; better results are obtained embedding the structure in the foundation level than embedding in the street level; the use of horizontal springs with Kuesel’s model with traction for the analysis of the structure yields appropriate results; it is necessary to carefully select the spring constants to be used, paying special attention to the vertical springs. Even though the results presented herein indicate that the use of vertical springs to simulate the SSI of the base slab can result in major differences concerning the real response, it is necessary to obtain more data from instrumentation across a wider variety of structures to continue to evaluate better design and modeling practices. Similarly, further analyses, including nonlinear time–history and high–intensity events, are needed to best regulate building design.

On Graeffe's Method for Complex Roots of Algebraic Equations

1924 ◽  
Vol 22 (2) ◽  
pp. 83-87 ◽  
Author(s):  
S. Brodetsky ◽  
G. Smeal
Keyword(s):  
Nineteenth Century ◽  
Real Axis ◽  
Practical Method ◽  
Algebraic Equations ◽  
Argand Diagram ◽  
Considerable Difficulty ◽  
The Real ◽  
Real Roots ◽  
Bipolar Coordinates ◽  
Complex Roots

The only really useful practical method for solving numerical algebraic equations of higher orders, possessing complex roots, is that devised by C. H. Graeffe early in the nineteenth century. When an equation with real coefficients has only one or two pairs of complex roots, the Graeffe process leads to the evaluation of these roots without great labour. If, however, the equation has a number of pairs of complex roots there is considerable difficulty in completing the solution: the moduli of the roots are found easily, but the evaluation of the arguments often leads to long and wearisome calculations. The best method that has yet been suggested for overcoming this difficulty is that by C. Runge (Praxis der Gleichungen, Sammlung Schubert). It consists in making a change in the origin of the Argand diagram by shifting it to some other point on the real axis of the original Argand plane. The new moduli and the old moduli of the complex roots can then be used as bipolar coordinates for deducing the complex roots completely: this also checks the real roots.

Interaction between a nanocrack with surface elasticity and a screw dislocation

2016 ◽  
Vol 22 (2) ◽  
pp. 131-143 ◽  
Author(s):  
Xu Wang ◽  
Hui Fan
Keyword(s):  
Screw Dislocation ◽  
Real Axis ◽  
Analytical Study ◽  
Logarithmic Singularity ◽  
Surface Elasticity ◽  
Spontaneous Generation ◽  
The Real ◽  
Crack Tips ◽  
Interaction Problem ◽  
The Continuum

In the present analytical study, we consider the problem of a nanocrack with surface elasticity interacting with a screw dislocation. The surface elasticity is incorporated by using the continuum-based surface/interface model of Gurtin and Murdoch. By considering both distributed screw dislocations and line forces on the crack, we reduce the interaction problem to two decoupled first-order Cauchy singular integro-differential equations which can be numerically solved by the collocation method. The analysis indicates that if the dislocation is on the real axis where the crack is located, the stresses at the crack tips only exhibit the weak logarithmic singularity; if the dislocation is not on the real axis, however, the stresses exhibit both the weak logarithmic and the strong square-root singularities. Our result suggests that the surface effects of the crack will make the fracture more ductile. The criterion for the spontaneous generation of dislocations at the crack tip is proposed.

Successive coefficients of close-to-convex functions

2020 ◽  
Vol 32 (5) ◽  
pp. 1131-1141 ◽  
Author(s):  
Paweł Zaprawa
Keyword(s):  
Real Axis ◽  
Convex Functions ◽  
Positive Direction ◽  
The Real ◽  
Coefficient Problems ◽  
The Difference

AbstractIn this paper we discuss coefficient problems for functions in the class {{\mathcal{C}}_{0}(k)}. This family is a subset of {{\mathcal{C}}}, the class of close-to-convex functions, consisting of functions which are convex in the positive direction of the real axis. Our main aim is to find some bounds of the difference of successive coefficients depending on the fixed second coefficient. Under this assumption we also estimate {|a_{n+1}|-|a_{n}|} and {|a_{n}|}. Moreover, it is proved that {\operatorname{Re}\{a_{n}\}\geq 0} for all {f\in{\mathcal{C}}_{0}(k)}.

scholarly journals Zeros of Dirichlet L-functions near the Real Axis and Chebyshev's Bias

2001 ◽  
Vol 87 (1) ◽  
pp. 54-76 ◽  
Author(s):  
Carter Bays ◽  
Kevin Ford ◽  
Richard H Hudson ◽  
Michael Rubinstein
Keyword(s):  
Real Axis ◽  
The Real

PRELIMINARY STUDY ON NOVEL BEAM-TO-COLUMN CONNECTION BASED ON SMA PLATE

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Michael CH Yam ◽  
Ke Ke ◽  
Ping Zhang ◽  
Qingyang Zhao
Keyword(s):  
Friction Coefficient ◽  
Energy Dissipation ◽  
Numerical Study ◽  
Numerical Models ◽  
Numerical Technique ◽  
The Self ◽  
Hysteretic Behavior ◽  
The Novel ◽  
Energy Dissipation Capacity ◽  
Preliminary Study

A novel beam-to-column connection equipped with shape memory alloy (SMA) plates has been proposed to realize resilient performance under low-to-medium seismic actions. In this conference paper, the detailed 3D numerical technique calibrated by the previous paper is adopted to examine the hysteretic behavior of the novel connection. A parametric study covering a reasonable range of parameters including the thickness of the SMA plate, friction coefficient between SMA plate and beam flange and pre-load of the bolt was carried out and the influence of the parameters was characterized. In addition, the effect of the SMA Belleville washer on the connection performance was also studied. The results of the numerical study showed that the initial connection stiffness and the energy-dissipation capacity of the novel connection can be enhanced with the increase of the thickness of the SMA plate. In addition, the initial connection stiffness and energy-dissipation behavior of the novel connection can be improved by increasing the friction coefficient or pre-load of bolts, whereas the increased friction level could compromise the self-centering behavior of the connection. The hysteretic curves of the numerical models of the connection also implied that the SMA washers may contribute to optimizing the connection behavior by increasing the connection stiffness and energy-dissipation capacity without sacrificing the self-centering behavior.

scholarly journals NEGATIVE REFRACTION AND SUBWAVELENGTH FOCUSING USING PHOTONIC CRYSTALS

2004 ◽  
Vol 18 (25) ◽  
pp. 1275-1291 ◽  
Author(s):  
EKMEL OZBAY ◽  
KAAN GUVEN ◽  
ERTUGRUL CUBUKCU ◽  
KORAY AYDIN ◽  
B. KAMIL ALICI
Keyword(s):  
Optical Properties ◽  
Photonic Crystals ◽  
Negative Refraction ◽  
Numerical Study ◽  
Effective Index ◽  
Index Of Refraction ◽  
Far Field ◽  
Two Dimensional ◽  
Flat Lens ◽  
Effective Index Of Refraction

In this article, we present an experimental and numerical study of novel optical properties of two-dimensional dielectric photonic crystals (PCs) which exhibit negative refraction. We investigate two mechanisms which utilize the band structure of the PC to generate a negative effective index of refraction (n eff <0) and demonstrate the negative refraction experimentally. To the isotropic extend of n eff , different PC slab structures are employed to focus the radiation of a point source. It is shown experimentally that the PC can generate an image of the source with subwavelength resolution in the vicinity of the PC interface. Using a different PC, one can also obtain a far field focusing. In the latter case, we explicitly show the flat lens behavior of the structure. These examples indicate that PC-based lenses can surpass limitations of conventional lenses and lead to novel optics applications.

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