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.

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.

scholarly journals Dimer description of the SU(4) antiferromagnet on the triangular lattice

2020 ◽  
Vol 8 (5) ◽  
Author(s):  
Anna Keselman ◽  
Lucile Savary ◽  
Leon Balents
Keyword(s):  
Phase Diagram ◽  
Triangular Lattice ◽  
Ground State ◽  
Degrees Of Freedom ◽  
Numerical Study ◽  
Spin Model ◽  
Translation Invariance ◽  
Multilayer Graphene ◽  
High Symmetry ◽  
Starting Point

In systems with many local degrees of freedom, high-symmetry points in the phase diagram can provide an important starting point for the investigation of their properties throughout the phase diagram. In systems with both spin and orbital (or valley) degrees of freedom such a starting point gives rise to SU(4)-symmetric models. Here we consider SU(4)-symmetric "spin'' models, corresponding to Mott phases at half-filling, i.e. the six-dimensional representation of SU(4). This may be relevant to twisted multilayer graphene. In particular, we study the SU(4) antiferromagnetic "Heisenberg'' model on the triangular lattice, both in the classical limit and in the quantum regime. Carrying out a numerical study using the density matrix renormalization group (DMRG), we argue that the ground state is non-magnetic. We then derive a dimer expansion of the SU(4) spin model. An exact diagonalization (ED) study of the effective dimer model suggests that the ground state breaks translation invariance, forming a valence bond solid (VBS) with a 12-site unit cell. Finally, we consider the effect of SU(4)-symmetry breaking interactions due to Hund's coupling, and argue for a possible phase transition between a VBS and a magnetically ordered state.

Damage Detection in Rods Using Wave Propagation and Regression Analysis

1999 ◽  
Author(s):  
K. T. Feroz ◽  
S. O. Oyadiji
Keyword(s):  
Wave Propagation ◽  
Regression Analysis ◽  
Damage Detection ◽  
Numerical Study ◽  
Time History ◽  
Ball Impact ◽  
Spherical Ball ◽  
Time Histories ◽  
Measured Strain ◽  
Force Time

Abstract The phenomena of wave propagation in rods was studied both numerically and experimentally. The finite element (FE) code ABAQUS was used for the numerical study while PZT (lead zirconium titanate) sensors and a 50 MHz transient recorder were used experimentally to monitor and to capture the propagation of stress pulses. For the study of damage detection in the rods the analyses and the experiments were repeated by introducing slots in a fixed axial location of the rod. A longitudinal wave was induced in the rod via collinear impact which was modelled in the FE analyses using the force-time history computed from the classical Hertz contact theory. In the experimental measurements this was achieved by a spherical ball impact at one plane end of the rods. It is shown that the predicted and measured strain-time histories for the defect-free rod and for the rods with defect correlate quite well. These results also show that defects can be located using the wave propagation phenomena. A regression analysis technique of the predicted and measured strain histories of the defect free rod and of the rod with defect was also performed. The results show that this technique is more efficient for smaller defects. In particular, it is shown that the area enclosed by the regression curve increases as the defect size increases.

scholarly journals Quasi-static ensemble variational data assimilation: a theoretical and numerical study with the iterative ensemble Kalman smoother

2018 ◽  
Vol 25 (2) ◽  
pp. 315-334 ◽  
Author(s):  
Anthony Fillion ◽  
Marc Bocquet ◽  
Serge Gratton
Keyword(s):  
Data Assimilation ◽  
Cost Function ◽  
Global Minimum ◽  
Numerical Study ◽  
Variational Data Assimilation ◽  
Kalman Smoother ◽  
Local Extrema ◽  
Starting Point ◽  
The Cost ◽  
Temporal Extent

Abstract. The analysis in nonlinear variational data assimilation is the solution of a non-quadratic minimization. Thus, the analysis efficiency relies on its ability to locate a global minimum of the cost function. If this minimization uses a Gauss–Newton (GN) method, it is critical for the starting point to be in the attraction basin of a global minimum. Otherwise the method may converge to a local extremum, which degrades the analysis. With chaotic models, the number of local extrema often increases with the temporal extent of the data assimilation window, making the former condition harder to satisfy. This is unfortunate because the assimilation performance also increases with this temporal extent. However, a quasi-static (QS) minimization may overcome these local extrema. It accomplishes this by gradually injecting the observations in the cost function. This method was introduced by Pires et al. (1996) in a 4D-Var context. We generalize this approach to four-dimensional strong-constraint nonlinear ensemble variational (EnVar) methods, which are based on both a nonlinear variational analysis and the propagation of dynamical error statistics via an ensemble. This forces one to consider the cost function minimizations in the broader context of cycled data assimilation algorithms. We adapt this QS approach to the iterative ensemble Kalman smoother (IEnKS), an exemplar of nonlinear deterministic four-dimensional EnVar methods. Using low-order models, we quantify the positive impact of the QS approach on the IEnKS, especially for long data assimilation windows. We also examine the computational cost of QS implementations and suggest cheaper algorithms.

A New Matrix Formula for the Inverse Laplace Transformation

1967 ◽  
Vol 89 (2) ◽  
pp. 269-272 ◽  
Author(s):  
C. F. Chen ◽  
R. E. Yates
Keyword(s):  
Laplace Transformation ◽  
Transfer Functions ◽  
High Order ◽  
Partial Fraction ◽  
Inverse Laplace Transformation ◽  
Numerical Errors ◽  
Matrix Operations ◽  
Simple Matrix ◽  
Matrix Formula ◽  
Single Matrix

A new matrix formula for the inverse Laplace transformation is established. After substituting the eigenvalues and coefficients and performing some simple matrix operations, one can obtain the inverse Laplace transformation of the function in question. The regular Heaviside techniques involving partial fraction expansions, function differentiations, and so on, are avoided. Since the formula is general, it is particularly advantageous for use on high-order transfer functions; since the formula is exact, the results have no numerical errors. Hundreds of commonly used transform pairs can be replaced by this single matrix formula.

An Unsteady Analysis on Thermal Stratification in the SCS Piping Branched Off the RCS Piping

2003 ◽  
Author(s):  
Kwang-Chu Kim ◽  
Man-Heung Park ◽  
Hag-Ki Youm ◽  
Sun-Ki Lee ◽  
Tae-Ryong Kim ◽  
...  
Keyword(s):  
Temperature Difference ◽  
Thermal Stratification ◽  
Nuclear Power ◽  
Cooling System ◽  
Numerical Study ◽  
Outer Wall ◽  
Maximum Temperature ◽  
Rear Side ◽  
Maximum Temperature Difference ◽  
Starting Point

A numerical study is performed to estimate on an unsteady thermal stratification phenomenon in the Shutdown Cooling System (SCS) piping branched off the Reactor Coolant System (RCS) piping of Nuclear Power Plant. In the results, turbulent penetration reaches to the 1st isolation valve. At 500sec, the maximum temperature difference between top and bottom inner wall in piping is observed at the starting point of horizontal piping passing elbow. The temperature of coolant in the rear side of the 1st isolation valve disk is very slowly increased and the inflection point in temperature difference curve for time is observed at 2700sec. At the beginning of turbulent penetration from RCS piping, the fast inflow generates the higher temperature for the inner wall than the outer wall in the SCS piping. In the case the hot-leg injection piping and the drain piping are connected to the SCS piping, the effect of thermal stratification in the SCS piping is decreased due to an increase of heat loss compared with no connection case. The hot-leg injection piping affected by turbulent penetration from the SCS piping has a severe temperature difference that exceeds criterion temperature stated in reference. But the drain piping located in the rear compared with the hot-leg injection piping shows a tiny temperature difference. In a viewpoint of designer, for the purpose of decreasing the thermal stratification effect, it is necessary to increase the length of vertical piping in the SCS piping, and to move the position of the hot-leg injection piping backward.

scholarly journals A Procedure to Select Earthquake Time Histories for Deterministic Seismic Hazard Analysis: Case Studies of Major Cities in Taiwan

2017 ◽  
Author(s):  
Duruo Huang ◽  
Wenqi Du
Keyword(s):  
Seismic Hazard ◽  
Ground Motion ◽  
Ground Surface ◽  
Strong Motion ◽  
Response Spectra ◽  
Dynamic Responses ◽  
Motion Time ◽  
Acceleration Time Histories ◽  
Time Histories ◽  
Deterministic Seismic Hazard

Abstract. In performance-based seismic design, ground-motion time histories are needed for analyzing dynamic responses of nonlinear structural systems. However, the number of strong-motion data at design level is often limited. In order to analyze seismic performance of structures, ground-motion time histories need to be either selected from recorded strong-motion database, or numerically simulated using stochastic approaches. In this paper, a detailed procedure to select proper acceleration time histories from the Next Generation Attenuation (NGA) database for several cities in Taiwan is presented. Target response spectra are initially determined based on a local ground motion prediction equation under representative deterministic seismic hazard analyses. Then several suites of ground motions are selected for these cities using the Design Ground Motion Library (DGML), a recently proposed interactive ground-motion selection tool. The selected time histories are representatives of the regional seismic hazard, and should be beneficial to earthquake studies when comprehensive seismic hazard assessments and site investigations are yet available. Note that this method is also applicable to site-specific motion selections with the target spectra near the ground surface considering the site effect.

Numerical study on wave propagation in a low-rigidity elastic medium considering the effects of gravity

Wave Motion ◽  
2014 ◽  
Vol 51 (5) ◽  
pp. 729-742 ◽  
Author(s):  
Yoshikazu Shingaki ◽  
Hiroyuki Goto ◽  
Sumio Sawada
Keyword(s):  
Wave Propagation ◽  
Elastic Medium ◽  
Numerical Study

An Advanced Test Method to Determine Viscous Damping of Floating Structures

2010 ◽  
Author(s):  
Z. J. Huang ◽  
B. J. O’Donnell ◽  
T. W. Yung ◽  
S. T. Slocum
Keyword(s):  
Low Frequency ◽  
Test Method ◽  
Total Force ◽  
Viscous Damping ◽  
Damping Force ◽  
Restoring Force ◽  
Viscous Forces ◽  
Motion Time ◽  
Research Company ◽  
Time Histories

ExxonMobil Upstream Research Company developed an advanced model test method to determine reliable damping values for predicting low frequency motions of an FLNG barge and an LNG carrier. Since viscous damping forces are a very small portion of the total force on the model, how to separate the viscous forces from the total forces is the key technical challenge. To better isolate viscous damping forces, an inertial compensation system consisting of springs was employed in the test. The spring stiffness was designed such that the restoring force cancelled the large inertial loads at the oscillation frequency. Furthermore, double-body models were built and were deeply submerged to minimize surface wave damping. With such an experimental setup, the total force measured was mainly the viscous damping force. Viscous damping was derived from the measured force and motion time histories.

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