Nonlinear wave propagation in sandstone: A numerical study

Geophysics ◽  
1996 ◽  
Vol 61 (6) ◽  
pp. 1935-1938 ◽  
Author(s):  
Ningya Cheng
Keyword(s):  
Seismic Waves ◽  
Numerical Study ◽  
Nonlinear Effects ◽  
Crystalline Rock ◽  
Harmonic Spectrum ◽  
Structural Defects ◽  
Single Frequency ◽  
Elastic Behavior ◽  
Nonlinear Wave Propagation ◽  
Frequency Wave

Elastic nonlinear effects in rocks are observed widely in laboratory experiments. For example, Toksöz et al. (1976) measured the pressure dependence of wave speed in the rocks. In crystalline rock and sandstone, Johnson et al. (1987) and Johnson and Shankland (1989) have demonstrated the nonlinear generation of elastic waves. The importance of nonlinear effects in seismic waves in the earth in regard to models of the source is given in Johnson and McCall (1994). The evolution of the harmonic spectrum of a single frequency wave propagated in Berea Sandstone was shown in Meegan et al. (1993). The structural defects contained in rock, such as microcracks and grain‐to‐grain contacts, give rise to this strong elastic nonlinearity (e.g., Gist, 1994). A new theoretical model is developed in McCall and Guyer (1994) to describe elastic behavior of hysteretic nonlinear materials, such as rock. In general, the third‐order elastic constants of the rocks have much larger values than ordered solids.

Numerical Study of Viscous Flows Inside Partially Filled Spinning and Coning Cylinders

1996 ◽  
Vol 118 (2) ◽  
pp. 335-340 ◽  
Author(s):  
Mohamed Selmi
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Center Of Mass ◽  
Steady Motion ◽  
Practical Interest ◽  
Nonlinear Effects ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Practical Applications ◽  
Analysis And Design

This paper is concerned with the solution of the 3-D-Navier-Stokes equations describing the steady motion of a viscous fluid inside a partially filled spinning and coning cylinder. The cylinder contains either a single fluid of volume less than that of the cylinder or a central rod and a single fluid of combined volume (volume of the rod plus volume of the fluid) equal to that of the cylinder. The cylinder rotates about its axis at the spin rate ω and rotates about an axis that passes through its center of mass at the coning rate Ω. In practical applications, as in the analysis and design of liquid-filled projectiles, the parameter ε = τ sin θ, where τ = Ω/ω and θ is the angle between spin axis and coning axis, is small. As a result, linearization of the Navier-Stokes equations with this parameter is possible. Here, the full and linearized Navier-Stokes equations are solved by a spectral collocation method to investigate the nonlinear effects on the moments caused by the motion of the fluid inside the cylinder. In this regard, it has been found that nonlinear effects are negligible for τ ≈ 0.1, which is of practical interest to the design of liquid-filled projectiles, and the solution of the linearized Navier-Stokes equations is adequate for such a case. However, as τ increases, nonlinear effects increase, and become significant as ε surpasses about 0.1. In such a case, the nonlinear problem must be solved. Complete details on how to solve such a problem is presented.

scholarly journals The transformation of an interfacial solitary wave of elevation at a bottom step

2009 ◽  
Vol 16 (1) ◽  
pp. 33-42 ◽  
Author(s):  
V. Maderich ◽  
T. Talipova ◽  
R. Grimshaw ◽  
E. Pelinovsky ◽  
B. H. Choi ◽  
...  
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Numerical Study ◽  
Nonlinear Effects ◽  
Ocean Model ◽  
Gardner Equation ◽  
Fully Nonlinear ◽  
Layer Flow ◽  
The One ◽  
Bottom Step

Abstract. In this paper we study the transformation of an internal solitary wave at a bottom step in the framework of two-layer flow, for the case when the interface lies close to the bottom, and so the solitary waves are elevation waves. The outcome is the formation of solitary waves and dispersive wave trains in both the reflected and transmitted fields. We use a two-pronged approach, based on numerical simulations of the fully nonlinear equations using a version of the Princeton Ocean Model on the one hand, and a theoretical and numerical study of the Gardner equation on the other hand. In the numerical experiments, the ratio of the initial wave amplitude to the layer thickness is varied up one-half, and nonlinear effects are then essential. In general, the characteristics of the generated solitary waves obtained in the fully nonlinear simulations are in reasonable agreement with the predictions of our theoretical model, which is based on matching linear shallow-water theory in the vicinity of a step with solutions of the Gardner equation for waves far from the step.

scholarly journals Numerical Study on Crack Distributions of the Single-Layer Building under Seismic Waves

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-16
Author(s):  
Fenghui Dong ◽  
Zhipeng Zhong ◽  
Jin Cheng
Keyword(s):  
Seismic Waves ◽  
Numerical Study ◽  
Single Layer ◽  
Experimental Tests ◽  
Masonry Structure ◽  
Original Model ◽  
Dynamic Responses ◽  
Masonry Structures ◽  
Reinforced Masonry ◽  
Longitudinal Cracks

This paper conducts a numerical simulation of the antiseismic performance for single-layer masonry structures, completes a study on crack distributions and detailed characteristics of masonry structures, and finally verifies the correctness of the numerical model by experimental tests. This paper also provides a reinforced proposal to improve the antiseismic performance of single-layer masonry structures. Results prove that the original model suffers more serious damage than the reinforced model; in particular, longitudinal cracks appear on bottoms of two longitudinal walls in the original model, while these cracks appear later in the reinforced model; a lot of cracks appear on the door hole of the original model, and no crack appears in the reinforced model till the end of seismic waves; seismic damage of walls in the reinforced model is obviously lighter than that in the original model; dynamic responses at all observed points of the reinforced masonry are obviously less than those of the original model. Strains at all positions of the reinforced model are obviously smaller than those of the original model. From macroscopic and microscopic perspectives, the computational results prove that the reinforced proposal proposed in this paper can effectively improve the antiseismic performance of the masonry structure.

scholarly journals Graded and Anisotropic Porous Materials for Broadband and Angular Maximal Acoustic Absorption

Materials ◽  
2020 ◽  
Vol 13 (20) ◽  
pp. 4605
Author(s):  
Théo Cavalieri ◽  
Jean Boulvert ◽  
Gwénaël Gabard ◽  
Vicent Romero-García ◽  
Marie Escouflaire ◽  
...  
Keyword(s):  
Porous Materials ◽  
Sound Absorption ◽  
Effective Properties ◽  
Numerical Study ◽  
Optimization Technique ◽  
Single Frequency ◽  
Acoustic Absorption ◽  
Graded Material ◽  
Manufacturing Techniques ◽  
Designed Materials

The design of graded and anisotropic materials has been of significant interest, especially for sound absorption purposes. Together with the rise of additive manufacturing techniques, new possibilities are emerging from engineered porous micro-structures. In this work, we present a theoretical and numerical study of graded and anisotropic porous materials, for optimal broadband and angular absorption. Through a parametric study, the effective acoustic and geometric parameters of homogenized anisotropic unit cells constitute a database in which the optimal anisotropic and graded material will be searched for. We develop an optimization technique based on the simplex method that is relying on this database. The concepts of average absorption and diffuse field absorption coefficients are introduced and used to maximize angular acoustic absorption. Numerical results present the optimized absorption of the designed anisotropic and graded porous materials for different acoustic targets. The designed materials have anisotropic and graded effective properties, which enhance its sound absorption capabilities. While the anisotropy largely enhances the diffuse field absorbing when optimized at a single frequency, graded properties appear to be crucial for optimal broadband diffuse field absorption.

Phase saddles and dislocations in two-dimensional waves such as the tides

1988 ◽  
Vol 417 (1852) ◽  
pp. 7-20 ◽  
Keyword(s):  
Three Dimensional ◽  
Single Frequency ◽  
External Parameter ◽  
Two Dimensional ◽  
Basic Pattern ◽  
Fixed Frequency ◽  
Frequency Wave ◽  
Tidal Theory ◽  
The Antarctic ◽  
Three Dimensional Vector Field

A two-dimensional scalar wavefield of fixed frequency contains, in general, points where the amplitude is zero and the phase is indeter­minate. On a map of contours of equal phase these wave dislocations (interference nulls) are accompanied by saddles. When an external parameter is changed dislocations can be created in pairs or a pair can meet and destroy one another. For the simplest single-frequency wave equation it is a topological necessity that two saddles should participate in this event; moreover, they have to lie, in the final stage before annihilation, on the circle whose diameter is the line joining the dislocations. Examples are given to show how this basic pattern is always ultimately attained even when initially the configuration is quite different. In tidal theory, where the dislocations are amphidromic points, the external parameter that moves them can be the frequency. An example of an annihilation event occurs in the South Atlantic, and a close pair of amphidromic points may explain anomalous tidal observations from the Antarctic Peninsula. The tidal current, as distinct from the tidal rise and fall, provides an example of a two or three-dimensional vector field, and it is pointed out that the singularities in this field are precisely the same as those to be found in the polarization field of an electromagnetic wave.

MODELING AND ANALYSIS OF A PLATE ON ELASTIC FOUNDATION SUBJECTED TO LANDING AIRPLANES' FORCES

2010 ◽  
Vol 10 (01) ◽  
pp. 37-54 ◽  
Author(s):  
T. G. KOSTANTAKOPOULOS ◽  
G. T. MICHALTSOS
Keyword(s):  
Elastic Foundation ◽  
Numerical Study ◽  
Elastic Behavior ◽  
Spring Model ◽  
Modeling And Analysis ◽  
Load Model ◽  
Winkler Model ◽  
Mass Load ◽  
Plate On Elastic Foundation ◽  
Plate Deflection

This paper deals with the problem of the dynamic behavior of a plate on elastic foundation under the action of forces produced by a landing airplane. A partially plastic impact is postulated for the contact between the airplane and the plate. The Winkler model is used to simulate the ground's elastic behavior, by which the foundation reaction is proportional to the plate deflection, along with dampers for energy dissipation. Two models are used for the airplane, i.e. a simplified mass-load model and a mass-dashpot-spring model, and their influences on the dynamic response of the plate are evaluated. Moreover, various parameters concerning the salient features of the airplane and its landing on the plate are studied with conclusions drawn. The efficiency of the methodology proposed herein was demonstrated in the numerical study.

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