• Geomechanics and Engineering
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• v.8 no.3
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• pp.377-390
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• 2015

The governing equations of wave propagation in one dimension of elastic continuum materials are investigated by taking the influence of the initial stress into account. After a short review of the theory of elastic wave propagation in a rock mass with an initial stress, results indicate that the initial stress differentially influences P-wave and S-wave propagation. For example, when the initial stress is homogeneous, for the P-wave, the initial stress only affects the magnitude of the elastic coefficients, but for the S-wave, the initial stress not only influences the elastic coefficients but also changes the governing equation of wave propagation. In addition, the P-wave and S-wave velocities were measured for granite samples at a low initial stress state; the results indicate that the seismic velocities increase with the initial stress. The analysis of the previous data of seismic velocities and elastic coefficients in rocks under ultra-high hydrostatic initial stress are also investigated.

• Geomechanics and Engineering
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• v.10 no.3
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• pp.285-296
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• 2016

The investigation of stress wave propagation in a medium with initial stress has very important application in the field of engineering. However, the previous research less consider the influence of initial stress gradient on wave propagation. In the present paper, the governing equation of wave propagation in elastic continuum material with inhomogeneous initial stress is derived, which indicated that the inhomogeneous initial stress changed the governing equation of wave propagation. Additionally, the definite problem of wave propagation in material with initial stress gradient is verified by using mathematical physics method. Based on the definite problem, the elastic displacement-time relationship of wave propagation is explored, which indicated that the inhomogeneous initial stress changed waveform and relationship of displacement-time histories. Furthermore, the spall process of blasting wave propagation from underground to earth surface is simulated by using LS-DYNA.

• Structural Engineering and Mechanics
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• v.62 no.6
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• pp.781-788
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• 2017

In this paper, a stress wave model is established to describe the three states (separate, contact and impact) of clearance joints. Based on this stress wave model, the propagation characteristics of stress wave generated in clearance joints is revealed. First, the stress wave model of clearance joints is established based on the viscoelastic theory. Then, the reflection and transmission characteristics of stress wave with different boundaries are studied, and the propagation of stress wave in viscoelastic rods is described by the characteristics method. Finally, the stress wave propagation in clearance joints with three states is analyzed to validate the proposed model and method. The results show the clearance sizes, initial axial speeds and material parameters have important influences on the stress wave propagation, and the new stress waves will generate when the clearance joint in contact and impact states, and there exist some high stress region near contact area of clearance joints when the incident waves are superposed with reflection waves, which may speed up the damage of joints.

• Geomechanics and Engineering
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• v.22 no.2
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• pp.187-196
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• 2020

The changeable stress environment directly affect the propagation law of a stress wave. Stress wave propagation tests in sandstone with different axial stresses were carried using a modified split Hopkinson Pressure bar (SHPB) assuming the sandstone has a uniform pore distribution. Then the waveform and stress wave energy dissipation were analyzed. The results show that the stress wave exhibits the double peak phenomenon. With increasing axial stress, the intensity difference decreases exponentially and experiences first a dramatic decrease and then gentle development. The demarcation stress is σ/σ_c=30%, indicating that the closer to the incident end, the faster the intensity difference attenuates. Under the same axial stress, the intensity difference decreases linearly with propagation distance and its attenuation intensity factor displays a quadratic function with axial stress. With increasing propagation distance, the time difference decays linearly and its delay coefficient reflects the damage degree. The stress wave energy attenuates exponentially with propagation distance, and the relations between attenuation rate, attenuation coefficient and axial stress can be represented by the quadratic function.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2008.04a
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• pp.39-44
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• 2008

Stress wave propagation plays an important role in many engineering problems for reducing industrial noise and vibrations. In this paper, the dispersion-corrected finite element model is proposed for reducing the dispersion error in simulation of stress wave propagation. At eliminating the numerical dispersion error arising from the numerical simulation of stress wave propagation, numerical dispersion characteristics of the wave equation based finite element model are analyzed and some dispersion control scheme are proposed. The validity of the dispersion correction techniques is demonstrated by comparing the numerical solutions obtained using the present techniques.

• Structural Engineering and Mechanics
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• v.14 no.4
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• pp.455-472
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• 2002

The paper involves the study on the elastic and elasto-plastic stress wave propagation in the 1-D and 2-D solid media. The Smooth Particle Hydrodynamics equations governing the elastic and elasto-plastic large deformation dynamic response of solid structures are presented. The proposed additional stress points are introduced in the formulation to mitigate the tensile instability inherent in the SPH approach. Both incremental rate approach and leap-frog algorithm for time integration are introduced and the new solution algorithm is developed and implemented. Two examples on stress wave propagation in aluminium bar and 2-D elasto-plastic steel plate are included. Results from the proposed SPH approach are compared with available analytical values and finite element solutions. The comparison illustrates that the stress wave propagation problems can be effectively solved by the proposed SPH method. The study shows that the SPH simulation is a reliable and robust tool and can be used with confidence to treat transient dynamics such as linear and non-linear transient stress wave propagation problems.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.04a
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• pp.232-239
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• 1997

The phenomenology of shock loading effects in brittle mass has been of interest to researchers and engineers. The shock loading as blasting causes strong stress waves in the structures. Discontinuous faces due to shock waves interrupt the tensile stress wave propagation and reflect the stress wave propagation. To predict the fracturing behavior of brittle mass, it is required for the numerical method that can analyze the colliding and slipping behavior of discontinuous faces and the wave propagation in the mass, simultaneously In this study, the wave propagation in the brittle materials is analyzed using the modified distinct element method to be able to predict the behavior of discontinuous structures. The behavior of an unsupported bar subjected to loading at the end is analyzed to verify the rigid body motion of a bar and the relative displacement in the bar. The colliding behavior of two bars is analyzed to investigate the propagation of stress waves in the bar. The fracturing behavior of a bar due to impact loading is analyzed to investigate the propagation of stress waves in the bar with and without the discontinuous faces. The applicability of the modified distinct element method to the wave propagation problems is investigated.

• Proceedings of the Korean Geotechical Society Conference
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• 2005.03a
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• pp.515-520
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• 2005

The behavior of jointed rock mass is much different from that of intact rock due to the presence of joints. Similarly, the characteristics of elastic wave propagation in jointed rock are considerably different from those of intact rock. The propagation of elastic waves in jointed rock is greatly dependent on the state of stress. The roughness, filling materials, and spacing of joints also affect wave propagation in jointed rock. If the wavelength of elastic waves is much larger than the spacing between joints, wave propagation in jointed rock mass can be considered as wave propagation in equivalent continuum. A rock resonant column testing apparatus is made to measure elastic waves propagating through jointed rock in the state of equivalent continuum. Three types of wave, i.e, torsional, longitudinal and flexural waves are monitored during rock resonant column tests. Various roughness and filling materials are applied to joints, and rock columns with various spacings are used to understand how these factors affect wave propagation under a small strain condition. The experimental results suggest that the characteristics of wave propagation in jointed rock mass are governed by the state of stress and influenced by roughness, filling materials and joint spacings.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.12
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• pp.3369-3376
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• 1994

A finite element program for elastic stress wave propagation is developed in order to investigate the shape of stress field and analysis the magnitude of stress wave intensity at time increment. Accuracy and reliance of the finite element analysis are acquired when the element size is smaller than the product of the stress wave speed and the critical value of increasing time step. In the finite element analysis and theoretical solution, the longitudinal stress wave is propagated to the similar direction of impact load, and the stress wave intensity is expressed in terms of the ratio of propagated area. The direction of shear wave is declined at an angle of 45 degrees compared with longitudinal stress wave and the speed of shear wave is half of the longitudinal stress wave.

• Steel and Composite Structures
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• v.32 no.2
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• pp.213-223
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• 2019

For the first time, longitudinal and transverse wave propagation of triclinic nanobeam is investigated via a size-dependent shear deformation theory including stretching effect. Furthermore, the influence of initial stress is studied. To consider the size-dependent effects, the nonlocal strain gradient theory is used in which two small scale parameters predict the behavior of wave propagation more accurately. The Hamiltonian principle is adopted to obtain the governing equations of wave motion, then an analytic technique is applied to solve the problem. It is demonstrated that the wave characteristics of the nanobeam rely on the wave number, nonlocal parameter, strain gradient parameter, initial stress, and elastic foundation. From this paper, it is concluded that the results of wave dispersion in isotropic and anisotropic nanobeams are almost the same in the presented case study. So, in this case, triclinic nanobeam can be approximated with isotropic model.