• Structural Engineering and Mechanics
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• v.88 no.4
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• pp.335-354
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• 2023

In this study, analysis of wave propagation characteristics for functionally graded carbon nanotube-reinforced composite (FG-CNTRC) nanoplates is performed using first-order shear deformation theory (FSDT) and nonlocal strain gradient theory. Uniform distribution (UD) and three types of functionally graded distributions of carbon nanotubes (CNTs) are assumed. The effective mechanical properties of the FG-CNTRC nanoplate are assumed to vary continuously in the thickness direction and are approximated based on the rule of mixture. Also, the governing equations of motion are derived via the extended Hamilton's principle. In numerical examples, the effects of nonlocal parameter, wavenumber, angle of wave propagation, volume fractions, and carbon nanotube distributions on the wave propagation characteristics of the FG-CNTRC nanoplate are studied. As represented in the results, it is clear that the internal length-scale parameter has a remarkable effect on the wave propagation characteristics resulting in significant changes in phase velocity and natural frequency. Furthermore, it is observed that the strain gradient theory yields a higher phase velocity and frequency compared to those obtained by the nonlocal strain gradient theory and classic theory.

• 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.

• Journal of the Korean Society for Nondestructive Testing
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• v.17 no.4
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• pp.227-236
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• 1997

Quantitative analysis and imaging of elastic wave propagation are very important for the materials evaluation as well as flaw detection. The elastic wave propagation in an anisotropic media is more complex, and analysis and imaging become essential for flaw detection and materials evaluation. In the anisotropic media, the wave velocity is dependent on the propagation direction. In addition, the direction of group velocity is different from that of phase velocity, the direction of energy flow is not same as the propagation direction of wavefront (beam skewing effect). Especially, this effect becomes critical for the large anisotropic media such as fiber composite materials, and the results using elastic waves for those materials have to be analyzed considering the wave propagation mechanism. Since the analytical approach for the wave propagation in the anisotropic materials is limited, the numerical analysis such as finite difference method (FDM) have been used for these case. Therefore, 2-dimensional FDM program for the elastic wave propagation is developed, and wave propagation in anisotropic media are simulated.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.10
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• pp.2201-2210
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• 2002

The accurate analysis of ultrasonic wave propagation and scattering plays an important role in many aspects of nondestructive evaluation. A numerical analysis makes it possible to perform parametric studies, and in this way the probability of detection and reliability of test results can be improved. In this paper, a finite element method was employed for the analysis of ultrasonic wave propagation in anisotropic materials, and the accuracy of results was checked by comparing with analytical predictions. The element size and the integral time step, which are the critical components for the convergence of finite element solutions, were determined using a commercial finite element code. Some differences for wave propagation in anisotropic media were illustrated when plane waves are propagating in a unidirectionally reinforced composite materials. When plane waves are propagating in nonsymmetric directions in a symmetric plane, deviation angles between the wave vector and the energy vector were found from finite element analyses and the results agreed well with analytical calculations.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.32 no.3
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• pp.267-273
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• 2008

The circular cylinder pipes are used in the many industrial areas. In this paper, the acoustic wave propagation in the pipe containing a gas is researched. First of all, the theory for the coupled acoustic wave propagation in a pipe is investigated. Acoustic wave propagation in pipe can not be occurred independently between the wave of the fluid and the shell. It requires complicated analysis. However, as a special case, the coupled wave in a high density pipe containing a light density medium is corresponded closely to the uncoupled in-vacuo shell waves and to the rigid-walled duct fluid waves. The coincidence frequencies of acoustic and shell modes contribute to the predominant energy transmission. The coincidence frequency means the frequency corresponding to the coincidence of the wavenumber in both acoustic and shell. In this paper, it is assumed that the internal medium is much lighter than the pipe shell. After the uncoupled acoustic wave in the internal medium and uncoupled shell wave are considered, the coincidence frequencies are found. The analysis is successfully confirmed by the verification of the experiment using the real long steel pipe. This work verifies that the coupled wave characteristic of the shell and the fluid is occurred as predominant energy transmission at the coincidence frequencies.

• 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.

• Journal of electromagnetic engineering and science
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• v.18 no.3
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• pp.212-214
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• 2018

The finite-difference time-domain (FDTD) model was developed to analyze electromagnetic (EM) wave propagation in an inhomogeneous ionosphere. The EM analysis of ionosphere is complicated, owing to various propagation environments that are significantly influenced by plasma frequency, cyclotron frequency, and collision frequency. Based on the simple auxiliary differential equation (ADE) technique, we present an accurate FDTD algorithm suitable for the EM analysis of complex phenomena in the ionosphere under arbitrary-direction geomagnetic field. Numerical examples are used to validate our FDTD model in terms of the reflection coefficient of a single magnetized plasma slab. Based on the FDTD formulation developed here, we investigate EM wave propagation characteristics in the ionosphere using realistic ionospheric data for South Korea.

• Structural Engineering and Mechanics
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• v.70 no.1
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• pp.55-66
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• 2019

This work deals with the size-dependent wave propagation analysis of functionally graded (FG) anisotropic nanoplates based on a nonlocal strain gradient refined plate model. The present model incorporates two scale coefficients to examine wave dispersion relations more accurately. Material properties of FG anisotropic nanoplates are exponentially varying in the z-direction. In order to solve the governing equations for bulk waves, an analytical method is performed and wave frequencies and phase velocities are obtained as a function of wave number. The influences of several important parameters such as material graduation exponent, geometry, Winkler-Pasternak foundation parameters and wave number on the wave propagation of FG anisotropic nanoplates resting on the elastic foundation are investigated and discussed in detail. It is concluded that these parameters play significant roles on the wave propagation behavior of the nanoplates. From the best knowledge of authors, it is the first time that FG nanoplate made of anisotropic materials is investigated, so, presented numerical results can serve as benchmarks for future analysis of such structures.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.8
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• pp.1931-1939
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• 1993

The wave propagation characteristics of laminated composites subjected to a transverse high-velocity impact of a steel ball is investigated. For this purpose, high-velocity impact experiments were conducted to obtain the strain response histories, and a finite element analysis based on the higher-order shear deformation theory in conjunction with the static contact law is used. Test materials for investigation are glass/epoxy laminated composite materials with $[0^{\circ}/45^{\circ}/0^{\circ}/-45^{\circ}]_{2s}$ and $[90^{\circ}/-45^{\circ}/90^{\circ}-45^{\circ}/90^{\circ}]_{2s}$ stacking sequences. As a result, the strain responses obtained from the experiments represented the wave propagation characteristics in the transversely impact, also the wave propagation velocities obtained from high-velocity impact experiments and wave propagation theory agree well.

• Structural Engineering and Mechanics
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• v.87 no.2
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• pp.165-172
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• 2023

This paper presents a novel method for modeling elastic wave propagation in long beams. The proposed method derives a solution for the transient transverse displacement of the beam's neutral axis without assuming the separation of variables (SV). By mapping the governing equation from the space domain to the frequency domain using Fourier transformation (FT), the transverse displacement function is determined as a convolution integral of external loading functions and a combination of trigonometric and Fresnel functions. This method determines the beam's response to general loading conditions as a linear combination of the analytical response of a beam subjected to an abrupt localized loading. The proposed solution method is verified through finite element analysis (FEA) and wave propagation patterns are derived for tone burst loading with specific frequency contents. The results demonstrate that the proposed solution method accurately models wave dispersion, reduces computational cost, and yields accurate results even for high-frequency loading.