• Structural Engineering and Mechanics
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• v.72 no.5
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• pp.597-615
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• 2019

The paper studies the dispersion of the axisymmetric longitudinal wave propagating in the "hollow cylinder + surrounding medium" system with inhomogeneous initial stresses caused by the uniformly distributed radial compressional forces acting at infinity. Up to now in the world literature, there exist only a few investigations related to the wave dispersion in a hollow cylinder with inhomogeneous initial stresses. Therefore, this paper is one of the first attempts in this field in the sense of the development of investigations for the case where the cylinder is surrounded with an infinite medium. The three-dimensional linearized theory of elastic waves is used for describing the considered wave propagation problem and, for a solution to the corresponding mathematical problem, the discrete-analytical solution method is developed and employed. The corresponding dispersion equation is obtained and this equation is solved numerically and, as a result of this solution, the dispersion curves are constructed for the first and second modes. By analyzing these curves, the character of the influence of the inhomogeneous initial stresses on the dispersion curves is established. In particular, it is established that as a result of the inhomogeneity of the initial stresses both new dispersion curves and the "band gap" for the wave frequencies can appear.

• Journal of the Korean Society for Nondestructive Testing
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• v.34 no.3
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• pp.233-240
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• 2014

In this study, we investigated the dispersion characteristics of guided waves in thin films. Dispersion curves are essential for understanding not only the behavior of ultrasonic waves, but also the mechanical properties of thin films. Matrix techniques are presented for modeling ultrasonic waves in multilayered structures before being used to calculate the dispersion curves for Al-steel and Al-composite specimens. When compared with the dispersion curves obtained using the commercial program (Disperse), the dispersion curves generated from the transfer matrix method show its validity. These developed methods are used to obtain dispersion curves for Al thin films deposited on a Si substrate. The resulting dispersion curves enable observation of both dispersive and non-dispersive behavior for the guided waves, depending on the thickness of the thin films.

• Coupled systems mechanics
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• v.10 no.2
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• pp.123-142
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• 2021

The paper deals with the study of the dispersion of quasi-Lamb waves in a hydro-elastic system consisting of an elastic plate, barotropic compressible inviscid fluid, and rigid wall. The motion of the plate is described using the exact equations of elastodynamics, however, the flow of the fluid using the linearized equations and relations of the Navier-Stokes equations. The corresponding dispersion equation is obtained and this equation is solved numerically, as a result of which the corresponding dispersion curves are constructed. The main attention is focused on the effect of the presence of the fluid and the effect of the fluid layer thickness (i.e., the fluid depth) on the dispersion curves. The influence of the problem parameters on the dispersion curves related to the quasi-Scholte wave is also considered. As a result of the analyses of the numerical results, concrete conclusions are made about the influence of the fluid depth, the rigid wall restriction on the fluid motion, and the material properties of the constituents on the dispersion curves. During the analyses, the zeroth and the first four modes of the propagating waves are considered.

• The Journal of the Acoustical Society of Korea
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• v.20 no.4E
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• pp.45-51
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• 2001

This paper examines the dispersion relation governing the wave propagation on cylindrical shells. The assumption of thin shells allows the dispersion relation to be separated into three relations related to the propagation of flexural waves and two types of membrane waves. Those relations are used to identify the characteristics of the wave number curves. The dispersion relation provides two and three closed wave number curves below and above the ring frequency. Above the ring frequency three wave number curves are clearly identified to be those of flexural, shear and longitudinal waves, respectively. Below the ring frequency, the characteristics of two wave number curves are identified with dependence of the direction of wave propagation.

• Journal of the Korean Society for Nondestructive Testing
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• v.30 no.6
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• pp.548-557
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• 2010

An ultrasonic resonance scattering spectroscopy technique is developed and applied for reconstructing elastic constants of a transversely isotropic cylindrical component. Immersion ultrasonic measurements are performed on tube samples made from a boron/aluminum composite material to obtain resonance frequencies and dispersion curves of different guided wave modes propagating in the tube. Theoretical analysis on the acoustic resonance scattering from a transversely isotropic cylindrical tube is also performed, from which complete backscattering and resonance scattering spectra and theoretical dispersion curves are calculated. A sensitive change of the dispersion curves to the elastic properties of the composite tube is observed for both normal and oblique incidences; this is exploited for a systematic evaluation of damage and elastic constants of the composite tube samples. The elastic constants of two boron/aluminum composite tube samples manufactured under different conditions are reconstructed through an optimization procedure in which the residual between the experimental and theoretical phase velocities (dispersion curves) is minimized.

• 한국지구물리탐사학회:학술대회논문집
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• 2006.06a
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• pp.51-59
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• 2006

The surface wave data obtained in a tidal flat located in the sw coast of the Korean Peninsula were used to analyse the shear wave velocity structure of the area. First, the phase velocity dispersion curves were obtained by the tau-p stacking method and the group velocity dispersion curves by a wavelet transform method and the Multiple Filtering Technique by Dziewonski. The phase velocity dispersion curves exhibited bigger errors than the group velocity curves. The results showed that the wavelet transform method was more effective in separating the fundamental and the 1st higher mode group velocity curves than the Multiple Filtering Technique. Combined use of the fundamental and the 1st higher mode group velocity dispersion curves in the inversion for the shear wave velocity structure gave better spatial resolution compared when the fundamental mode group velocity was used alone. This study indicates that the group velocity dispersion curves can be used in the inversion of Rayleigh waves for the shear wave velocity structure, especially effectively with the higher mode group velocity curves together.

• Structural Engineering and Mechanics
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• v.81 no.4
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• pp.443-459
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• 2022

The paper studies the dispersion and attenuation of propagating waves in the "plate+compressible viscous fluid layer" system in the case where the fluid layer flow is restricted with a rigid wall, and in the case where the fluid layer has a free face. The motion of the plate is described by the exact equations of elastodynamics and the flow of the fluid by the linearized Navier-Stokes equations for compressible barotropic Newtonian viscous fluids. Analytical expressions are obtained for the amplitudes of the sought values, and the dispersion equation is derived using the corresponding boundary and compatibility conditions. To find the complex roots of the dispersion equation, an algorithm based on equating the modulus of the dispersion determinant to zero is developed. Numerical results on the dispersion and attenuation curves for various pairs of plate and fluid materials under different fluid layer face conditions are presented and discussed. Corresponding conclusions on the influence of the problem parameters on the dispersion and attenuation curves are made and, in particular, it is established that the change of the free face boundary condition with the impermeability condition can influence the dispersion and attenuation curves not only in the quantitative, but also in the qualitative sense.

• Structural Engineering and Mechanics
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• v.41 no.5
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• pp.605-615
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• 2012

In this paper, guided circumferential wave propagating in an orthotropic viscoelastic cylindrical curved plate subjected to traction-free conditions is investigated in the frame of the Kelvin-Voight viscoelastic theory. The obtained three wave equations are decoupled into two groups, Lamb-like wave and SH wave. They are separately solved by the Legendre polynomial series approach. The availability of the method is confirmed through the comparison with the published data of the SH wave for a viscoelastic flat plate. The dispersion curves and attenuation curves for the carbon fiber and prepreg cylindrical plates are illustrated and the viscous effect on dispersion curves is shown. The influences of the ratio of radius to thickness are analyzed.

• Journal of the Korean Society for Nondestructive Testing
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• v.21 no.4
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• pp.391-397
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• 2001

The guided wave propagation in inhomogeneous multi-layered structures is experimentally explored based on theoretical dispersion curves. It turns out that proper selection of incident angel and frequency is critical for guided wave generation in multi-layered structures. Theoretical dispersion curves greatly depend on adhesive zone thickness, layer thickness and material properties. It was possible to determine the adhesive zone thickness of an inhomogeneous multi-layered structure by monitoring experimentally the change of dispersion curves.

• Journal of the Korean Geotechnical Society
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• v.22 no.12
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• pp.15-24
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• 2006

The evaluation of shear modulus is very important in various fields of civil engineering. Non-destructive seismic methods can be used to determine shear wave velocity ($V_s$) profile. Non-destructive seismic methods geneally consist of three steps: field testing, evaluation of dispersion curve, and determination of Vs profile by inversion process. Non-destructive seismic methods can be divided into two categories according to the number of receivers used for data reduction: two-channel tests and multi-channel tests. Two channel tests use apparent velocity dispersion curve and multi-channel tests use mode dispersion curves. Multi-channel tests using mode dispersion curve can reduce calculation time to determine soil profile and uncertainties in inversion process. So far, only multi-channel tests can determine mode dispersion curves but multi-channel test needs many receivers to determine reasonable mode dispersion curves. In this paper, HWAW (Harmonic Wavelet Analysis of Wave) method is applied to determine mode dispersion curves. HWAW method uses short test setup which consists of two receivers with a spacing of 1 to 3 m. Through numerical simulations and field application, it is shown that HWAW can determine resonable mode disperson curves.