• Structural Monitoring and Maintenance
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• v.11 no.1
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• pp.19-40
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• 2024

The elastic theory of beams is fundamental in engineering of design and structure. In this study, we construct Green's function for inhomogeneous fourth-order differential operators subjected to associated constraints that arises in dealing with dynamic problems in the Rayleigh beam. We obtain solutions for homogeneous and completely inhomogeneous beam problems using Green's function. This enables us to consider rotational influences in determining the eigenfrequency of beam vibrations. Additionally, we investigate the dynamic vibration model of inhomogeneous beams incorporating rotational effects. The eigenvalues of Rayleigh beams, including first-order correction terms, are also computed and displayed in tabular forms.

• Economic and Environmental Geology
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• v.40 no.6
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• pp.739-749
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• 2007

The seismic velocity at the formation varies widely with physical properties in the layers. These features on seismic shot gathers are not capable of reproducing normally by numerical modeling of homogeneous medium, so that we need that of random inhomogeneous medium instead. In this study, we conducted Gaussian autocorrelation function (ACF), exponential autocorrelation function and von Karman autocorrelation function for getting inhomogeneous velocity model and applied a simple geological model. According to the results, von Karman autocorrelation function showed short wavelength to the inhomogeneous velocity medium. For numerical modeling for a gas hydrate, we determined a geological model based on field data set gathered in the East sea. The numerical modeling results showed that the von Karman autocorrelation function could properly describe scattering phenomena in the gas hydrate velocity model which contains an inhomogeneous layer. Besides, bottom-simulating-reflectors and scattered waves which appear at seismic shot gather of the field data showed properly in the inhomogeneous numerical modeling.

• 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.

• Structural Engineering and Mechanics
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• v.71 no.2
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• pp.153-163
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• 2019

Longitudinal fracture behavior of non-linear elastic beam configurations is studied in terms of the strain energy release rate. It is assumed that the beams exhibit continuous material inhomogeneity along the width as well as along the height of the crosssection. The Ramberg-Osgood stress-strain relation is used for describing the non-linear mechanical behavior of the inhomogeneous material. A solution to strain energy release rate is derived that holds for inhomogeneous beams of arbitrary cross-section under combination of axial force and bending moments. Besides, the solution may be applied at any law of continuous distribution of the modulus of elasticity in the beam cross-section. The longitudinal crack may be located arbitrary along the beam height. The solution is used to investigate a longitudinal crack in a beam configuration of rectangular cross-section under four-point bending. The crack is located symmetrically with respect to the beam mid-span. It is assumed that the modulus of elasticity varies continuously according a cosine law in the beam cross-section. The longitudinal fracture behavior of the inhomogeneous beam is studied also by applying the J-integral approach for verification of the non-linear solution to the strain energy release rate derived in the present paper. Effects of material inhomogeneity, crack location along the beam height and non-linear mechanical behavior of the material on the longitudinal fracture behavior are evaluated. Thus, the solution derived in the present paper can be used in engineering design of inhomogeneous non-linear elastic structural members to assess the influence of various material and geometrical parameters on longitudinal fracture.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11a
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• pp.395.2-395
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• 2002

Recently, as size of building structure becomes larger, mat area of building structure is supported on Inhomogeneous foundation. The equipment machineries in building are mostly on basement story. The slab of the lowest basement story with equipment machineries is considerded as concentrated masses on plate supported on foundation. In this paper. vibration analysis of rectangular thin plate is done by use of rectangular finite element with 4 nodes. (omitted)

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1601-1615
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• 2019

We show the existence of ground state and orbital stability of standing waves of nonlinear $Schr{\ddot{o}}dinger$ equations with singular linear potential and essentially mass-subcritical power type nonlinearity. For this purpose we establish the existence of ground state in $H^1$. We do not assume symmetry or monotonicity. We also consider local and global well-posedness of Strichartz solutions of energy-subcritical equations. We improve the range of inhomogeneous coefficient in [5, 12] slightly in 3 dimensions.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.32A no.2
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• pp.31-37
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• 1995

A ray-based approach is developed to calculate the scattering from inhomogeneous dielectric objects. This approach is a natural extension of the "shooting and bouncing ray(SBR)" technique developed earlier for calculating the radar cross section of cavity structures and complex targets. In this formulation, a dense grid of rays representing the incident field is shot toward the scatterer. The curved trajectory, amplitude, phase and polarization of the ray fields inside the inhomogeneous object are computed numerically based on the laws of geometrical optics. The contributions of the exting rays to the exterior scattered field are then calculated by using the equivalence principle in conjunction with " a ray-tube integration" scheme. The ray-based approach is applied for the effect of an arcjet plasma plume on satellite reflector performance and backscattering from inhomogeneous objects.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.711-714
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• 2005

This paper is for the vibration analysis of thick plate with concentrated mass on a inhomogeneous pasternak foundation. the thick rectangular plate resting on a inhomogeneous pasternak foundation is isotropic, homogeneous and composite with linearly elastic material. In order to analyize plat which is supported on inhomogeneous pasternak foundation, the value of winkler foundation parameter(WFP) of centural and border zone of plate are chosen as Kw1 and Kw2 respectively. The value of Kw1 and Kw2 can be changed as 0, 10, $10^2,\;10^3$ and the value of SFP(shear foundation parameter) also be changed 0, 5, 10, 15 respectively. Finally, In this paper, vibration of retangular plate on the inhomogeneous pasternak foundation, natural frequency of this plate with Concentrated Mass are calculated

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11b
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• pp.982-987
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• 2002

Recently, as size of building structure becomes larger, mat area of building structure is supported on Inhomogeneous foundation. The equipment machineries in building are mostly on basement story. The slab of the lowest basement story with equipment machineries is considered as plate supported on foundation with concentrated masses. In this paper, vibration analysis of rectangular thin plate is done by use of rectangular finite element with 4 nodes. The solution of this paper are compared with existing solution and natural frequencies of thin plates, with concented mass, on inhomogeneous Pasternak foundation are calculated

• Earthquakes and Structures
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• v.9 no.4
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• pp.753-766
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• 2015

An investigation has been carried out for the propagation of torsional surface waves in an inhomogeneous prestressed layer over an inhomogeneous half space when the upper boundary plane is assumed to be rigid. The inhomogeneity in density, initial stress (tensile and compressional) and rigidity are taken as an arbitrary function of depth, where as for the elastic half space, the inhomogeneity in density and rigidity is hyperbolic function of depth. In the absence of heterogeneities of medium, the results obtained are in agreement with the same results obtained by other relevant researchers. Numerically, it is observed that the velocity of torsional wave changes remarkably with the presence of inhomogeneity parameter of the layer. Curves are compared with the corresponding curve of standard classical elastic case. The results may be useful to understand the nature of seismic wave propagation in geophysical applications.