• Earthquakes and Structures
• /
• 제9권2호
• /
• pp.305-320
• /
• 2015

The present paper is devoted to study SH-wave propagation in heterogeneous layer laying over an inhomogeneous isotropic elastic half-space. The dispersion relation for propagation of said waves is derived with Green's function method and Fourier transform. As a special case when the upper layer and lower half-space are homogeneous, our derived equation is in agreement with the general equation of Love wave. Numerically, it is observed that the velocity of SH-wave increases with the increase of inhomogeneity parameter.

• 한국공간구조학회논문집
• /
• 제18권3호
• /
• pp.75-82
• /
• 2018

Large space structures exhibit different natural vibration characteristics depending on the aspect ratio of structures such as half-open angle. In addition, since the actual large space structure is mostly supported by the lower structure, it is expected that the natural vibration characteristics of the upper structure and the entire structure will vary depending on the lower structure. Therefore, in this study, the natural vibration characteristics of the dome structure are analyzed according to the natural frequency ratio by controlling the stiffness of the substructure. As the natural frequency of the substructure increases, the natural frequency of the whole structure increases similarly to the natural frequency of the upper structure. Vertical vibration modes dominate at $30^{\circ}$ and $45^{\circ}$, and horizontal vibration modes dominate at $60^{\circ}$ and $90^{\circ}$.

• Earthquakes and Structures
• /
• 제9권4호
• /
• pp.753-766
• /
• 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.

• 대한수학회논문집
• /
• 제17권1호
• /
• pp.31-36
• /
• 2002

In this paper we first introduce a space of homogeneous type X, and we consider a kind of generalized upper half-space X $\times$ (0, $\infty$). We are mainly concerned with some inequalities in terms of Carleson measures or in terms of certain maximal operators with respect to general approach regions in X $\times$ (0, $\infty$). The main tool of the proof is the Whitney decomposition.

• 충청수학회지
• /
• 제23권3호
• /
• pp.453-461
• /
• 2010

We first introduce a space of homogeneous type X, and develop the theory of the tent spaces on the generalized upper half-space $X{\times}(0,{\infty})$. The goal of this paper is to study that every element of the tent spaces $T_{\Omega}^{p}$($X{\times}(0,{\infty})$, $0, can be decomposed into elementary particles which are called "atoms."

• East Asian mathematical journal
• /
• 제21권1호
• /
• pp.41-48
• /
• 2005

In this paper we first introduce a space of homogeneous type X, and then consider a kind of generalized upper half-space $X{\times}(0,\;\infty)$. We are mainly considered with inequalities for the $L^p$ norms of area functions associated with approach regions in $X{\times}(0,\;\infty)$.

• Geomechanics and Engineering
• /
• 제15권1호
• /
• pp.645-657
• /
• 2018

The paper aims to analyze the behaviour of torsional type surface waves propagating through fluid saturated inhomogeneous porous media clamped between two inhomogeneous anisotropic media. We considered three types of inhomogeneities in upper anisotropic layer which varies exponentially, quadratically and hyperbolically with depth. The anisotropic half space inhomogeneity varies linearly with depth and intermediate layer is taken as inhomogeneous fluid saturated porous media with sinusoidal variation. Following Biot, the dispersion equation has been derived in a closed form which contains Whittaker's function and its derivative, for approximate result that have been expanded asymptotically up to second term. Possible particular cases have been established which are in perfect agreement with standard results and observe that when one of the upper layer vanishes and other layer is homogeneous isotropic over a homogeneous half space, the velocity of torsional type surface waves coincides with that of classical Love type wave. Comparative study has been made to identify the effects of various dimensionless parameters viz. inhomogeneity parameters, anisotropy parameters, porosity parameter, and initial stress parameters on the torsional wave propagation by means of graphs using MATLAB. The study has its own relevance in connection with the propagation of seismic waves in the earth where fluid saturated poroelastic layer is present.

• Structural Engineering and Mechanics
• /
• 제56권3호
• /
• pp.491-506
• /
• 2015

Propagation of the generalized Rayleigh waves in an initially stressed elastic half-space covered by an elastic layer is investigated. It is assumed that the initial stresses are caused by the uniformly distributed normal compressional forces acting on the face surface of the covering layer. Two different cases where the compressional forces are "dead" and "follower" forces are considered. Three-dimensional linearized theory of elastic waves in initially stressed bodies in plane-strain state is employed and the elasticity relations of the materials of the constituents are described through the Murnaghan potential where the influence of the third order elastic constants is taken into consideration. The dispersion equation is derived and an algorithm is developed for numerical solution to this equation. Numerical results for the dispersion of the generalized Rayleigh waves on the influence of the initial stresses and on the influence of the character of the external compressional forces are presented and discussed. These investigations provide some theoretical foundations for study of the near-surface waves propagating in layered mechanical systems with a liquid upper layer, study of the structure of the soil of the bottom of the oceans or of the seas and study of the behavior of seismic surface waves propagating under the bottom of the oceans.

• 한국해양공학회지
• /
• 제13권1호통권31호
• /
• pp.51-61
• /
• 1999

When a structure is built on the ground under consolidation, the instant corresponding contact pressure which the upper structure exerts on the ground is established. But, as the consolidation of the ground proceeds, the contact pressure is changed because of the flexural rigidity of the upper structure. This varied contact pressure exerts influence on the consolidation behavior of the ground. And, this varied consolidation behavior exerts on the contact pressure in retum. This kind of interaction between the upper struture and the olwer ground under consolidation contimues till all the consolidation process in finished. So this problem cannot be defined as a linear problem. In this paper an approximation method which can analyse this non-linear interaction problem is proposed by the FEM.

• 한국전자파학회논문지
• /
• 제11권2호
• /
• pp.313-321
• /
• 2000

본 논문은 등방성 상반 매질과 단축 이방성 하반 매질의 경계변에 위치하는 수평 미세 전류원이 시간 영역에 서 충격적으로 가해칠 때, 경계변에 발생하는 수평 전기장을 구하는 반공간 경계면 문제를 다룬다. 경계변 전기 장에 대해 Cagniard -de- Hoop 법을 변형 적용함으로써. 이 전기장에 대한 명시적 해를 얻는다 또한' 경계변상 에서 퍼져 나가는 Dirac $\delta$- 함수 형태의 충격 성분에 대한 방사 특성에 대해서 논의하는데, 이 충격 성분은 원 방 경계장 특성을 이해하는데 있어서 중요하다. 한편, 단축 이방성은 등방성보다 일반화된 개념이므로 이 논문 에서 구한 전기장 해에서 이방성을 제거하면 등방성 매칠에 대한 해로 환원된다