• Structural Engineering and Mechanics
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• 제62권3호
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• pp.325-344
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• 2017

The present paper investigates the propagation of Love-type wave in a composite structure comprised of imperfectly bonded piezoelectric layer with lower fiber-reinforced half-space with rectangular shaped irregularity at the common interface. Closed-form expression of phase velocity of Love-type wave propagating in the composite structure has been deduced analytically for electrically open and short conditions. Some special cases of the problem have also been studied. It has been found that the obtained results are in well-agreement to the Classical Love wave equation. Significant effects of various parameters viz. irregularity parameter, flexibility imperfectness parameter and viscoelastic imperfectness parameter associated with complex common interface, dielectric constant and piezoelectric coefficient on phase velocity of Love-type wave has been reported. Numerical computations and graphical illustrations have been carried out to demonstrate the deduced results for various cases. Moreover, comparative study has been performed to unravel the effects of the presence of reinforcement and piezoelectricity in the composite structure and also to analyze the existence of irregularity and imperfectness at the common interface of composite structure in context of the present problem which serves as a salient feature of the present study.

• Structural Engineering and Mechanics
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• 제68권4호
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• pp.443-457
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• 2018

In this article, a comparative study has been made to investigate the scattering behaviour of three layered structure model on torsional surface wave. For such model intermediate layer is taken as fiber reinforced composite, resting over a dry sandy Gibson substratum and underlying by different anelastic media. We consider two distinct mediums for topmost layer. In the first case, topmost layer has been taken as fluid saturated homogeneous porous layer, while in the second case the fluid saturated porous layer has been replaced by a transversely isotropic layer. Simple form expression for the secular equation of torsional surface wave has been worked out in both the cases by executing specific boundary conditions, which comprises Whittaker's function and its derivative, for imminent result that have been elaborated asymptotically. Some special cases have been constituted which are in excellent compliance with recorded literatures. For the sake of comparative study, numerical estimation and graphical illustration have been accomplished to identify the effects of the width ratio of the layers, Biot's gravity parameter, sandy parameter, porosity parameter and other heterogeneity parameters corresponding to the layers and half spaces, horizontal compressive and tensile initial stress on the phase velocity of torsional surface wave.

• Geomechanics and Engineering
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• 제15권1호
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• pp.645-657
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• 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
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• 제74권1호
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• pp.91-104
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• 2020

A mathematical analysis has been carried out for understanding the traversal attributes of torsional waves in a Voigt-type viscoelastic porous layer bounded with corrugated surfaces resting over a heterogeneous transversely isotropic gravitating semi-infinite medium. Both the media are assumed to be under the effect of initial stresses acting along horizontal directions. In the presumed geometry, continuous and periodic type of corrugation has been considered. The condensed form of dispersion relation has been obtained analytically with the aid of the Whittaker's function and suitable boundary conditions. The influence of viscoelasticity, porosity, initial stresses, heterogeneity, gravity, undulation and position parameters on the phase and damped velocities has been illustrated graphically. In addition, relative examination investigating the impact of corrugated and planar bounded surfaces on the dispersion and damping characteristics is one of the important highlights of this study.

• Journal of applied mathematics & informatics
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• 제30권3_4호
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• pp.489-498
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• 2012

Most of the software reliability models are based on black box approach and these models consider the entire software system as a single unit. Present day software development process has changed a lot. In present scenario these models may not give better results. To overcome this problem an improved additive model has been proposed in this paper, to estimate the reliability of software with modular structure. Also the concept of imperfect debugging has been also considered. A maximum likelihood estimation technique has been used for estimating the model parameters. Comparison has been made with an existing model. ${\chi}^2$ goodness of fit has been used for model fitting. The proposed model has been validated using real data.

• 한국수학사학회지
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• 제23권1호
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• pp.41-52
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• 2010

고대의 인도수학은 산스크리트어로 쓰여 있고, 수학의 법칙이나 문제들은 구전되었거나 필사본의 형태로 경전 속에 포함되어 있으며, 학생들이 암기를 쉽게 할 수 있도록 아주 간결하게 정리되어 있다. 고대 인도의 많은 수학자들은 일찍이 십진법, 계산법, 방정식, 대수학, 기하학, 삼각법 등의 연구에 공헌하였다. 이 논문은 고대 인도수학과 다른 문명권의 수학발전을 비교하였다. 고대 그리스 수학이 공리적이고 연역적이라면, 인도수학은 양적이며 계산적이지만 원리를 가지고 문제를 해결하는 특성이 있다. 고대 인도와 타 문명권의 수학을 비교하는 것은 오늘날 수학교육과 수학사 연구에 의미가 있는 것으로 사료된다.

• Journal of applied mathematics & informatics
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• 제32권1_2호
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• pp.153-159
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• 2014

In this paper, we introduce a pair of higher-order symmetric dual models/problems. Weak, strong and converse duality theorems for this pair are established under the assumption of higher-order invexity. Moreover, self duality theorem is also discussed.

• Journal of applied mathematics & informatics
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• 제11권1_2호
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• pp.273-281
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• 2003

The purpose of this paper is to study the duality theorems in cone constrained multiobjective nonlinear programming for pseudo-invex objectives and quasi-invex constrains and the constraint cones are arbitrary closed convex ones and not necessarily the nonnegative orthants.

• 대한수학회보
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• 제51권6호
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• pp.1605-1614
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• 2014

In continuation to the investigation initiated by Ferraz, Goodaire and Milies in [4], we provide an explicit description for the Wedderburn decomposition of finite semisimple group algebras of the class of finite groups G, such that $$G/Z(G){\simeq_-}C_2{\times}C_2$$, where Z(G) denotes the center of G.

• Journal of applied mathematics & informatics
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• 제15권1_2호
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• pp.1-28
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• 2004

We first apply a first order splitting to a semilinear reaction-diffusion equation and then discretize the resulting system by an $H^1$-Galerkin mixed finite element method in space. This semidiscrete method yields a system of differential algebraic equations (DAEs) of index one. A priori error estimates for semidiscrete scheme are derived for both differ-ential as well as algebraic components. For fully discretization, an implicit Runge-Kutta (IRK) methods is applied to the temporal direction and the error estimates are discussed for both components. Finally, we conclude the paper with a numerical example.