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1
Content available Water wave scattering by an infinite step in the presence of an ice-cover
Ray S., De S., Mandal B. N.
International Journal of Applied Mechanics and Engineering
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2019
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Vol. 24, no. 4
157--168
EN
The classical problem of water wave scattering by an infinite step in deep water with a free surface is extended here with an ice-cover modelled as a thin uniform elastic plate. The step exists between regions of finie and infinite depths and waves are incident either from the infinite or from the finite depth water region. Each problem is reduced to an integral equation involving the horizontal component of velocity across the cut above the step. The integral equation is solved numerically using the Galerkin approximation in terms of simple polynomial multiplied by an appropriate weight function whose form is dictated by the behaviour of the fluid velocity near the edge of the step. The reflection and transmission coefficients are obtained approximately and their numerical estimates are seen to satisfy the energy identity. These are also depicted graphically against thenon-dimensional frequency parameter for various ice-cover parameters in a number of figures. In the absencje of ice-cover, the results for the free surface are recovered.
2
Content available Scattering of oblique water waves by an infinite step
Dolai P., Dolai D. P.
International Journal of Applied Mechanics and Engineering
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2018
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Vol. 23, no. 2
327--338
EN
The present paper is concerned with the problem of scattering of obliquely incident surface water wave train passing over a step bottom between the regions of finite and infinite depth. Havelock expansions of water wave potentials are used in the mathematical analysis to obtain the physical parameters reflection and transmission coefficients in terms of integrals. Appropriate multi-term Galerkin approximations involving ultra spherical Gegenbauer polynomials are utilized to obtain very accurate numerical estimates for reflection and transmission coefficients. The numerical results are illustrated in tables.
3
Content available Response of corrugated interface on incident qSV-wave in monoclinic elastic half-spaces
Singh S. S., Lalvohbika J.
International Journal of Applied Mechanics and Engineering
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2018
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Vol. 23, no. 3
727--750
EN
This paper is concerned with the problem of reflection and transmission of elastic waves due to an incident plane qSV-wave at a corrugated interface between two dissimilar monoclinic elastic half-spaces. Due to the corrugated nature of the interface, there exist regularly and irregularly reflected and transmitted elastic waves. Using Rayleigh’s method of approximation, the reflection and transmission coefficients of regular and irregular waves are obtained for the first order of approximation. We have found that these coefficients are functions of the angle of incidence, elastic constants, corrugation and the frequency parameter. These coefficients are obtained for a special type of interface, z =dcos py. We have computed these coefficients for a particular model and discussed the effects of corrugation and frequency parameter.
4
Content available Oblique water wave diffraction by a step
Dolai P.
International Journal of Applied Mechanics and Engineering
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2017
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Vol. 22, no. 1
35--47
EN
This paper is concerned with the problem of diffraction of an obliquely incident surface water wave train on an obstacle in the form of a finite step. Havelock expansions of water wave potentials are used in the mathematical analysis to obtain the physical parameters reflection and transmission coefficients in terms of integrals. Appropriate multi-term Galerkin approximations involving ultraspherical Gegenbauer polynomials are utilized to obtain a very accurate numerical estimate for reflection and transmission coefficients which are depicted graphically. From these figures various interesting results are discussed.
5
Content available remote Reflection and transmission of plane SH-wave at an interface between two different self-reinforced elastic half-spaces
Chaudhary S., Rani R.
International Journal of Applied Mechanics and Engineering
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2011
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Vol. 16, no 4
977-988
EN
Reflection and transmission of plane SH-waves interacting at an interface between two self-reinforced elastic half-spaces is investigated. The expressions for reflection and transmission coefficients are obtained in a closed from and are computed for different values of non-dimensional self-reinforced elastic parameters and presented graphically. The problem studied by Bullen and Bolt (1985.p.143), when both the self-reinforced elastic solid half-spaces M1 and M2 are isotropic elastic and the SH-wave is made incident at an interface has been reduced as a special case of our problem.
6
Content available remote Calculation of reflection and transmission coefficients for qP waves incident on a planar interface between isotropic and triclinic media
Li L.
Acta Geophysica
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2008
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Vol. 56, no. 2
518-528
EN
In the paper by Chattopadhyay and Rajneesh (2006, "Reflection and refraction of waves at the interface of an isotropic medium over a highly anisotropic medium", Acta Geophysica, vol. 54, no. 3, pp. 239-249), the authors proposed a process to calculate R/T (reflection and transmission) coefficients at the interface between isotropic and triclinic half-spaces, with incident qP waves in triclinic media. Unfortunately, besides several misprints, the authors made a fatal assumption that there is no transmitted SH wave generated in isotropic media, which led the successive analytical derivations and numerical calculations thoroughly wrong. In this paper, the errors are analyzed at length and corrections are given. Then an alternative approach to solve the problem is proposed and numerical results are shown and discussed.
7
Content available remote Theoretical and numerical analysis of double-negative slab
Sabah C.
Optica Applicata
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2007
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Vol. 37, nr 1-2
123-131
EN
Reflection and transmission analysis due to the interaction of electromagnetic waves with a frequency dispersive double-negative slab are investigated in detail. In particular, the reflection and the transmission coefficients are found and defined. The incident field is assumed to be a plane monochromatic wave of transverse magnetic polarization. Imposing the boundary conditions at the interfaces, the transmission and the reflection coefficients at each interface can be obtained. Numerical results are presented for both cases of transverse magnetic and electric waves to show the effects of the incidence angle, the frequency, and the structure parameters on the reflection and the transmission coefficients.
8
Content available remote Plane SH-wave response from elastic slab interposed between two different self-reinforced elastic solids
Chaudhary S., Kaushik V. P., Tomar S. K.
International Journal of Applied Mechanics and Engineering
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2006
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Vol. 11, no 4
787-801
EN
Closed form expressions of reflection and transmission coefficients are obtained when a plane SH-wave becomes incident at a uniform elastic layer interposed between two different self-reinforced elastic solid half-spaces. It is found that the reflection and transmission coefficients are strongly influenced by the reinforcement parameters of the half-spaces. Numerical computations are performed for a specific model to study the effect of reinforcement parameters and angle of incidence of the incident wave on these coefficients. Numerical study reveals that both reflection and transmission coefficients are significantly influenced by the reinforcement parameters in the entire range of angle of incidence, except at normal and grazing incidence where the effect of reinforcement parameters is found minimum. Known results of some earlier workers are reduced from the present formulations.
9
Content available remote Reflection and refraction of thermoelastic plane waves at an interface between two thermoelastic media without energy dissipation
Kumar R., Sarthi P.
Archives of Mechanics
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2006
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Vol. 58, nr 2
155-185
EN
The reflection and refraction of thermoelastic plane waves at an imperfect interface between two dissimilar thermoelastic solid half-spaces has been investigated. The thermoelastic theory without energy dissipation developed by Green Naghdi [18] has been used to study the problem. The amplitude ratios of various reflected and refracted waves are obtained for an imperfect boundary. Particular cases of normal stiffness, transverse stiffness, slip and welded boundaries are discussed. The amplitude ratios are also deduced at the interface of two semi-infinite media (I) Elastic/Thermoelastic without energy dissipation, (II) Thermal Conducting Liquid/Thermoelastic without energy dissipation, (III) Non-viscous Fluid/Thermoelastic without energy dissipation, (IV) Thermal Conducting Liquid/Thermal Conducting Liquid and (V) Elastic/Elastic. It is found that the amplitude ratios of various reflected and refracted waves are affected by the stiffness and thermal properties of the media. The amplitude ratios of reflected waves are also deduced for a special case of stress-free boundary.
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