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1

Scattering of interface wave by bottom undulations in the presence of thin submerged vertical wall with a gap

Dolai P.

International Journal of Applied Mechanics and Engineering

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2016

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Vol. 21, no. 2

303--322

EN

In this paper, the problem of interface wave scattering by bottom undulations in the presence of a thin submerged vertical wall with a gap is investigated. The thin vertical wall with a gap is submerged in a lower fluid of finite depth with bottom undulations and the upper fluid is of infinite height separated by a common interface. In the method of solution, we use a simplified perturbation analysis and suitable applications of Green’s integral theorem in the two fluid regions produce first-order reflection and transmission coefficients in terms of integrals involving the shape function describing the bottom undulations and solution of the scattering problem involving a submerged vertical wall present in the lower fluid of uniform finite depth. For sinusoidal bottom undulations, the first-order transmission coefficient vanishes identically. The corresponding first-order reflection coefficient is computed numerically by solving the zero-order reflection coefficient and a suitable application of multi-term Galerkin approximations. The numerical results of the zero-order and first-order reflection coefficients are depicted graphically against the wave number in a number of figures. An oscillatory nature is observed of first-order reflection coefficient due to multiple interactions of the incident wave with bottom undulations, the edges of the submerged wall and the interface. The first-order reflection coefficient has a peak value for some particular value of the ratio of the incident wavelength and the bottom wavelength. The presence of the upper fluid has some significant effect on the reflection coefficients.

2

Interface wave diffraction by bottom undulations in the presence of a thin plate submerged in lower fluid

Dolai D. P., Dolai P.

International Journal of Applied Mechanics and Engineering

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2010

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Vol. 15, no 4

1017-1036

EN

The problem of interface wave diffraction by bottom undulations in the presence of a thin vertical plate is investigated in this paper. The plate is submerged in the lower fluid of finite depth with bottom undulations and the upper fluid is of infinite height separated by a common interface. In the method of solution, we use a simplified perturbation analysis and suitable applications of Green's integral theorem in the two fluid regions produce first-order reflection and transmission coefficients in terms of integrals involving the shape function describing the bottom undulations and solution of the scattering problem involving a submerged vertical plate present in the lower fluid of uniform finite depth. For sinusoidal bottom undulations, the first-order transmission coefficient vanishes identically. The corresponding first-order reflection coefficient is computed numerically by solving the zero-order reflection coefficient and suitable application of multi-term Galerkin approximations. The numerical results of zero-order and first-order reflection coefficients are depicted graphically against the wave number in a number of figures. An oscillatory nature of first-order reflection coefficient due to multiple interaction of the incident wave with bottom undulations is observed. The first-order reflection coefficient has a peak value for some particular value of the ratio of the incident wavelength and the bottom wavelength. The presence of the upper fluid has some significant effect on the reflection coefficients.

3

Conditioning and error estimates in LQG design

Petkov P. Hr., Konstantinov M. M., Christov N. D.

Control and Cybernetics

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2008

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Vol. 37, no 1

85-87

EN

Efficient conditioning and error estimates are presented for the numerical solution of matrix Riccati equations in the continuous-time and discrete-time LQG design. The estimates implemented involve the solution of triangular Lyapunov equations along with usage of the LAPACK norm estimator.

4

A reliable synthesis of discrete-time Η∞ control. Part I: basic theorems and J-lossless conjugators

Suchomski P. J.

Control and Cybernetics

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2007

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Vol. 36, no 1

97-141

EN

The paper gives a basis for solving many problems of numerically reliable synthesis of sub-optimal discrete-time control in Η∞. The approach is based on J-lossless factorisations of the delta-domain chain-scattering descriptions of continuous-time plants being controlled. Relevant properties of poles and zeros of chain-scattering models are given. Necessary and sufficient conditions for the existence of stabilising J-lossless conjugators are presented and discussed. Some aspects of numerical conditioning of synthesis of such conjugators are considered. A numerical example illustrating synthesis of stabilising right J-lossless conjugators is also included.

5

Oblique wave scattering by undulations on the bed of an ice-covered ocean

Mandal B. N., Maiti P.

Archives of Mechanics

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2004

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Vol. 56, nr 6

485-493

EN

The problem of oblique wave scattering by cylindrical undulations on the bed of an ice-covered ocean is investigated by using a simplified perturbation analysis. The first-order potential function satisfies a boundary value problem (BVP) which is solved by employing the Green integral theorem after constructing an appropriate Green function. Analytical expressions for the first-order reflection and transmission coefficients are then obtained from the solution of this BVP, in terms of the integrals involving the shape function describing undulations. Three particular forms of the shape function are considered for which the reflection and transmission coefficients up to the first-order are obtained exactly.

6

Lubrication of a slider bearing with a special third grade fluid

Yurusoy M., Pakdemirli M.

Applied Mechanics and Engineering

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1999

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Vol. 4, no 4

759-772

EN

Lubrication of a slider bearing with a non-Newtonian fluid is considered. The fluid is a third grade fluid. Under the assumptions of the order of magnitudes of the variables, it is seen that only viscous and third grade terms are effective, whereas second grade terms and inertia terms are negligible. Choosing third grade effects to be smaller than the viscous effects, a perturbation solution is constructed. The velocity profile and the pressure distribution in the bearing is calculated approximately.