Mezhlum A. Sumbatyan
Southern Federal University
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Featured researches published by Mezhlum A. Sumbatyan.
International Journal of Engineering Science | 2003
Michele Ciarletta; Gerardo Iovane; Mezhlum A. Sumbatyan
Abstract The paper deals with classical problem for cracks dislocated in a certain very specific porous elastic material, described by a Cowin–Nunziato model. We propose a method based upon a reducing of stress concentration problem for cracks to some integral equations. By applying Fourier integral transforms the problem is reduced to some integral equations. For the plane-strain problem we operate with a direct numerical treatment of a hypersingular integral equation. In the axially symmetric case, for the penny-shaped crack, the problem is reduced to a regular Fredholm integral equation of the second kind. In the both cases we study stress-concentration factor, and investigate its behavior versus porosity of the material. More in particular the stress concentration factor in the medium with voids is always higher, under the same conditions, than in the classical elastic medium made of material of the skeleton. Further, as can be seen, the influence of the porosity becomes more significant for larger cracks; that is also quite natural from a physical point of view.
Archive | 2004
Mezhlum A. Sumbatyan; Antonio Scalia
Some Preliminaries from Analysis and the Theory of Wave Processes. Integral Equations of Diffraction Theory for Obstacles in Unbounded Medium. Wave Fields in a Layer of Constant Thickness. Analytical Methods for Simply Connected Bounded Domains. Integral Equations in Diffraction by Linear Obstacles. Short-Wave Asymptotic Methods on the Basis of Multiple Integrals. Inverse Problems of the Short-Wave Diffraction. Ill-Posed Equations of Inverse Diffraction Problems for Arbitrary Boundary. Numerical Methods for Irregular Operator Equations.
Wave Motion | 1997
Edoardo Scarpetta; Mezhlum A. Sumbatyan
Abstract In the context of wave propagation in damaged (elastic) solids, an analytical approach for normal penetration of a plane wave through a doubly periodic array of cracks is developed. Using a uniform approximation in a one-mode range previously obtained, we give explicit representations for the wave field throughout the structure (including reflection and transmission coefficients) and for the relevant dispersion equation.
Ultrasonics | 1999
Antonio Scalia; Mezhlum A. Sumbatyan
Abstract This paper deals with an efficient algorithm applied to a real-time detection of cracks by ultrasonic techniques. Being founded upon dynamic equations of linear isotropic elasticity, it operates with a uniform approximate representation for the Green tensor. The proposed method demonstrates high efficiency for arbitrary shape of the transducer and the crack in plane, as well as for arbitrary distribution of the stress over the probe basis. Some asymptotic estimates are proposed, to test accuracy of the classical ‘engineering’ far-field approximations. The algorithm permits calibration by a bottom echo-signal, as well as by an echo-amplitude reflected from a side-drilled hole.
Journal of Elasticity | 2000
Antonio Scalia; Mezhlum A. Sumbatyan
The paper is concerned with a static contact problem about a rigid punch on the free surface of a linear porous elastic half-plane. With the use of the Fourier transform the problem is reduced to a singular integral equation holding over the contact zone. This integral representation permits consideration of the Flamant problem (a line load on the half-plane) to be explicitly reduced to some quadratures. It is shown that in the classical linear elasticity limit the main integral equation has a Cauchy-type kernel, so distribution of the contact pressure is like in the Sadowsky punch-problem. For arbitrary porosity a numerical co-location technique is applied that allows one to analyze in detail the distribution of the contact pressure versus porosity. Both in the Flamant and Sadowsky problems we demonstrate a higher compliance of the porous foundation, with respect to the classical linear elastic results.
Research in Nondestructive Evaluation | 2010
M. Brigante; Mezhlum A. Sumbatyan
In the present article we study the reconstruction problem for clusters of linear cracks inside a rectangular domain. The parameters to be reconstructed are the number of cracks and the size and slope of each defect. The scanning is performed by a single ultrasonic transducer placed at a certain boundary point. The input data, used for the reconstruction algorithm, is taken as measured oscillation amplitudes over an array of chosen boundary points. The proposed numerical algorithm is tested on some examples with multiple clusters of cracks whose position and geometry are known a priori.
Inverse Problems in Science and Engineering | 2010
M. Brigante; Mezhlum A. Sumbatyan
In the present work, a direct numerical reconstruction algorithm is proposed, which is applied to the identification of the position and shape of cracks detected in elastic solid samples, in the case when the input data available for the reconstruction is provided by a circular ultrasonic (US) scanner. The US probe gives the far-field back scattered pattern over the full interval of the incident polar angle. The problem is first reduced to a system of basic boundary integral equations. Then the inverse reconstruction problem is formulated as a minimization problem for a certain strongly nonlinear functional. The proposed numerical algorithm is tested on some examples of complex-shaped cracks. Then the influence of the error in the input data on the precision of the reconstruction is studied in detail.
Journal of the Acoustical Society of America | 1994
Mezhlum A. Sumbatyan; Nickolaj V. Boyev
The paper is devoted to the development of ray diffraction theory for arbitrary nonconvex smooth obstacles both for the scalar and elastic case. The consideration is restricted to two‐dimensional problems. An exact expression for the ray amplitude with an arbitrary number of reflections is derived from repeated Kirchhoff integrals using the stationary phase method. It is shown that the difference between scalar and elastic cases consists of the reflection coefficients that are present for the second case. Some examples are considered as a demonstration of the theory.
European Journal of Mechanics A-solids | 2000
Edoardo Scarpetta; Mezhlum A. Sumbatyan
Abstract In the frame of wave propagation in damaged (elastic) solids, an analytical approach for normal penetration of a plane wave through a periodic array of inclined cracks is developed. The problem is reduced to an integral equation holding over the length of each crack; approximated forms (of one-mode and low-frequency types) are then given to the kernel, so as to derive explicit formulas for the reflection and transmission coefficients. Numerical resolution of the relevant equations finally provides some graphs that are compared.
Acta Acustica United With Acustica | 2011
Edoardo Scarpetta; Mezhlum A. Sumbatyan
In the context of wave propagation through a three-dimensional acoustic medium, we develop an analytical approach to study high-frequency diffraction by multiple reflections from curved surfaces of arbitrary shape. Following a previous paper (of one of us) devoted to two-dimensional problems, we combine some ideas of Kirchhoffs physical diffraction theory with the use of (multidimensional) asymptotic estimates for the arising diffraction integrals. Some concrete examples of single and double reflection are treated. The explicit formulas obtained by our approach are compared with known results from classical geometrical diffraction (or Ray-) theory, where this is applicable, and their precision is tested by a direct numerical solution of the corresponding diffraction integrals.