Morteza Eskandari-Ghadi

Bio: Morteza Eskandari-Ghadi is an academic researcher from University of Tehran. The author has contributed to research in topics: Transverse isotropy & Isotropy. The author has an hindex of 17, co-authored 92 publications receiving 1075 citations. Previous affiliations of Morteza Eskandari-Ghadi include University of Mazandaran & Mazandaran University of Science and Technology.

A Complete Solution of the Wave Equations for Transversely Isotropic Media

Abstract: A transversely isotropic material in the sense of Green is considered. A complete solution in terms of retarded potential functions for the wave equations in transversely isotropic media is presented. In this paper we reduce the number of potential functions to only one, and we discuss the required conditions. As a special case, the torsionless and rotationally symmetric configuration with respect to the axis of symmetry of the material is discussed. The limiting case of elastostatics is cited, where the solution is reduced to the Lekhnitskii–Hu–Nowacki solution. The solution is simplified for the special case of isotropy. In this way, a new series of potential functions (to the best knowledge of the author) for the elastodynamics problem of isotropic materials is presented This solution is reduced to a special case of the Cauchy–Kovalevski–Somigliana solution, if the displacements satisfy specific conditions. Finally, Boggio's Theorem is generalized for transversely isotropic media which may be of interest to the reader beyond the present application.

Elastodynamic Potential Method for Transversely Isotropic Solid

Abstract: A theoretical formulation is presented for the determination of the displacements, strains, and stresses in a three-dimensional transversely isotropic linearly elastic medium. By means of a complete representation using two displacement potentials, it is shown that the governing equations of motion for this class of problems can be uncoupled into a fourth-order and a second-order partial differential equation in terms of the spatial and time coordinate under general conditions. Compatible with Fourier expansions and Hankel transforms in a cylindrical coordinate system, the formulation includes a complete set of transformed displacement-potential, strain-potential, and stress-potential relations that can be useful in a variety of elastodynamic as well as elastostatic problems. As an illustration of the application of the method, the solution for a half-space under the action of arbitrarily distributed, time-harmonic surface traction is derived, including its specialization to uniform patch loads and point forces. To confirm the accuracy of the numerical evaluation of the integrals involved, numerical results are also included for cases of different degree of the material anisotropy, frequency of excitation, and compared with existing solutions.

Forced Vertical Vibration of Rigid Circular Disc on a Transversely Isotropic Half-Space

Abstract: Vertical vibration of a rigid circular disc attached to the surface of a transversely isotropic half-space is considered in such a way that the axis of material symmetry is normal to the surface of the half-space and parallel to the vibration direction. By using Hankel integral transforms, the mixed boundary-value problem is transformed to a pair of integral equations termed dual integral equations in the literature, which generally can be reduced to a Fredholm integral equation of the second kind. With the aid of complex variable or contour integration the governing integral equation is numerically solved in the general dynamic case. The reduced static case of the dual integral equations is solved analytically and the vertical displacement, the contact pressure, and the static impedance/compliance function are explicitly solved. The dynamic contact pressure under the disc and the impedance function are numerically evaluated, and it is shown that the singularity that exists at the edge of the disc is the same as the one obtained for the static case. In addition, the impedance functions evaluated here are identical to the solution given by Luco and Mita for the isotropic domain. To show the effect of different material anisotropy, the numerical evaluations are given for some different transversely isotropic materials and compared.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Integral transforms and their applications

Abstract: Integral transforms (Laplace, Fourier and Mellin) are introduced with their properties, the relationship between these transforms was discussed and some important applications in physics and engineering were given. ااااااا دقل مت ضارعتسإ ةساردو ل ةيلماكتلا تليوحتلا لك ، سلبل تلوحت نم روف ي ر نيليمو عم ةشقانم كلذكو ،اهنم لك صاوخ و صئاصخ ةقلعلا ةشقانم مت هذه نيب طبرلاو و ،تليوحتلا مت ميدقت تاقيبطتلا ضعب تليوحتلا هذهل ةمهملا يف تلاجم ءايزيفلا ةسدنهلاو.

On the solution of integral equations with strong ly singular kernels

Abstract: In this paper some useful formulas are developed to evaluate integrals having a singularity of the form (t-x) sup-m, m or = 1 Interpreting the integrals with strong singularities in Hadamard sense, the results are used to obtain approximate solutions of singular integral equations A mixed boundary value problem from the theory of elasticity is considered as an example Particularly for integral equations where the kernel contains, in addition to the dominant term (t,x) sup-m, terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results