Modeling of imperfect contact interfaces in sonic composites

In this paper, the tangential and normal discontinuities at the interface between the scatterer and the matrix are independently modeled, and these relative displacements are directly proportional to the corresponding components of tractions at the interface. The generation of full band-gaps is investigated on the basis of the derived imperfect interface conditions for a sonic plate with an array of acoustic piezoceramic hollow spheres scatterers embedded in an epoxy matrix. The scatterers are made from functionally graded materials with radial polarization. Numerical evaluation has shown that imperfect interface may have a significant effect on the increasing of the length of the full band-gaps. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the acoustics of sonic composites

The primary goal of this paper is to propose an alternative method for obtaining the band structures of the 3D sonic composites without/ with point defects. The point defects are vacancies or foreign interstitial atoms which are supported by the interfaces between the hollow spheres and the matrix. The proposed method is used to simulate a sonic plate composed of an array of acoustic scatterers which are piezoceramic hollow spheres embedded in an epoxy matrix. The scatterers are made from functionally graded materials with radial polarization [1, 2]. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the sonic composites subjected to severe acoustic loads

Transformation acoustics opens a new avenue towards the fabrication of a new class of sonic composites with scatterers made of auxetic materials embedded in the epoxy matrix. The design of the acoustic scatterers is based on the property of Helmoltz equations to be invariant under coordinate transformations, i.e. a specific spatial compression is equivalent to a variation of the material parameters in the original space. In this paper, the noise suppression for a wide full band-gap of frequencies is discussed for spherical shell scatterers made of auxetic materials. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the sonic composites with scatterers made from auxetic material

A finite size periodic array of resonators made from auxetic material embedded into an epoxy matrix is analyzed in this paper. According to the Bragg's theory, the sound attenuation band is due to the superposition of multiple reflected waves inverse proportional to the central distance between resonators. The sound attenuation in such composites is studied using a method that combines the features of the cnoidal method and the genetic algorithm [1-3]. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Localized modes at defects in sonic composites

The paper discusses a sonic composite consisting of an array of silicone rubber coated hollow steel cylinders embedded in an epoxy matrix, with linear defects. Such structures allow localization of modes in the vicinity of the line defect with propagation along this line. The material in the vicinity of the line behaves like frequency-specific mirrors. The mirrors localize waves within a finite region of the line defect, and modes are quantized into discrete frequencies. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On sonic discontinuities in an ideal radiating gas

Following Elcrat the phenomena associated with the sonic discontinuities in an ideal radiating gas are studied here. The differential equations for growth and decay of these discontinuities are formulated. In order to integrate them in full generality they are transformed to an equation along the bicharacteristic curve in the characteristic manifold. The criterion for the decay or blow up of weak discontinuities has been given. Radiation contributes to the fast development of shock.

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Résumé Dans cet article il s'agit de l'étude des phénomènes associés aux discontinuités soniques dans un gaz parfait rayonnant. On formule les équations différentielles gouvernant la croissance et l'amortissement de ces discontinuités. Afin de pouvoir les intégrer en toute généralité, on les transforme en une équation sur la courbe bicaractéristique dans la variété caractéristique. On donne le critère d'amortissement ou d'éclatement des discontinuités faibles. Le rayonnement contribue au développement rapide du choc.

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This author is thankful to CSIR, India for financial assistance for this work.     

On the theory of oscillating airfoils in supersonic and sonic flow

Summary On the basis of the fundamental solutions method, the theory of oscillating airfoils in supersonic and sonic flow is given. The solution obtained allows an easy calculation of the lift and moment coefficients.

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Zusammenfassung Die Theorie der Flügelschwingungen in Überschall- und Schallströmung wird mit der Methode der Fundamentallösungen hergeleitet. Die Lösung gestattet eine einfache Bestimmung des Auftriebes und des Momentes.

     

On the entropy inequality for material interfaces

The form of entropy inequality appropriate to material interfaces, when viewed as bidimensional continua, is established from three-dimensional considerations.     

On the entropy inequality for material interfaces

Summary The form of entropy inequality appropriate to material interfaces, when viewed as bidimensional continua, is established from three-dimensional considerations.

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Zusammenfassung Ausgehend von einer dreidimensionalen Untersuchung wird durch Grenzübergang die Entropie-Ungleichung für materielle Trennflächen gewonnen, die als zweidimensionale Kontinua zu betrachten sind.

     

An analysis of contact deformation of auxetic composites

The adaptive mode of frictional interaction has been studied as a self-locking effect upon contact deformation of isotropic and anisotropic auxetic materials with a negative Poisson ratio. This effect manifests itself in the fact that the bearing capacity of the joint rises with increasing shear load. In particular, the parameters of stress state (contact load, tangential stresses, slippage, etc.) were determined for a double-lap joint under conditions of compression with or with out shear. The contact interaction was analyzed by the finite-element method for three profiles of symmetrically located contact elements (plane, cylindrical, and wedge-shaped). The Poisson ratio was varied within the range theoretically admissible for isotropic elastic media. Analogous calculations were also performed for a joint with a deformed element made of an anisotropic auxetic composite, whose reinforcement angle was varied. The maximum loads, tangential stresses, and slippage are obtained as nonlinear functions of Poisson ratio (in the isotropic case) and reinforcement angle of the composite material. The stress concentration and the increased ultimate shear forces are also estimated. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 5, pp. 681–692, September–October, 2006.     

On the existence of almost contact structure and the contact magnetic field

We give a simple proof of the existence of an almost contact metric structure on any orientable 3-dimensional Riemannian manifold (M ³, g) with the prescribed metric g as the adapted metric of the almost contact metric structure. By using the key formula for the structure tensor obtained in the proof this theorem, we give an application which allows us to completely determine the magnetic flow of the contact magnetic field in any 3-dimensional Sasakian manifold.     

On the contact dimensions of graphs

Every simple graphG=(V, E) can be represented by a family of equal nonoverlapping spheres {S _v :v V} in a Euclidean spaceR ⁿ in such a way thatuv E if and only ifS _u andS _v touch each other. The smallest dimensionn needed to representG in such a way is called the contact dimension ofG and it is denoted by cd(G). We prove that (1) cd(T)<(7.3) log |T| for every treeT, and (2)

Investigation of the wave field in an effective model of layered elastic media with slide contact on the interfaces

An effective model of media consisting of two alternating elastic layers with slide contact on the boundaries is investigated. The wave field in this model is represented as Fourier and Mellin integrals. In the Mellin integrals we replace the contours of integration by stationary contours. In the expressions obtained, we change the order of integration and calculate the inner integral. The outer integral is equal to two residues. The corresponding poles are roots of two equations of the sixth order. These roots may be situated in the right half-plane and may be complex or real. The representation obtained of the wave field corresponds to expressions derived by the Smirnov-Sobolev method. Bibliography: 5 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 342, 2007, pp. 187–205.     

On the existence of optimal shapes in contact problems

The optimal shape design of a two-dimensional elastic body on a rigid frictionless foundation is analyzed. The problem is to find the boundary part of the body where the unilateral boundary conditions are assumed, in such a way that the total energy of the system in the equilibrium state will be minimized. The solvability of the problem is proved.     

On the curvature of contact metric manifolds

Some results on Ricci-symmetric contact metric manifolds are obtained. Second order parallel tensors and vector fields keeping curvature tensor invariant are characterized on a class of contact manifolds. Conformally flat contact manifolds are studied assuming certain curvature conditions. Finally some results onk-nullity distribution of contact manifolds are obtained.     

On the contact geometry of nodal sets

In the 3-dimensional Riemannian geometry, contact structures equipped with an adapted Riemannian metric are divergence-free, nondegenerate eigenforms of the Laplace-Beltrami operator. We trace out a two-dimensional consequence of this fact: there is a close relationship between the topology of the contact structure on a convex surface in the 3-manifold (the dividing curves) and the nodal curves of Laplacian eigenfunctions on that surface. Motivated by this relationship, we consider a topological version of Payne's conjecture for the free membrane problem. We construct counterexamples to Payne's conjecture for closed Riemannian surfaces. In light of the correspondence between the nodal lines and dividing curves, we interpret the conjecture in terms of the tight versus overtwisted dichotomy for contact structures.