Wavelet and Wave Analysis as Applied to Materials with Micro or Nanostructure

Cattani, Carlo; Rushchitsky, J. J.

doi:10.1142/9789812709769

Cited by 34 publications

(73 citation statements)

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“…Therefore, they are planned to be used in the theory of functionally gradient materials, in which one of the authors is somewhat experienced. Also, the proposed general solutions can be used in the theory of micro-and nanocomposites, in which the other author is somewhat experienced [10,11,[17][18][19][20][21][22][23][24].…”

Section: Love Solution In the Inhomogeneous Linear Isotropic Theory Omentioning

confidence: 99%

General hoyle–youngdahl and love solutions in the linear inhomogeneous theory of elasticity

Kashtalyan

Rushchitsky

2010

Int Appl Mech

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The general Hoyle-Youngdahl and Love solutions in the three-dimensional theory of inhomogeneous linear elastic materials are proposed. Following a brief historical outline of various general solutions existing in the classical linear elasticity of homogeneous isotropic media, key steps of the derivation of the Hoyle-Youngdahl and Love solutions are presented. The procedure is then generalized to the case of inhomogeneous elastic materials with elastic constants depending on the z-coordinate. The significance of the solutions and their relevance to modeling of functionally graded materials is discussed in brief

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Section: Love Solution In the Inhomogeneous Linear Isotropic Theory Omentioning

confidence: 99%

General hoyle–youngdahl and love solutions in the linear inhomogeneous theory of elasticity

Kashtalyan

Rushchitsky

2010

Int Appl Mech

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“…Therefore, the results obtained are planned to be used in the theory of functionally gradient materials in which one of the authors is somewhat experienced. Also, the general solutions proposed can be used in the theory of micro-and nanocomposites, in which the other author is somewhat experienced [7,8,[11][12][13][14][15][16][17][18].…”

Section: Remarkmentioning

confidence: 99%

General love solution in the linear isotropic inhomogeneous theory of radius-dependent elasticity

Kashtalyan

Rushchitsky

2010

Int Appl Mech

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A general Love solution for the inhomogeneous linear isotropic theory of elasticity with the elastic constants dependent on the coordinate r is proposed. The axisymmetric case is analyzed and cylindrical coordinates are used. This is the fourth publication in the series on general solutions in the inhomogeneous theory of elasticity. The new results are promising for the modern theory of functionally graded materials. The key steps of deriving the Love solutions are described for further use of the derivation procedure. The procedure of generalizing the Love solutions to the inhomogeneous theory of elasticity is detailed. The results obtained are discussed Keywords: linear inhomogeneous isotropic elasticity, radially variable elastic parameters, general Love solution, functionally graded materialIntroduction. Cylindrical objects are surprisingly often found in nature, engineering, and even in the home. A classical natural example is the trunk of a tree (for example, bamboo). A bolt is another example from engineering; people always use something cylindrical in their everyday life, from an ordinary stick, a pencil, a water pipe to a rolling pin. When is service, all these objects are subject to various mechanical loads-they are stretched, compressed, bent, twisted, cut, etc. This is why the mechanics of materials and structures has always put emphasis on cylindrical bodies. Thousands of scientific publications study their mechanical behavior. As a rule, solid or hollow cylinders are assumed homogeneous in mechanical properties. According to real observations, however, cylindrical objects are highly inhomogeneous. Such inhomogeneity is often manifested as radial variation in density and other mechanical properties. It is appropriate to mention bamboo because it is denser and stronger on the outside surface, and its density and mechanical characteristics such as tensile and shear moduli decrease with distance from this surface. Not only natural materials are inhomogeneous, but technologically it seems to make sense to introduce artificially inhomogeneity into materials. The recently formulated and actively developing theory of functionally gradient materials (FGMs) focuses on artificial inhomogeneous materials and is the main consumer of achievements in the analysis of inhomogeneous materials.Remark 1. The following significant publications confirm that the FGM theory is successful and relevant: the pioneering studies [24][25][26]32], the recent review [6] in the world's best survey journal, the two comprehensive monographs [30,35], the typical papers [10,27,28,34] published in 2008.While the mechanics of homogeneous bodies may be considered a well-developed science, the mechanics of inhomogeneous bodies abounds in poorly studied fragments. This is especially true of the analytic mechanics of inhomogeneous bodies that develops rigorous mathematical models leading to differential or integral equations (which are solved by analytic methods).It is one of the fragments mentioned above that is examined here. The present p...

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“…It will be shown that wavelet [2,4,6,16,26] analysis is able to offer a more detailed and localized analysis so that we can single out symmetries and regular distribution on the wavelet coefficients [19,20,55,59]. The analysis of wavelet coefficients will show that DNA sequences and random sequences have, more or less, the same wavelet coefficients; however, if we analyze by wavelets the walks, on DNA compared with random walks, we can see that there exists some differences.…”

Section: Introductionmentioning

confidence: 99%

“…A very expedient method to analyze the influence of close base pairs (bp), by focusing on local average and jumps, is to compute the short (or window) wavelet transform [14][15][16][17][18]20]. It will be shown that wavelet [2,4,6,16,26] analysis is able to offer a more detailed and localized analysis so that we can single out symmetries and regular distribution on the wavelet coefficients [19,20,55,59].…”

Section: Introductionmentioning

confidence: 99%