Effects of fiber ellipticity and orientation on dynamic stress concentrations in porous fiber-reinforced composites |
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Authors: | Seyyed M Hasheminejad Roozbeh Sanaei |
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Affiliation: | (1) Acoustics Research Laboratory, Department of Mechanical Engineering, Iran University of Science and Technology Narmak, Tehran, 16844, Iran |
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Abstract: | Interaction of time harmonic fast longitudinal and shear incident plane waves with an elliptical fiber embedded in a porous
elastic matrix is studied. The novel features of Biot dynamic theory of poroelasticity along with the classical method of
eigen-function expansion and the pertinent boundary conditions are employed to develop a closed form series solution involving
Mathieu and modified Mathieu functions of complex arguments. The complications arising due to the non-orthogonality of angular
Mathieu functions corresponding to distinct wave numbers in addition to the problems associated with appearance of additional
angular dependent terms in the boundary conditions are all avoided by expansion of the angular Mathieu functions in terms
of transcendental functions and subsequent integration, leading to a linear set of independent equations in terms of the unknown
scattering coefficients. A MATHEMATICA code is developed for computing the Mathieu functions in terms of complex Fourier coefficients
which are themselves calculated by numerically solving appropriate sets of eigen-systems. The analytical results are illustrated
with numerical examples in which an elastic fiber of elliptic cross section is insonified by a plane fast compressional or
shear wave at normal incidence. The effects of fiber cross sectional ellipticity, angle of incidence (fiber two-dimensional
orientation), and incident wave polarization (P, SV, SH) on dynamic stress concentrations are studied in a relatively wide
frequency range. Limiting cases are considered and fair agreements with well-known solutions are established. |
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Keywords: | Elliptic fiber Dynamic stress concentrations Elastic waves Porous matrix |
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