Effective Young's moduli of quasilayered bars using bar resonance frequencies


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Abstract

Rectangular-bar specimens with nonhomogeneous (quasilayered) porosity distribution were prepared from an iron powder. Using these specimens, differences were observed in effective Young's modulus values determined experimentally by means of specimen flexural vibrations with bending in the plane of quasilayers and in the plane perpendicular to quasilayers. To account for these differences, general expressions for resonance frequencies of flexural vibrations of model quasilayered bars were derived in a theoretical way. The model quasilayered bar means a prismatic bar of rectangular cross section, with material Young's modulus varying continuously only along one of transverse directions. Substituting theoretical resonance frequencies, instead of experimentally measured ones, into the routine evaluation procedure of the dynamical resonant method, theoretical values of effective Young's modulus were calculated. In majority of theoretically investigated simple model examples with lowered modulus of surface regions the effective modulus determined by means of the frequency of sample flexural vibration perpendicular to layers is lower than the effective modulus determined by means of the vibration parallel to the layers. These theoretical results explain qualitatively the effective modulus differences obtained for our quasilayered samples in an experimental way.

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