The applicability of the effective medium theory to the dynamics of cellular beams

Banerjee, S. and Bhaskar, A. (2009) The applicability of the effective medium theory to the dynamics of cellular beams. International Journal of Mechanical Sciences, 51, (8), 598-608. (doi:10.1016/j.ijmecsci.2009.06.001).


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The applicability and the limitations of the effective medium assumption forthe dynamics of cellular beams are studied. Beams made of uniform triangular and regular hexagonal cellsare analysed. The natural frequencies and modal distributions are calculated using the detailed finite element model of the cellular networks are compared with those predicted basedon equivalent homogenous media of the same overall size and shape. It is observed that, for low mode number, a cellular beam behaves as a continuum, provided the cell size is significantly smaller than the external dimensions of the beam. Due to different deformation mechanisms triangular cells show frequencies independent of area fraction whereas hexagonal cells show this dependence clearly. As the wave length starts to become of the order of the heterogeneity, the continuum behaviour begins to break down. With the increase in mode number, cellular beams exhibit inherent flexibility with a progressive increase in their modal densities as compared to those of a homogeneous continuum. The modal density increases further when the cell walls start to resonate. During resonance, an abrupt rise in the modal density is observed for the triangular cellsas the cell walls start deforming in the flexural mode instead of the axial mode. In contrast, for hexagonal cells, the predominant mode of cell wall deformationis always flexural.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1016/j.ijmecsci.2009.06.001
ISSNs: 0020-7403 (print)
Keywords: cellular solids, structural vibration
Subjects: T Technology > TJ Mechanical engineering and machinery
Divisions : University Structure - Pre August 2011 > School of Engineering Sciences > Computational Engineering and Design
ePrint ID: 69940
Accepted Date and Publication Date:
August 2009Published
12 June 2008Made publicly available
Date Deposited: 05 Jan 2010
Last Modified: 31 Mar 2016 12:58

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