Quantifying numerically forecast size effects in the free vibration of heterogeneous beams

Bahman Hassanati, Marcus Wheel

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This paper reports on the influence that a periodic microstructure has on the unconstrained flexural vibration of geometrically similar but differently sized heterogeneous beam samples. A numerical investigation was conducted by finite element analysis (FEA) incorporating the detailed heterogeneity to identify and quantify any effect of beam size on the transverse modal frequencies when the microstructural scale is comparable to the overall size. Finite element models of the macroscopic beam samples were created by firstly specifying microstructural scale unit cells containing a single void or inclusion using ANSYS Mechanical APDL and then repeatedly regenerating these as required. Four beam sizes consisting of one, two, three or four layers of unit cells were created while the length to depth aspect ratio was kept constant for all sizes. Void or inclusion volume fraction was also altered while keeping the homogenised mass and stiffness properties of each beam fixed. The influence of the beam boundary texture on the results was also investigated. The ANSYS results were compared to the analytical solution for a conventional Timoshenko beam and a nonlocal Timoshenko beam. Using the nonlocal Timoshenko analysis, the Eringen small length scale coefficients were estimated but found to be size dependent. Numerical predictions obtained from a novel control volume based finite element (CVFEM) procedure incorporating micropolar constitutive behaviour were therefore matched to the ANSYS results and thereby used to identify the two additional constitutive parameters featuring in planar micropolar elasticity theory, namely the characteristic length in bending and coupling number.
Original languageEnglish
Pages (from-to)298-311
Number of pages14
JournalInternational Journal of Mechanical Sciences
Early online date7 Jan 2019
Publication statusPublished - 1 Mar 2019
EventInternational Conference on Engineering Vibration - Sofia, Bulgaria
Duration: 4 Sep 20177 Sep 2017


  • finite element analysis
  • heterogeneous materials
  • Eringen's micropolar theory
  • free vibration
  • modal analysis
  • Beams' dynamics


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