Journal of Theoretical
and Applied Mechanics
56, 4, pp. 1163-1178, Warsaw 2018
DOI: 10.15632/jtam-pl.56.4.1163

Bending, buckling and free vibration of a beam with unsymmetrically varying mechanical properties

Krzysztof Magnucki, Jerzy Lewiński, Ewa Magdalena Magnucka-Blandzi, Piotr Kędzia
The subject of the paper is a beam with unsymmetrically varying mechanical properties in
the depth direction. The nonlinear hypothesis of plane cross section deformation is assumed.
Based on Hamilton’s principle, two differential equations of motion are obtained. The system
of equations is analytically solved with a view to analyse the bending, buckling and free
vibration problems of the beam. Moreover, the FEM model of the beam is developed and
deflections, critical axial forces and natural frequencies of the beam are calculated. The
results of these two methods are compared.
Keywords: FGM beam, mathematical modelling, numerical FEM calculations

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