In this paper, the effect of different profile variations on vibrational properties of non-uniform beams made of graded
porous materials is studied. Timoshenko beam theory is used to present the mathematical formulation of the problem
including shear deformation, rotary inertia, non-uniformity of the cross-section, and graded porosity of the beam
material. Three different variations of porosities through the thickness direction are introduced. The beam is assumed
with the clamped condition at both ends. To obtain a numerical solution, finite element formulations of the governing
equations are presented. The non-uniform beam is approximated by another beam consisting of n elements with
piecewise constant thickness to keep the volume and hence the total mass unchanged for each element. The beam
response has been calculated for the first three modes of vibration. In each case, the results for different types of
thickness variation and porosity distribution are compared with those obtained for a beam with uniform thickness. The
effects of non-uniformity, taper parameters, and porosity distribution on the frequencies and mode shapes are investigated. It is observed that a considerable change in frequencies and mode shapes can be achieved by selection of different thickness variation and porosity distribution.