Acta Scientiarum Polonorum

The Rayleigh’s method can be used to determine the first natural frequency of bars (beams or posts) with
non-uniform cross-section. The authors have analysed slender bars made of an elastic material and having the
shape of a solid of revolution: a curvilinear truncated cone and curvilinear conical pipe. It has been assumed
that the bar axis deflected during vibrations has a shape of a beam deflected by a static constant continuous
load. The Rayleigh’s method has been applied in the paper in aim to determine the first frequency of free
(transverse) vibrations of posts formed as a cantilever bars having the shape of solid and hollow curvilinear
truncated cone with the generatrix being a parabola which is convex in relation to the cone axis. The results
of calculations are very close to those obtained with finite element method (FEM).