Acta Scientiarum Polonorum

Using the Rayleigh’s method, the first natural frequency and period corresponding to the first mode of transversal
vibrations for cone and wedge beams, having non-uniform cross-section, are calculated in this study.
Six different supporting schemes are considered. It has been assumed that the beams are made of a homogeneous
and elastic material and the deflection line of the beam axis during vibrations has the same shape as the
axis deflected by a static constant uniform continuous load. The values of frequencies, calculated according
to the presented procedure, have been compared to the results obtained in the Finite Element Method as well
as to the benchmark solutions given in the literature for the natural vibrations of Euler-Bernoulli’s beam. High
conformity of results, enough for engineering calculations, is concluded.