FREE VIBRATION OF CANTILEVERS – HOLLOW OR MASSIVE TWO-PART SOLIDS OF REVOLUTION

Abstract

The Rayleigh’s method can be used to determine the first natural frequency of bars (beams or posts) with variable cross-section. The authors analyze slender cantilever bars - solids of revolution, made of an elastic material. The bars consist of two parts, each having the shape of massive or hollow curvilinear truncated cone, with the internal and external generatrices being a straight line or curve (parabola, exponential line). It has been assumed that the neutral bar axis deflected during vibrations has a shape of a beam deflected by a static uniform load. The calculations were made in MATHEMATICA environment and their results are very close to those obtained with FEM.