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Analysis of free vibrations of cantilever bars with parabolically variable cross-sections using the Rayleigh's method

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Szlachetka O., Jaworski J., Chalecki M.

Acta Scientiarum Polonorum. Architectura

2017

tom 16

nr 4

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).

Ograniczanie wyników

1 Acta Scientiarum Polonorum. Architectura

1 Chalecki M.

1 Jaworski J.

1 Szlachetka O.

1 2017

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Analysis of free vibrations of cantilever bars with parabolically variable cross-sections using the Rayleigh's method