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First natural frequency of multi-segment floor joists with variable cross section

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Chalecki M. , Jaworski J. , Szlachetka O.

tom Vol. 28, No. 4

526--538

The Rayleigh’s method can be used to determine the first natural frequency of beams with variable cross-section. The authors analyse multi-segment simply supported beams, symmetrical with respect to their midpoint, having a constant width and variable height. The beams consist generally of five segments. 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.