BENDING FREQUENCIES OF BEAMS, RODS, AND …

1 BENDING FREQUENCIES OF BEAMS, rods , AND PIPES Revision S By Tom Irvine Email: November 20, 2012 _____ Introduction The fundamental FREQUENCIES for typical beam configurations are given in Table 1. Higher FREQUENCIES are given for selected configurations. Table 1. Fundamental BENDING FREQUENCIES Configuration Frequency (Hz) Cantilever f1 = f2 = f1 f3 = f1 Cantilever with End Mass m f1 = Simply-Supported at both Ends (Pinned-Pinned) fn = EILn212, n=1, 2, 3, .. Free-Free f1 = 0 (rigid-body mode) f2 = f3 = f1 f4 = f1 2 Table 1. Fundamental BENDING FREQUENCIES (continued) Configuration Frequency (Hz) Fixed-Fixed Same as free-free beam except there is no rigid-body mode for the fixed-fixed beam . Fixed - Pinned f1 = where E is the modulus of elasticity I is the area moment of inertia L is the length is the mass density (mass/length) P is the applied force Note that the free-free and fixed-fixed have the same formula.

2 Table 1. Fundamental Bending Frequencies (continued) Configuration Frequency (Hz) Fixed-Fixed Same as free-free beam except there is no rigid-body

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  Beam, Rods, Bending, Frequencies, Bending frequencies of beams

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