BENDING FREQUENCIES OF BEAMS, RODS, AND PIPES Revision P By Tom Irvine Email: tomirvine@aol.com April 19, 2011 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) f1 = Cantilever f2 = 6.268 f1 f3 = 17.456 f1 Cantilever with f1 = End Mass m Simply-Supported at both Ends fn = , n=1, 2, 3, …. (Pinned-Pinned) f1 = Free-Free f2 = 2.757 f1 f3 = 5.404 f1 Fixed-Fixed Same as Free-Free Fixed - Pinned f1 = where E is the modulus of elasticity I is the area moment of inertia L is the length
BENDING FREQUENCIES OF BEAMS, RODS, AND PIPES Revision P By Tom Irvine Email: tomirvine@aol.com April 19, 2011 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 = 6.268 f1 f3 = 17.456 f1 Cantilever with End Mass m f1 = Simply-Supported at both Ends (Pinned-Pinned) fn = , n=1, 2, 3, …. Free-Free f1 = f2 = 2.757 f1 f3 = 5.404 f1 Fixed-Fixed Same as Free-Free Fixed - Pinned f1 = where E is the modulus of elasticity I is the area moment of inertia L is the length