Page 523 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

510 Normal Modes of Uniform Beams Appen. D

D.1 CLAMPED-CLAMPED BEAM
n ß j i ß j y
1 4.7300 22.3733 1.0000
2 7.8532 61.6728 2.7565
3 10.9956 120.9034 5.4039

D.2 FREE-FREE BEAM
The natural frequencies of the free-free beam are equal to those of the clam ped-
clam ped beam. The characteristic functions of the free-free beam are related to
those of the clam ped-clam ped beam as follows:

free-free clam ped-d
=
4>n 4>:
=
4>'n c
4>"n 4>n
C = <t>'n

D.3 CLAMPED-FREE BEAM

n ß J ( ß j y
1 1.8751 3.5160 1.0000
2 4.6941 22.0345 6.2669
3 7.8548 61.6972 17.5475

D.4 CLAMPED-PINNED BEAM

n ß n L ( ß j y
1 3.9266 15.4182 1.0000
2 7.0686 49.9645 3.2406
3 10.2101 104.2477 6.7613