Page 530 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Appen. D Normal Modes of Uniform Beams 517

TABLE D.6
CHARACTERISTIC FUNCTIONS AND DERIVATIVES
CLAMPED-CLAMPED BEAM
SECOND MODE

X 1 ^ , _ 1
1 <t>2 ß l d x ^ ß l d x ^
^ '
0.00 0.00000 0.00000 2.00000 -2.00000
0.04 0.07241 0.48557 1.43502 -1.99300
0.08 0.25958 0.81207 0.87658 -1.94824

0.12 0.51697 0.98325 0.33937 - 1.83960
0.16 0.80176 1.00789 -0.15633 - 1.65333
0.20 1.07449 0.90088 -0.58802 -1.38736
0.24 1.30078 0.68345 -0.93412 -1.05012
0.28 1.45308 0.38242 - 1.17673 -0.65879

0.32 1.51208 0.02894 - 1.30380 -0.23724
0.36 1.46765 -0.34350 - 1.31068 0.18649
0.40 1.31923 -0.70122 - 1.20092 0.58286
0.44 1.07550 - 1.01270 -0.98634 0.92349
0.48 0.75348 - 1.25090 -0.68631 1.18364

0.52 0.37700 - 1.39515 -0.32640 1.34442
0.56 -0.02536 - 1.43265 0.06348 1.39438
0.60 -0.42268 - 1.35944 0.45136 1.33056
0.64 -0.78413 - 1.18058 0.80569 1.15876
0.68 -1.08158 -0.90972 1.09776 0.89319

0.72 -1.29186 -0.56793 1.30395 0.55537
0.76 - 1.39858 -0.18205 1.40755 0.17245
0.80 - 1.39351 0.21752 1.40010 -0.22494
0.84 - 1.27726 0.59923 1.28198 -0.60506
0.88 -1.05919 0.93288 1.06244 -0.93759

0.92 -0.75676 1.19208 0.75879 -1.19604
0.96 -0.39406 1.35629 0.39504 - 1.35983
1.00 0.00000 1.41251 0.00000 -1.41592