Page 528 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Appen. D Normal Modes of Uniform Beams 515

TABLE D.4
CHARACTERISTIC FUNCTIONS AND DERIVATIVES
CLAMPED-CLAMPED BEAM
SECOND MODE

X 1 ^ 1 ^^2 _ 1

1 <#>2 ^ ß l dx ß i dx^ ' ß i dx^
0.00 0.00000 0.00000 2.00000 -2.03693
0.04 0.03301 0.33962 1.61764 -2.03483
0.08 0.12305 0.60754 1.23660 -2.02097

0.12 0.25670 0.80728 0.86004 -1.98590
0.16 0.42070 0.93108 0.49261 -1.92267
0.20 0.60211 0.99020 0.14007 -1.82682
0.24 0.78852 0.98502 -0.19123 -1.69625
0.28 0.96827 0.92013 -0.49475 -1.53113

0.32 1.13068 0.80136 -0.76419 -1.33373
0.36 1.26626 0.63565 -0.99384 -1.10821
0.40 1.36694 0.43094 - 1.17895 -0.86040
0.44 1.42619 0.19593 -1.31600 -0.59748
0.48 1.43920 -0.06012 -1.40289 -0.32772

0.52 1.40289 -0.32772 - 1.43920 -0.06012
0.56 1.31600 -0.59748 - 1.42619 0.19593
0.60 1.17895 -0.86040 -1.36694 0.43094
0.64 0.99384 -1.10821 -1.26626 0.63565
0.68 0.76419 - 1.33373 -1.13068 0.80136

0.72 0.49475 - 1.53113 -0.96827 0.92013
0.76 0.19123 -1.69625 -0.78852 0.98502
0.80 -0.14007 - 1.82682 -0.60211 0.99020
0.84 -0.49261 -1.92267 -0.42070 0.93108
0.88 -0.86004 - 1.98590 -0.25670 0.80428

0.92 -1.23660 -2.02097 -0.12305 0.60754
0.96 -1.61764 -2.03483 -0.03301 0.33962
1.00 -2.00000 -2.03693 0.00000 0.00000