To find the fundamental frequency of vibration for a simply supported beam with a uniform mass.
Reference
Thomson, W.T., Vibration Theory and Applications, Prentice-Hall, Inc., 1965. Also compared with ANSYS® Finite Element Software.
Problem
Find the fundamental frequency, f, of a simply supported beam of uniform cross-section.
Model for dynamic beam no. 3
Comparison
Table 1. Comparison of results
Result Type |
Theory |
ANSYS
|
STAAD.Pro
|
Difference |
Frequency, f (Hz) |
28.766 |
28.767 |
28.7438 (Rayleigh) |
none |
28.761 (Eigensolution) |
none |
STAAD Output
CALCULATED FREQUENCIES FOR LOAD CASE 1
MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC)
1 28.761 0.03477
2 114.242 0.00875
3 242.560 0.00412
MODAL WEIGHT (MODAL MASS TIMES g) IN POUN GENERALIZED
MODE X Y Z WEIGHT
1 0.000000E+00 6.551152E+01 0.000000E+00 4.496000E+01
2 0.000000E+00 1.870800E-31 0.000000E+00 4.496000E+01
3 0.000000E+00 1.928479E+00 0.000000E+00 4.496000E+01
MASS PARTICIPATION FACTORS
MASS PARTICIPATION FACTORS IN PERCENT
--------------------------------------
MODE X Y Z SUMM-X SUMM-Y SUMM-Z
1 0.00 97.14 0.00 0.000 97.140 0.000
2 0.00 0.00 0.00 0.000 97.140 0.000
3 0.00 2.86 0.00 0.000 100.000 0.000
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* *
* RAYLEIGH FREQUENCY FOR LOADING 1 = 28.74379 CPS *
* MAX DEFLECTION = 0.01499 INCH GLO Y, AT JOINT 3 *
* *
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