Vibration Analysis of Euler-Bernoulli Beams Partially Immersed in a Viscous Fluid

Table 1

The first 24 coupled natural angular frequencies of the partially immersed beams in a viscous fluid. Comparison of frequency between FEM and present method.

Order	Present	FEM	Difference
1	4.90	4.86	0.82
2	18.18	17.91	1.50
3	20.26	20.01	1.24
4	21.11	20.86	1.19
5	24.68	24.50	0.73
6	30.48	30.20	0.92
7	31.59	31.44	0.47
8	39.24	38.91	0.84
9	44.68	44.51	0.38
10	47.65	47.31	0.71
11	50.20	49.72	0.96
12	54.68	54.02	1.22
13	56.10	55.33	1.39
14	61.47	61.25	0.35
15	61.90	61.36	0.88
16	64.57	64.15	0.65
17	67.29	66.72	0.85
18	73.47	72.99	0.65
19	79.63	79.21	0.53
20	80.06	79.42	0.80
21	85.67	85.41	0.30
22	87.58	87.09	0.56
23	91.33	90.85	0.52
24	97.44	97.10	0.35