Three-Dimensional Investigation of the Stokes Eigenmodes in Hollow Circular Cylinder

Table 4

Coupled natural nfrequencies 𝜔 [rd/s] for various mode shapes.

No.	(𝑛,𝑚)	Present	FEM	Mode shape
1	(0,1)	0.535	0.535	Torsional
2	(1,1)	0.566	0.566	Flexural
3	(2,1)	0.645	0.645	Breathing
4	(0,2)	0.678	7.145	Torsional
5	(1,2)	0.699	0.699	Flexural
6	(2,0)	0.702	0.702	Breathing
7	(3,1)	0.749	0.749	Breathing
8	(2,2)	0.760	0.760	Breathing
9	(0,1)	0.780	0.780	Longitudinal
10	(1,1)	0.813	0.813	Flexural
11	(3,2)	0.854	0.854	Breathing
12	(4,1)	0.872	0.872	Breathing
13	(0,3)	0.917	0.917	Torsional
14	(3,0)	0.924	0.924	Breathing
15	(1,3)	0.935	0.935	Flexural
16	(4,2)	0.978	0.978	Breathing
17	(2,3)	0.988	0.988	Breathing
18	(5,1)	1.019	1.019	Breathing