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

Table 2

Natural nfrequencies 𝜔 [rd/s] for various mode shapes in the case of “no-slip-normal stress-free” boundary conditions.

No.	(𝑛,𝑚)	Present	FEM	Mode shape
1	(1,1)	0.889	0.889	Flexural
2	(0,0)	0.898	0.898	Torsional
3	(2,1)	0.908	0.908	Breathing
4	(0,1)	0.946	0.946	Torsional
5	(0,1)	0.951	0.951	Longitudinal
6	(3,1)	0.984	0.984	Breathing
7	(1,0)	0.990	0.990	Flexural
8	(1,2)	1.087	1.087	Flexural
9	(0,2)	1.089	1.089	Torsional
10	(2,2)	1.1070	1.1070	Breathing
11	(4,1)	1.1073	1.1073	Breathing
12	(1,1)	1.113	1.113	Flexural
13	(3,2)	1.171	1.171	Breathing
14	(2,0)	1.251	1.251	Breathing
15	(5,1)	1.271	1.271	Breathing
16	(4,2)	1.281	1.281	Breathing
17	(0,3)	1.327	1.327	Torsional
18	(1,3)	1.337	1.337	Flexural