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

Table 1

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

No.	(𝑛,𝑚)	Present	FEM	Mode shape
1	(0,0)	2.694	2.694	Torsional
2	(0,1)	2.742	2.742	Torsional
3	(1,1)	2.755	2.755	Flexural
4	(2,1)	2.800	2.800	Breathing
5	(3,1)	2.882	2.882	Breathing
6	(0,2)	2.885	2.885	Torsional
7	(1,2)	2.900	2.900	Flexural
8	(2,2)	2.948	2.948	Breathing
9	(4,1)	3.000	3.000	Breathing
10	(3,2)	3.030	3.030	Breathing
11	(0,3)	3.124	3.124	Torsional
12	(1,3)	3.140	3.140	Flexural
13	(4,2)	3.147	3.147	Breathing
14	(5,1)	3.153	3.153	Breathing
15	(2,3)	3.189	3.189	Breathing
16	(3,3)	3.271	3.271	Breathing
17	(5,2)	3.299	3.299	Breathing
18	(6,1)	3.341	3.341	Breathing