Vibration Characteristics of Ring-Stiffened Functionally Graded Circular Cylindrical Shells

Table 5

Variation of natural frequencies against circumferential wave number n, type I FG cylindrical shell with nickel ring stiffeners (𝑚=1, ℎ/𝑅=0.002, 𝐿/𝑅=20, 𝑑/𝑏=1.334).

𝑛	𝑁^𝑆𝑆=0	𝑁^𝑁=0	𝑁=0.5	𝑁=0.7	𝑁=1	𝑁=2	𝑁=5	𝑁=15	𝑁=30
1	26.831	25.864	26.497	26.421	26.335	26.176	26.018	25.922	25.894
2	30.397	29.289	30.014	29.926	29.828	29.645	29.466	29.355	29.323
3	47.192	45.494	46.603	46.468	46.317	46.037	45.762	45.594	45.545
4	82.416	79.471	81.393	81.158	80.896	80.411	79.935	79.643	79.559
5	131.10	126.42	129.47	129.10	128.68	127.91	127.16	126.69	126.56
6	191.52	184.69	189.14	188.60	187.99	186.86	185.76	185.09	184.89
7	263.21	253.82	259.59	259.20	258.37	256.82	255.30	254.37	254.11
8	346.02	333.69	341.74	340.75	339.66	337.62	335.63	334.41	334.o6
9	439.88	424.20	434.43	433.18	431.79	429.21	426.68	425.12	424.68
10	544.74	525.34	538.01	536.46	534.73	531.53	528.40	526.48	525.93