Vibration Characteristics of Ring-Stiffened Functionally Graded Circular Cylindrical Shells

Table 4

(a) Comparison of natural frequencies (Hz) for type I FG cylindrical shell with simply-supported boundary conditions. (𝑚=1, 𝐿/𝑅=20, 𝑅/ℎ=500)

𝑛	Naeem et al. [19]			Present
	𝑁=0.5	𝑁=1	𝑁=15	𝑁=0.5	𝑁=1	𝑁=15
1	13.321	13.211	12.933	13.321	13.211	12.932
2	4.5162	4.4794	4.3829	4.5164	4.4796	4.3830
3	4.1903	4.1562	4.0646	4.1909	4.1564	4.0641
4	7.0967	7.0379	6.8851	7.0976	7.0381	6.8836
5	11.335	11.241	10.998	11.336	11.241	10.996
6	16.594	16.455	16.101	16.595	16.455	16.097
7	22.826	22.635	22.148	22.828	22.635	22.143
8	30.023	29.771	29.132	30.025	29.771	29.125
9	38.181	37.862	37.048	38.185	37.862	37.039
10	47.301	46.905	45.897	47.305	46.905	45.886

(b) Comparison of natural frequencies (Hz) for type II FG cylindrical shell with simply-supported boundary conditions. (𝑚=1, 𝐿/𝑅=20, 𝑅/ℎ=500)

𝑛	Naeem et al. [19]			Present
	𝑁=0.5	𝑁=1	𝑁=15	𝑁=0.5	𝑁=1	𝑁=15
1	13.103	13.211	13.505	13.103	13.211	13.505
2	4.4382	4.4742	4.5759	4.4378	4.4739	4.5757
3	4.1152	4.1486	4.2451	4.1144	4.1481	4.2454
4	6.9754	7.0330	7.1943	6.9744	7.0327	7.1956
5	11.145	11.238	11.494	11.143	11.237	11.496
6	16.317	16.453	16.453	16.315	16.452	16.830
7	22.447	22.633	23.147	22.444	22.633	23.152
8	29.524	29.770	30.446	29.521	29.770	30.453
9	37.548	37.861	38.720	37.544	37.861	38.729
10	46.517	46.904	47.968	46.511	46.904	47.979