On the Validity of Flat-Plate Finite Strip Approximation of Circular Cylindrical Shells

Table 2

(a) Comparison of exact flat-plate finite strip results with analytical results [19] for the first 25 circumferential modes and longitudinal mode 𝑠=1 (𝑅/𝑡 = 20, 𝐿/𝑅 = 10, 𝐸=1, 𝜌=1, and 𝜇=0.3). (b) Comparison of exact flat-plate finite strip results with analytical results [19] for the first 25 circumferential modes and longitudinal mode 𝑠=1 (𝑅/𝑡 = 20, 𝐿/𝑅 = 2, 𝐸=1, 𝜌=1, and 𝜇=0.3).

(a)  

Mode	Reference [19]			Finite strip			% Error
	Root 1	Root 2	Root 3	Root 1	Root 2	Root 3	Root 1	Root 2	Root 3
1	0.003843	0.477163	2.248342	0.003839	0.477163	2.248369	−0.0935	−4𝐸−05	0.0012
2	0.0022	1.602974	5.57898	0.00218	1.602975	5.579023	−0.9331	4𝐸−05	0.0008
3	0.013578	3.513777	11.09063	0.013552	3.513777	11.09068	−0.1928	2𝐸−05	0.0004
4	0.04908	6.200527	18.79498	0.049052	6.200528	18.79503	−0.0582	6𝐸−06	0.0003
5	0.127713	9.659199	28.69627	0.127683	9.659199	28.69632	−0.0233	3𝐸−06	0.0002
6	0.274152	13.88832	40.79602	0.274122	13.88832	40.79607	−0.0111	2𝐸−06	0.0001
7	0.518586	18.8873	55.09486	0.518555	18.8873	55.09492	−0.006	9𝐸−07	1𝐸−04
8	0.896697	24.65585	71.59311	0.896665	24.65585	71.59316	−0.0035	5𝐸−07	8𝐸−05
9	1.449656	31.19384	90.29093	1.449624	31.19384	90.29098	−0.0022	3𝐸−07	6𝐸−05
10	2.224125	38.5012	111.1884	2.224092	38.5012	111.1885	−0.0015	2𝐸−07	5𝐸−05
11	3.272254	46.57787	134.2857	3.272221	46.57787	134.2858	−0.001	2𝐸−07	4𝐸−05
12	4.651681	55.42383	159.5829	4.651648	55.42383	159.583	−0.0007	1𝐸−07	4𝐸−05
13	6.425534	65.03907	187.08	6.425501	65.03907	187.0801	−0.0005	8𝐸−08	3𝐸−05
14	8.662426	75.42357	216.7772	8.662392	75.42357	216.7772	−0.0004	6𝐸−08	3𝐸−05
15	11.43646	86.57732	248.6744	11.43642	86.57732	248.6745	−0.0003	5𝐸−08	2𝐸−05
16	14.82722	98.50032	282.7718	14.82718	98.50032	282.7719	−0.0002	4𝐸−08	2𝐸−05
17	18.91978	111.1926	319.0696	18.91974	111.1926	319.0696	−0.0002	3𝐸−08	2𝐸−05
18	23.8047	124.6541	357.5677	23.80466	124.6541	357.5678	−0.0002	3𝐸−08	2𝐸−05
19	29.57802	138.8848	398.2663	29.57798	138.8848	398.2664	−0.0001	2𝐸−08	2𝐸−05
20	36.34127	153.8848	441.1656	36.34124	153.8848	441.1656	−0.0001	2𝐸−08	1𝐸−05
21	44.20147	169.654	486.2656	44.20143	169.654	486.2657	−9𝐸−05	2𝐸−08	1𝐸−05
22	53.27109	186.1924	533.5665	53.27105	186.1924	533.5666	−7𝐸−05	1𝐸−08	1𝐸−05
23	63.66811	203.5001	583.0685	63.66807	203.5001	583.0686	−6𝐸−05	1𝐸−08	1𝐸−05
24	75.51597	221.577	634.7718	75.51593	221.577	634.7719	−5𝐸−05	1𝐸−08	1𝐸−05
25	88.94361	240.4231	688.6765	88.94357	240.4231	688.6766	−5𝐸−05	9𝐸−09	9𝐸−06

(b)  

Mode	Reference [19]			Finite strip			% Error
	Root 1	Root 2	Root 3	Root 1	Root 2	Root 3	Root 1	Root 2	Root 3
1	0.361681	1.71255	4.171796	0.36151	1.712972	4.172137	−0.0471	0.0247	0.0082
2	0.123212	2.823816	7.757059	0.122714	2.824171	7.757795	−0.4045	0.0126	0.0095
3	0.063523	4.651966	13.42785	0.06297	4.652242	13.42882	−0.8711	0.0059	0.0072
4	0.081789	7.273435	21.22231	0.081068	7.273642	21.22342	−0.8823	0.0028	0.0052
5	0.161011	10.68842	31.17646	0.160256	10.68858	31.17765	−0.4689	0.0015	0.0038
6	0.315485	14.88867	43.30898	0.314711	14.88879	43.31023	−0.2454	0.0008	0.0029
7	0.572148	19.86809	57.62925	0.57136	19.86818	57.63054	−0.1376	0.0005	0.0022
8	0.965526	25.62299	74.14215	0.964728	25.62306	74.14347	−0.0826	0.0003	0.0018
9	1.536331	32.15115	92.85039	1.535524	32.15121	92.85173	−0.0525	0.0002	0.0014
10	2.331023	39.45124	113.7556	2.330207	39.4513	113.7569	−0.035	0.0001	0.0012
11	3.401653	47.52242	136.8586	3.400828	47.52247	136.86	−0.0243	9𝐸−05	0.001
12	4.805812	56.36415	162.1602	4.804977	56.36419	162.1616	−0.0174	7𝐸−05	0.0009
13	6.606596	65.97606	189.6609	6.605752	65.9761	189.6623	−0.0128	5𝐸−05	0.0007
14	8.872605	76.35792	219.3608	8.87175	76.35795	219.3622	−0.0096	4𝐸−05	0.0006
15	11.67793	87.50955	251.2603	11.67706	87.50958	251.2618	−0.0074	3𝐸−05	0.0006
16	15.10215	99.43084	285.3596	15.10127	99.43086	285.3611	−0.0058	2𝐸−05	0.0005
17	19.23033	112.1217	321.6589	19.22944	112.1217	321.6604	−0.0046	2𝐸−05	0.0005
18	24.15303	125.582	360.1584	24.15213	125.5821	360.1599	−0.0037	2𝐸−05	0.0004
19	29.96629	139.8118	400.8581	29.96537	139.8119	400.8596	−0.0031	1𝐸−05	0.0004
20	36.77163	154.811	443.7584	36.7707	154.8111	443.7599	−0.0025	1𝐸−05	0.0003
21	44.67606	170.5796	488.8592	44.67511	170.5797	488.8607	−0.0021	1𝐸−05	0.0003
22	53.79206	187.1176	536.1609	53.79109	187.1176	536.1624	−0.0018	8𝐸−06	0.0003
23	64.2376	204.4249	585.6635	64.23661	204.425	585.6651	−0.0015	7𝐸−06	0.0003
24	76.13612	222.5016	637.3673	76.13511	222.5016	637.3689	−0.0013	6𝐸−06	0.0002
25	89.61654	241.3476	691.2726	89.61551	241.3476	691.2742	−0.0011	6𝐸−06	0.0002