A Unified Spectro-Geometric-Ritz Method for Vibration Analysis of Open and Closed Shells with Arbitrary Boundary Conditions

Table 11

Comparison of the first four frequency parameters for an open spherical shell subjected to various boundary conditions.

Boundary conditions	Ref. [38]				Present
	1	2	3	4	1	2	3	4
F-F-F-F	13.46	19.56	25.99	34.85	13.40	19.44	25.77	34.59
SD-F-F-F	6.629	15.34	25.40	27.08	6.582	15.32	25.28	26.76
C-F-F-F	3.754	8.492	21.53	28.26	4.060	8.702	21.58	27.95
SD-SD-F-F	3.367	17.32	20.79	39.71	3.340	17.20	20.61	39.40
C-SD-F-F	5.566	19.35	25.47	44.64	5.753	19.19	25.38	44.47
C-C-F-F	7.894	23.90	27.92	49.27	8.172	23.79	27.75	49.02
SD-F-SD-F	10.07	16.10	38.89	39.59	10.03	15.98	38.43	39.54
C-F-SD-F	15.63	21.68	41.84	49.95	15.76	24.71	41.48	49.83
SD-SD-SD-F	12.22	30.50	41.85	60.14	12.15	30.15	41.77	59.80
C-SD-SD-F	18.01	33.76	52.05	65.24	18.13	33.56	51.89	64.57
C-C-SD-F	18.68	38.58	52.19	72.13	18.69	38.35	52.24	71.80
C-F-C-F	25.30	28.67	45.53	61.34	26.06	30.82	45.31	61.20
SD-C-SD-F	12.95	35.75	42.26	64.09	12.86	35.32	42.17	63.59
C-SD-C-F	26.34	38.07	63.08	68.01	27.07	38.02	63.23	67.31
C-C-C-F	26.62	42.71	63.56	77.64	27.68	42.53	63.53	76.98
SD-SD-SD-SD	23.70	51.04	51.04	80.02	23.45	50.33	50.82	79.36
C-SD-SD-SD	27.32	53.32	60.17	87.13	27.23	52.72	60.00	86.59
C-C-SD-SD	30.64	61.88	62.36	93.66	30.51	61.36	62.02	93.30
C-SD-C-SD	32.47	55.41	70.37	95.06	32.60	55.78	70.43	95.00
C-C-C-SD	35.51	64.76	72.13	101.40	35.63	64.13	72.15	101.09
C-C-C-C	40.26	74.17	74.43	108.66	40.49	73.77	74.42	108.32