An Improved Fourier Series Method for the Free Vibration Analysis of the Three-Dimensional Coupled Beams

Table 3

The natural frequency for coupled beams with various boundary condition f/Hz.

Boundary conditions	Mode					ANSYS	Errors/%
C-C	1	84.51	85.15	85.48	85.50	85.646	0.17
	2	235.15	235.26	235.61	236.10	237.19	0.46
	3	459.58	461.71	461.97	462.17	468.27	1.32
	4	773.66	773.72	773.98	774.11	781.46	0.95
	5	1159.23	1160.05	1160.86	1160.88	1181.4	1.77
	6	1641.33	1642.94	1643.21	1643.32	1674.1	1.87
	7	2220.49	2221.01	2225.91	2226.40	2266.7	1.81
	8	2917.79	2918.03	2923.76	2923.94	2967.7	1.50
S-S	1	37.40	37.57	37.70	37.73	37.75	0.06
	2	150.26	150.31	150.58	150.82	151.56	0.49
	3	339.04	339.12	339.40	339.53	343.15	1.07
	4	603.43	603.48	603.54	604.15	615.40	1.86
	5	962.25	962.49	962.78	962.88	972.43	0.99
	6	1384.01	1387.52	1387.63	1390.25	1419.70	2.12
	7	1937.93	1938.41	1944.44	1945.21	1963.90	0.96
	8	2569.58	2570.04	2583.40	2586.49	2613.10	1.03
F-F	1	84.54	85.32	85.46	85.49	85.56	0.09
	2	234.93	235.29	235.64	235.69	236.79	0.47
	3	462.03	462.03	462.30	462.36	467.15	1.04
	4	763.66	763.86	764.72	765.61	779.02	1.75
	5	1150.81	1151.17	1151.88	1152.57	1176.80	2.10
	6	1633.81	1633.82	1634.62	1634.73	1666.10	1.92
	7	2221.59	2221.78	2222.19	2222.43	2253.90	1.42
	8	2924.93	2925.99	2926.58	2926.61	2948.10	0.73