A General Fourier Formulation for In-Plane and Out-of-Plane Vibration Analysis of Curved Beams

Table 1

Improved Fourier series convergence and accuracy (unit Hz).

Improved Fourier series cutoff number M					Reference [5]	FEM
10	12	14	16	18
81.07	81.07	81.07	81.07	81.07	81.13	81.00
219.16	219.16	219.16	219.16	219.16	—	218.94
227.12	227.12	227.12	227.12	227.12	227.67	226.90
370.16	370.15	370.15	370.15	370.15	—	369.83
447.97	447.97	447.97	447.97	447.97	450.19	447.45
583.87	583.87	583.87	583.87	583.87	—	583.70
730.12	730.10	730.10	730.10	730.10	—	729.09
741.05	741.03	741.02	741.02	741.02	747.19	740.01
1104.85	1104.80	1104.79	1104.79	1104.79	1118.60	1103.00
1112.73	1112.68	1112.67	1112.67	1112.67	—	1110.90
1488.30	1487.86	1487.79	1487.79	1487.79	—	1485.60
1538.19	1537.55	1537.46	1537.45	1537.45	1564.40	1534.60
1666.75	1666.58	1666.56	1666.56	1666.56	—	1665.90
2036.73	2035.23	2035.01	2035.01	2035.00	—	2030.70
2038.73	2037.23	2037.01	2037.00	2037.00	2084.60	2032.60
2611.44	2603.23	2601.22	2601.18	2601.17	2611.60	2594.80
2643.64	2605.82	2603.83	2603.78	2603.78	—	2597.50
2646.42	2611.44	2611.44	2611.44	2611.44	2679.10	2611.40
3109.45	3097.49	3096.86	3096.84	3096.84	—	3095.30
3562.38	3231.21	3227.65	3227.57	3227.55	3347.90	3218.60