Free Transverse Vibration Analysis of Axially Functionally Graded Tapered Euler-Bernoulli Beams through Spline Finite Point Method

Table 8

Nondimensional transverse natural frequencies for axially FG tapered beam; boundary condition: P-P.

		0		0.2		0.4		0.6		0.8
		0	SFPM	9.0286	36.3718	9.0599	36.3418	9.0867	36.3153	9.0994	36.2969	9.0685	36.2769
Reference [3]	9.0285		36.3715	9.0599	36.3415	9.0867	36.3151	9.0994	36.2966	9.0685	36.2766
0.2	SFPM	8.1341	32.5236	8.1462	32.5123	8.1498	32.5079	8.1336	32.5164	8.0646	32.5326
	Reference [3]	8.1341	32.5234	8.1462	32.5121	8.1498	32.5077	8.1336	32.5161	8.0646	32.5323
0.4	SFPM	7.1531	28.4747	7.1455	28.4822	7.1254	28.5003	7.0794	28.5370	6.9703	28.5928
	Reference [3]	7.1531	28.4744	7.1455	28.4819	7.1254	28.5001	7.0794	28.5367	6.9703	28.5924
0.6	SFPM	6.0357	24.1101	6.0082	24.1371	5.9638	24.1791	5.8868	24.2469	5.7351	24.3497
	Reference [3]	6.0357	24.1098	6.0082	24.1367	5.9637	24.1787	5.8868	24.2465	5.7351	24.3491
0.8	SFPM	4.6520	19.1315	4.6046	19.1804	4.5355	19.2510	4.4264	19.3591	4.2284	19.5302
	Reference [3]	4.6520	19.1304	4.6045	19.1792	4.5354	19.2496	4.4263	19.3576	4.2281	19.5281