An Improved Analytical Method for Vibration Analysis of Variable Section Beam

Table 4

Comparison of results from ADTM and the semianalytical method in the trapezoid concave beam case.

Segments	Order of iteration	ADTM			Semianalytical method
		ω1 (rad/s)	ω2 (rad/s)	ω3 (rad/s)	ω1 (rad/s)	ω2 (rad/s)	ω3 (rad/s)
	n = 6	73.5041	491.8213	1362.2632	78.0726	489.2727	1369.9777
	n = 8	74.1666	497.3769	1372.2632
	n = 10	74.2328	497.3795	1376.9487
	n = 6	74.7595	497.1698	1377.4637	76.4328	488.4799	1350.0823
	n = 8	74.2509	497.9426	1378.4681
	n = 10	74.2340	497.9771	1378.6030
	n = 6	74.6325	497.3214	1378.1042	75.5023	495.5865	1355.1130
	n = 8	74.2414	497.9611	1378.5935
	n = 10	74.2337	497.9768	1378.6141