An Improved Analytical Method for Vibration Analysis of Variable Section Beam

Table 1

Comparison of results from ADTM and ADM in the uniform beam case.

Frequency	Order of iteration	ADM	ADTM		FEM result	Theoretical result
			(p = 2)	(p = 3)
ω1	n = 1	79.0341	78.2747	78.1178	77.7096	78.0726
	n = 2	78.0743	78.0727	78.0726
	n = 3	78.0726	78.0726	78.0726
Ω2	n = 1	417.6492	454.8542	492.8109	487.1444	489.2727
	n = 2	456.9292	488.6935	489.2750
	n = 3	488.3615	489.2715	489.2727
Ω3	n = 1	—	1290.2621	1309.2891	1362.8536	1369.9775
	n = 2	—	1350.1889	1365.6756
	n = 3	1095.9032	1369.6495	1369.9640