Application of Adomian Modified Decomposition Method to Free Vibration Analysis of Rotating Beams

Table 1

The first five dimensionless natural frequencies 𝜆(n) for a clamped-free beam with different dimensionless rotating speeds U and offset lengths R.

R	U	Methods	Mode index n
			1	2	3	4	5
0	0	Present	3.516015	22.034492	61.697214	120.901916	199.859530
		[4]	3.5160	22.0345	61.6972	120.902	199.860
	1	Present	3.681647	22.181011	61.841763	121.050922	200.011574
		[3]	3.6816	22.1810	61.8418	—	—
	2	Present	4.137320	22.614922	62.273184	121.496695	200.466923
		[3]	4.1373	22.6149	62.2732	—	—
	3	Present	4.797279	23.320264	62.984967	122.235547	201.223245
		[3]	4.7973	23.3203	62.9850	—	—
	12	Present	13.170150	37.603112	79.614478	140.534354	220.536322
		[4]	13.1702	37.6031	79.6145	140.534	220.536
1	1	Present	3.888824	22.375014	62.043053	121.263205	200.230870
		[3]	3.8888	22.3750	62.0431	—	—
	2	Present	4.833689	23.366042	63.067548	122.339546	201.340072
		[3]	4.8337	23.3660	63.0675	—	—
	4	Present	7.475048	26.957262	66.986772	126.537325	205.706683
		[3]	7.475	26.9573	66.9868	—	—
	8	Present	13.507389	37.953793	80.529532	141.877971	222.165291
		[3]	13.5074	37.9538	80.5295	—	—
	15	Present	24.409202	61.437052	113.488866	182.695785	268.831067
		[1]	24.4092	61.4371	113.4889	—	—
2	1	Present	4.085335	22.567257	62.243575	121.475038	200.449876
		[3]	4.0853	22.5673	62.2436	—	—
	2	Present	5.439949	24.092373	63.850233	123.175402	202.208659
		[3]	5.4399	24.0924	63.8502	—	—
	4	Present	8.966379	29.380507	69.852259	129.712377	209.068207
		[3]	8.9664	29.3805	69.8523	—	—
3	1	Present	4.272659	22.757784	62.443336	121.686425	200.668594
		[3]	4.2727	22.7578	62.4433	—	—
	2	Present	5.983713	24.796124	64.621696	124.004411	203.072744
		[3]	5.9837	24.7961	64.6217	—	—
	4	Present	10.236798	31.604901	72.583135	132.794372	212.364626
		[1]	10.2368	31.6049	72.5831	—	—