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

Table 2

The first five dimensionless natural frequencies 𝜆(n) for a clamped-clamped 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	22.373285	61.672823	120.903392	1.998594481274627	2.985555379664196
		[3]	22.3733	61.6728	120.9034	—	—
	1	Present	22.465244	61.801647	121.044116	200.006494	298.706437
		[3]	22.4652	61.8016	121.0441	—	—
	2	Present	22.738323	62.186191	121.465166	200.446898	299.158620
		[3]	22.7383	62.1862	121.4652	—	—
	4	Present	23.791502	63.696418	123.132818	202.197641	300.959712
		[3]	23.7915	63.6964	123.1328	—	—
1	1	Present	22.601469	61.987491	121.248139	200.220805	298.927273
		[3]	22.6015	61.9875	121.2481	—	—
	2	Present	23.269013	62.919871	122.275462	201.300307	300.039256
		[3]	23.2690	62.9199	122.2755	—	—
	4	Present	25.721997	66.488904	126.285440	205.551660	304.439765
		[3]	25.7220	66.4889	126.2854	—	—
2	1	Present	22.736642	62.172635	121.451744	200.434838	299.147913
		[3]	22.7366	62.1726	121.4517	—	—
	2	Present	23.784414	63.642885	123.079231	202.149350	300.916791
		[3]	23.7844	63.6429	123.0792	—	—
	4	Present	27.477304	69.138595	129.343258	208.839952	307.872284
		[3]	27.4773	69.1386	129.3433	—	—
3	1	Present	22.870783	62.3570858594266	121.6549319912815	200.6485958268648	299.3683574772145
		[3]	22.8708	62.3571	121.6549	—	—
	2	Present	24.285626	64.355627	123.876600	202.994081	301.791251
		[3]	24.2856	64.3556	123.8766	—	—
	4	Present	29.093946	71.663126	132.313123	212.065591	311.259430
		[3]	29.0939	71.6631	132.3131	—	—