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

Table 3

The first five dimensionless natural frequencies 𝜆(n) for a clamped-simply supported 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	15.418206	49.964862	104.247696	178.269729	272.030971
		[3]	15.4182	49.9649	104.2477	—	—
	1	Present	15.512970	50.093465	104.388569	178.416902	272.181974
		[3]	15.5130	50.0935	104.3886	—	—
	2	Present	15.793333	50.476967	104.809884	178.857595	272.634416
		[3]	15.7933	50.4770	104.8099	—	—
	4	Present	16.861201	51.977798	106.475988	180.608162	274.435777
		[3]	16.8612	51.9778	106.4760	—	—
1	1	Present	15.650431	50.276757	104.591434	178.630496	272.402329
		[3]	15.6504	50.2768	104.5914	—	—
	2	Present	16.324050	51.198754	105.614686	179.707690	273.512869
		[3]	16.3240	51.1988	105.6147	—	—
	4	Present	18.739775	54.700871	109.594297	183.942227	277.903130
		[3]	18.7398	54.7009	109.5943	—	—
2	1	Present	15.786476	50.459230	104.793819	178.843781	272.622470
		[3]	15.7865	50.4592	104.7938	—	—
	2	Present	16.834938	51.908185	106.412044	180.552930	274.387932
		[3]	16.8349	51.9082	106.4120	—	—
	4	Present	20.412962	57.264050	112.606262	187.203776	281.318676
		[3]	20.4130	57.2641	112.6063	—	—
3	1	Present	15.921144	50.640895	104.995728	179.056759	272.842396
		[3]	15.9211	50.6409	104.9957	—	—
	2	Present	17.327885	52.605804	107.202130	181.393382	275.259636
		[3]	17.3279	52.6058	107.2021	—	—
	4	Present	21.932288	59.690141	115.520706	190.396605	284.684295
		[3]	21.9323	59.6901	115.5207	—	—