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

Table 4

The first five dimensionless natural frequencies 𝜆(n) for the beam with different dimensionless offset lengths R and rotational spring stiffness 𝐾_𝐿1 and 𝐾_𝑅1 when the translational spring stiffness 𝐾_𝐿0=𝐾_𝑅0=1×10⁹ and the dimensionless offset length R = 3.

U	𝐾𝐿1	𝐾𝑅1	Mode index 𝑛
			1	2	3	4	5
1	0	0	10.728125	40.379864	89.736290	158.826493	247.654314
	10	20	18.722928	52.557379	104.894264	176.148714	266.614189
	100	200	22.240871	60.660903	118.406571	195.403654	291.714050
2	0	0	12.901808	42.950832	92.403230	161.529064	250.373747
	10	20	20.251238	54.708735	107.278904	178.653087	269.187647
	100	200	23.660610	62.669418	120.641412	197.764434	294.153770
3	0	0	15.741169	46.861509	96.655335	165.918965	254.831087
	10	20	22.506559	58.074886	111.115686	182.735812	273.412896
	100	200	25.806448	65.847359	124.257999	201.625455	298.167186
4	0	0	18.856444	51.730723	102.251676	171.841633	260.921080
	10	20	25.233188	62.406770	116.227213	188.272249	279.199963
	100	200	28.463584	69.993005	129.113530	206.884873	303.679326