Vibration Analysis of Multilink Manipulators Based on Timoshenko Beam Theory

Table 6

First ten natural frequencies (Hz); two-link manipulator; (𝐿₁/ℎ=8.33, 𝐿_𝑇/ℎ=17.33).

	𝜃2 = 0°					𝜃2 = 45°					𝜃2 = 90°
Mode	EB ^†	EB ^‡	T	Δ^†	Δ^‡	EB ^†	EB ^‡	T	Δ^†	Δ^‡	EB ^†	EB ^‡	T	Δ^†	Δ^‡
1	46.540	46.540	46.417	0.26	0.26	49.796	49.801	49.661	0.27	0.28	61.736	61.762	61.550	0.30	0.34
2	282.42	282.42	277.52	1.8	1.8	225.58	226.53	221.88	1.6	2.1	165.04	165.42	162.32	1.6	1.9
3	805.90	805.90	773.81	4.1	4.1	782.63	791.77	753.86	3.6	5.0	779.33	793.67	751.29	3.5	5.6
4	1229.9	axial	1229.9	0.0	—	1223.5	1356.8	1154.6	5.1	18	1221.2	1250.7	1132.4	7.1	10
5	1551.2	1551.2	1443.1	7.5	7.5	1841.4	2536.3	1780.6	2.4	42	2057.5	2522.5	1981.3	3.0	27
6	2589.5	2589.5	2326.6	11	11	2621.1	3515.9	2362.7	7.3	49	2737.4	3400.6	2515.9	6.5	35
7	3653.2	none	3294.0	11	—	3444.1	5198.8	3109.7	6.4	67	3271.8	5161.4	2887.0	7.5	79
8	3828.9	3828.9	3653.2	4.8	4.8	4124.3	6708.3	3906.9	3.2	72	4345.4	6603.4	4141.6	3.1	59
9	5336.2	5336.2	4425.3	21	21	5253.1	8728.3	4403.5	9.7	98	5165.3	8663.7	4372.5	9.2	98
10	6146.9	none	5590.4	10	—	6316.7	10799	5461.0	7.9	98	6548.3	10716	5305.6	12	102

^†Through the model by di Castri et al. [12]. ^‡Through implementation of the model by Milford and Asokanthan [11].