Vibration Analysis of Multilink Manipulators Based on Timoshenko Beam Theory

Table 5

First ten natural frequencies (Hz); two-link manipulator; (𝐿₁/ℎ=16.67, 𝐿_𝑇/ℎ=34.67).

	𝜃2 = 0°					𝜃2 = 45°					𝜃2 = 90°
Mode	EB ^†	EB ^‡	T	Δ^†	Δ^‡	EB ^†	EB ^‡	T	Δ^†	Δ^‡	EB ^†	EB ^‡	T	Δ^†	Δ^‡
1	22.771	22.771	22.756	0.07	0.07	24.349	24.350	24.333	0.07	0.07	30.107	30.110	30.085	0.07	0.08
2	135.87	135.87	135.28	0.44	0.44	109.58	109.68	109.12	0.42	0.51	80.514	80.557	80.178	0.42	0.47
3	395.12	395.12	391.11	1.0	1.0	386.31	387.26	382.59	0.97	1.2	385.43	387.00	381.78	0.96	1.4
4	750.85	750.85	736.83	1.9	1.9	656.26	666.58	643.75	1.9	3.5	615.82	618.74	603.33	2.1	2.6
5	1206.2	axial	1206.2	0.0	—	1203.8	1233.3	1174.8	2.5	5.0	1203.7	1224.6	1173.5	2.6	4.4
6	1261.0	1261.0	1226.1	2.8	2.8	1540.5	1729.7	1496.8	2.9	16	1650.5	1679.6	1579.7	4.5	6.3
7	1855.0	1855.0	1779.4	4.2	4.2	1965.7	2505.1	1918.4	2.5	31	2117.0	2484.5	2083.4	1.6	19
8	2570.1	2570.1	2440.4	5.3	5.3	2583.3	3263.2	2460.9	5.0	33	2604.7	3220.2	2504.8	4.0	29
9	3393.1	3393.1	3176.0	6.8	6.8	3267.1	4163.0	3080.3	6.1	35	3177.2	4128.4	2973.4	6.9	39
10	3567.6	axial	3567.6	0.0	—	3782.3	5096.1	3701.1	2.2	38	3959.8	5066.6	3788.9	4.5	34

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