Vibration Analysis of Multilink Manipulators Based on Timoshenko Beam Theory

Table 4

First ten natural frequencies (Hz); two-link manipulator; (𝐿₁/ℎ=33.33, 𝐿_𝑇/ℎ=69.33).

	𝜃2 = 0°					𝜃2 = 45°					𝜃2 = 90°
Mode	EB ^†	EB ^‡	T	Δ^†	Δ^‡	EB ^†	EB ^‡	T	Δ^†	Δ^‡	EB ^†	EB ^‡	T	Δ^†	Δ^‡
1	10.931	10.931	10.929	0.02	0.02	11.675	11.675	11.673	0.02	0.02	14.363	14.363	14.360	0.02	0.02
2	63.399	63.399	63.334	0.10	0.10	51.705	51.716	51.653	0.10	0.12	38.348	38.353	38.309	0.10	0.11
3	190.90	190.90	190.43	0.25	0.25	186.38	186.49	185.95	0.23	0.29	185.36	185.54	184.94	0.23	0.32
4	356.79	356.79	355.14	0.46	0.46	322.97	323.92	321.40	0.49	0.78	303.66	303.97	302.12	0.51	0.61
5	602.80	602.80	598.84	0.66	0.66	587.48	589.46	583.77	0.64	0.97	582.51	584.21	578.87	0.63	0.92
6	882.58	882.58	873.79	1.0	1.0	831.00	839.66	822.29	1.1	2.1	817.71	819.88	808.78	1.1	1.4
7	1162.5	Axial	1162.5	0.0	—	1162.3	1178.9	1149.2	1.1	2.6	1162.3	1168.2	1148.7	1.2	1.7
8	1205.5	1205.5	1190.7	1.2	1.2	1466.9	1534.0	1448.4	1.3	5.9	1505.2	1519.1	1482.2	1.6	2.5
9	1571.6	1571.6	1548.7	1.5	1.5	1713.9	1953.4	1699.7	0.8	15	1901.2	1937.2	1867.8	1.8	3.7
10	1998.1	1998.1	1953.3	2.3	2.3	2012.6	2331.0	1973.0	2.0	18	2017.8	2321.7	1998.5	0.97	16

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