Vibration Analysis of Multilink Manipulators Based on Timoshenko Beam Theory

Table 9

First ten natural frequencies (Hz); see Table 7; 𝜃_2,3=−45^∘,90^∘.

	Analytical solution			Finite Element solution
Mode	EB	𝑇	Δ )%)	ABAQUS R.6.6, B23	ABAQUS R.6.6, B22
1	6.1855	6.1701	0.25	6.1855	6.1701
2	25.596	25.222	1.48	25.596	25.222
3	59.147	56.594	4.51	59.147	56.594
4	208.91	199.87	4.52	208.91	199.87
5	309.93	280.47	10.5	309.93	280.47
6	398.82	368.74	8.16	398.82	368.74
7	534.23	496.22	7.66	534.23	496.22
8	647.83	571.65	13.3	647.83	571.65
9	762.02	702.55	8.46	762.02	702.55
10	890.88	802.90	11.0	890.88	802.90