Vibration Analysis of Multilink Manipulators Based on Timoshenko Beam Theory

Table 11

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

	Analytical solution			Finite element solution
Mode	EB	𝑇	Δ )%)	ABAQUS R.6.6, B23	ABAQUS R.6.6, B22
1	8.8552	8.8322	0.26	8.8552	8.8322
2	17.817	17.533	1.62	17.817	17.533
3	50.836	48.777	4.22	50.836	48.777
4	218.16	207.77	5.00	218.16	207.77
5	318.97	290.70	9.72	318.97	290.70
6	426.96	366.30	16.6	426.96	366.30
7	568.09	541.76	4.86	568.09	541.76
8	641.25	588.19	9.02	641.25	588.19
9	760.88	708.35	7.42	760.88	708.35
10	875.15	790.17	10.8	875.15	790.17