A formal method for improving the transient behaviour of a non-linear flexible link

Figures & data

Figure 1. Representation of the non-linear flexible link in the deformed and unstressed configurations.

Table 1. Variable correspondence for the eigenvalue problem [24]

Variable	Value
b
r ^2
s ^2
α
α′
β

Table 2. Natural frequencies of the beam

Mode number	Frequency (Hz)	Participation factor
0	0	1.5
1	1.340	−0.74069
2	3.6727	0.39966
3	7.6557	−0.27003
4	13.076	0.21184
5	19.920	−0.17149

Figure 2. Comparison between the response provided by and the FE models. (a) Input signal u(t). (b) The beam response y(t).

Figure 3. The control setup.

Figure 4. Tracking performances with feed-forward unit only. (a) The beam response y(t). (b) Tracking error.

Figure 5. Tracking performances with feed-back and feed-forward units. (a) The beam response y(t). (b) Tracking error.

Huang , T.C. 1961 . The effect of rotatory inertia and of shear deformation on the frequency and normal mode equations of uniform beams with simple end conditions . ASME J. Appl. Mech. , 28 : 579 – 584 .

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