Figures P6.5a through P6.5e show direct, \(X_{1} / F_{1}\), and cross FRFs, \(X_{2} / F_{1}\) through \(X_{5} / F_{1}\), measured on a fixed-free beam. They were measured at the beam's free end and in \(20 \mathrm{~mm}\) increments toward its base; see Fig. 6.36. Determine the mode shape associated with the \(200 \mathrm{~Hz}\) natural frequency.

Fig. P6.5a Direct FRF \(X_{1} / F_{1}\).

Fig. P6.5b Cross FRF \(X_{2} / F_{1}\).

Fig. P6.5c Cross FRF \(X_{3} / F_{1}\).

Fig. P6.5d Cross FRF \(X_{4} / F_{1}\).

Fig. P6.5e Cross FRF \(X_{5} / F_{1}\).

Fig. P6.5f Coordinates for direct and cross FRF measurements.
When plotting the mode shape, normalize the free end response at coordinate \(x_{1}\) to 1 (this is normalizing the mode shape to \(x_{1}\) ) and show the relative amplitudes at the other coordinates \(x_{2}\) through \(x_{5}\). See Fig. P6.5f.

Transcribed Image Text:

x 10-6 -1 -2 Imag(X/F) (m/N) + 100 200 Frequency (Hz) 300 400