Find the fundamental frequency of longitudinal vibration of the tapered bar shown in Fig. 8.41, using Rayleigh's method with the mode shape

\[U(x)=c_{1} \sin \frac{\pi x}{2 l}\]

The mass per unit length is given by

\[m(x)=2 m_{0}\left(1-\frac{x}{l}\right)\]

and the stiffness by

\[E A(x)=2 E A_{0}\left(1-\frac{x}{l}\right)\]

Transcribed Image Text:

m(x), EA(x) FIGURE 8.41 Tapered bar. X