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

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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

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

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Mechanical Vibrations

ISBN: 9780134361925

6th Edition

Authors: Singiresu S Rao

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Question Posted: May 04, 2024 05:32 AM

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

Question:

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

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Mechanical Vibrations

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