For the tapered beam sketched in Figure 8.17 undergoing transverse vibration, estimate the first two natural frequencies using the Rayleigh-Ritz procedure. Assume a trial function of the form \(\mathcal{Y}(x)=\) \(c_{1} x^{2}+c_{2} x^{3}\) and beam properties,

\[ m(x)=ho A(x)=ho H(1-x / L) \]

and

\[ E I(x)=(E / 12)[H(1-x / L)]^{3} \]

Transcribed Image Text:

X EA(x), m(x)- y H L Figure 8.17: Tapered beam in longitudinal vibration.