Example - Modal Truncation

Problem

The given cantilevered beam ($//<![CDATA[ \begin{array}{l}l=0.8\end{array} //]]>$$//<![CDATA[ \begin{array}{l}\mathrm{m}\end{array} //]]>$) has a quadratic cross section ($//<![CDATA[ \begin{array}{l}a=0.01\end{array} //]]>$$//<![CDATA[ \begin{array}{l}\mathrm{m}\end{array} //]]>$) with $//<![CDATA[ \begin{array}{l}E=2.1\times 10^{11}\end{array} //]]>$$//<![CDATA[ \begin{array}{l}\mathrm{N/m^2}\end{array} //]]>$, $//<![CDATA[ \begin{array}{l}\nu=0.3\end{array} //]]>$, $//<![CDATA[ \begin{array}{l}\rho=7850\end{array} //]]>$$//<![CDATA[ \begin{array}{l}\mathrm{kg/m^3}\end{array} //]]>$. It is discretized using the Finite Element Method and excited at the tip with $//<![CDATA[ \begin{array}{l}F=1\end{array} //]]>$$//<![CDATA[ \begin{array}{l}\mathrm{N}\end{array} //]]>$ and of varying circular frequency ($//<![CDATA[ \begin{array}{l}\Omega=\frac{s}{\mathrm{i}}\end{array} //]]>$).

Solution

Considering more mode shapes, the frequency response of the system can be reproduced for a broader range