1. Reference problem

1.1. Geometry

Length: \(L\mathrm{=}10\)

\((a\mathrm{=}\stackrel{ˉ}{\mathit{AD}}b\mathrm{=}\stackrel{ˉ}{\mathit{DB}})\)

\(\begin{array}{c}{m}_{e}\mathrm{=}\mathit{lmabda}\rho AL\mathrm{=}780\lambda \mathit{kg}\\ {k}_{e}\mathrm{=}{\pi }^{4}{m}_{e}\mathrm{=}780\lambda {\pi }^{4}N\mathrm{/}m\end{array}\)

Straight section:

air	\(A\mathrm{=}{1.10}^{\mathrm{-}2}{m}^{2}\)
moment of inertia	\(\mathit{Iz}\mathrm{=}3.9{10}^{\mathrm{-}6}{m}^{4}\)

3 cases to study:

\(\lambda =0.\)

\(\lambda =0.001\)

\(\lambda =0.01\)

Point coordinates (meters):

	\(A\)	\(B\)	\(C\)	\(D\)
\(x\)			2.5	2.5
\(y\)			\(\mathit{qcq}\mathrm{\ne }0\)

1.2. Material properties

\(E={2.10}^{11}\mathrm{Pa}\)

\(\rho =7800.\mathrm{kg}/{m}^{3}\)

1.3. Boundary conditions and loads

Point \(A\):	\(u=v=0.\)
Point \(B\):	\(v=0.\)
Point \(C\):	\(u=0.\) \(\theta =0.\) vertical slide

1.4. Initial conditions

Not applicable for modal analysis.