1. Reference problem#
1.1. Geometry#
Point coordinates (in \(m\) ) :
\(A\) |
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\(x\) |
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\(y\) |
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\(z\) |
length of the beam: \(\mathit{AB}\mathrm{=}L\mathrm{=}10m\)
Point mass in \(C\): \({m}_{c}\mathrm{=}1000\mathit{kg}\)
Tubular section:
outside diameter |
\(\mathrm{de}=0.350m\) |
inner diameter |
\(\mathit{di}\mathrm{=}0.320m\) |
air |
\(A\mathrm{=}1.57865{10}^{\mathrm{-}2}{m}^{2}\) |
inertia |
\(\mathrm{Iy}=\mathrm{Iz}=2.21899{10}^{-4}{m}^{4}\) |
polar inertia |
\(\mathit{Ip}\mathrm{=}4.43798{10}^{\mathrm{-}4}{m}^{4}\) |
2 cases studied: |
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1.2. Material properties#
\(E\mathrm{=}2.1{10}^{11}\mathit{Pa}\)
\(\rho \mathrm{=}7800\mathit{kg}\mathrm{/}{m}^{3}\)
1.3. Boundary conditions and loads#
Embedded point \(A\): (\(u\mathrm{=}v\mathrm{=}w\mathrm{=}0\), \({\theta }_{x}\mathrm{=}{\theta }_{y}\mathrm{=}{\theta }_{z}\mathrm{=}0\)).
1.4. Initial conditions#
Not applicable for modal analysis.