1. Reference problem#

1.1. Geometry#

_images/100016B20000165300000C3284D2CC84EAAE1335.svg

Point coordinates (in \(m\) ) :

\(A\)

\(B\)

\(C\)

\(x\)

\(y\)

\(\mathit{yc}\)

\(z\)

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:

  1. \(\mathrm{yc}=0.\)

  1. \(\mathit{yc}\mathrm{=}1.m\)

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.