1. Reference problem#

1.1. Geometry#

_images/10000201000002B1000000BA6A48693DAB1E1B1E.png

The figure above is taken from [bib1].

1.2. Material properties#

Beam:

Stiffness

\({k}_{1}={10}^{7}\) and \({k}_{2}=1\)

Masses

\({m}_{1}={m}_{2}={m}_{3}=1\)

1.3. Boundary conditions and loads#

The problem is unidirectional according to \(x\).

The displacement of the first mass is imposed \({u}_{1}=\mathrm{sin}({\omega }_{p}t)\) with \({\omega }_{p}=2.\).

1.4. Initial conditions#

The initial conditions are given by \({u}_{2}(0)={\dot{u}}_{2}(0)={u}_{3}(0)={\dot{u}}_{3}(0)=0\)