1. Reference problem#

1.1. Geometry#

_images/100011200000298C0000094DFC99D4915D1C0F90.svg

Point masses:

\({m}_{{P}_{1}}={m}_{{P}_{2}}={m}_{{P}_{3}}=\dots \dots ={m}_{{P}_{8}}=m\)

Link stiffness:

\({k}_{A{P}_{1}}={k}_{{P}_{1}{P}_{2}}={k}_{{P}_{2}{P}_{3}}=\dots \dots ={k}_{{P}_{8}B}=k\)

Viscous damping:

\({c}_{A{P}_{1}}\mathrm{=}{c}_{{P}_{1}{P}_{2}}\mathrm{=}{c}_{{P}_{2}{P}_{3}}\mathrm{=}\dots \dots \mathrm{=}{c}_{{P}_{8}B}\mathrm{=}c\)

1.2. Material properties#

Linear elastic translation spring

\(k={10}^{5}N/m\)

Point mass

\(m=10\mathrm{kg}\)

Unidirectional viscous damping

\(c=50N/(m/s)\)

1.3. Boundary conditions and loads#

Boundary conditions: embedded \(A\) and \(B\) points (\(u=0\)).

Loading: force concentrated at point \({P}_{4}\) in the form of a niche:

1.4. Initial conditions#

For \(t=0\), in every way, \(u=0\) and \(\frac{\mathit{du}}{\mathit{dt}}\mathrm{=}0\).