1. Reference problem#

1.1. Geometry#

We consider the system represented by the diagram below:

_images/100000000000028000000180A97838A70A6D00BD.png

Point masses:

\({m}_{1}\) and \({m}_{2}\)

Link stiffness:

\({k}_{1}\) and \({k}_{2}\)

Hysteretic damping:

\({\eta }_{1}\) and \({\eta }_{2}\)

1.2. Material properties#

Linear elastic translation spring

\({K}_{1}\mathrm{=}28000N\mathrm{/}m\)

\({K}_{2}\mathrm{=}28000N\mathrm{/}m\)

Point mass

\({M}_{1}\mathrm{=}10\mathit{kg}\)

\({M}_{2}\mathrm{=}5\mathit{kg}\)

Hysteretic damping

\({\eta }_{1}\mathrm{=}0.1\)

\({\eta }_{2}\mathrm{=}0.0\)

1.3. Boundary conditions and loads#

Boundary conditions:

Points \(A\), \(B\), \(C\) embedded in \(\mathit{DY}\) and \(\mathit{DZ}\)

Points \(A\): recessed \((\mathit{DX}\mathrm{=}0)\).

Loading: Sinusoidal concentrated force with variable frequency at point \(C\)

\(\begin{array}{c}{F}_{{x}_{4}}\mathrm{=}{F}_{0}\mathrm{sin}\Omega t\\ \Omega \mathrm{=}2\pi f0\mathit{Hz}\mathrm{\le }f\mathrm{\le }21.0543\mathit{Hz}\\ {F}_{0}\mathrm{=}\mathit{constante}\mathrm{=}\mathrm{100N}\end{array}\)

1.4. Initial conditions#

Not applicable to the study of the permanent harmonic regime.