1. Reference problem#

1.1. Geometry#

_images/100011200000298C0000094D11B1F3F93BC4BD8E.svg

Point masses:

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

Link stiffness:

\({k}_{\mathrm{AP1}}={k}_{\mathrm{P1P2}}={k}_{\mathrm{P2P3}}=\dots \dots ={k}_{\mathrm{P8B}}=k\)

Viscous damping:

\({c}_{\mathrm{AP1}}={c}_{\mathrm{P1P2}}={c}_{\mathrm{P2P3}}=\dots \dots ={c}_{\mathrm{P8B}}=c\)

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:

Points \(A\) and \(B\): recessed \((u=0)\).

Loading: Sinusoidal concentrated force with variable frequency at point \({P}_{4}\)

Point \({P}_{4}\)

\({F}_{{x}_{4}}\mathrm{=}{F}_{0}\mathrm{sin}\Omega t\)

\(\Omega \mathrm{=}2\pi f\) \(5\mathrm{Hz}\le f\le 40\mathrm{Hz}\)

\({F}_{0}\mathrm{=}\mathit{constante}\mathrm{=}\mathrm{1N}\)

Other points \({P}_{i}\)

\({f}_{{x}_{i}}=0\)

1.4. Initial conditions#

Not applicable to the study of the permanent harmonic regime.