1. Reference problem#

1.1. Geometry#

_images/100011200000298C0000094DD1650C0A20C4841F.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#

Point \(A\) and \(B\): built-in (\(u=0\))

Acceleration spectrum at supports \(\ddot{u}(f,a)\) standardized to \(1.m{s}^{-2}\)

Points \(A\) and \(B\): \(\ddot{u}=\ddot{u}(f,a)\)

_images/100017B60000228500000E93E040EBECA411D228.svg