1. Reference problem#

1.1. Geometry#

We consider a slender structure with a length \(0.25m\) and a section \(0.05m\ast 0.03m\).

_images/10000000000004F200000251BEE5495EA3EDE7FB.png

1.2. Material properties#

The material is isotropic elastic whose properties are:

  • Young’s module \(E=2.1{10}^{11}\mathit{Pa}\)

  • Poisson’s ratio \(\nu =0.3\)

  • Density \(\rho =7800\mathit{kg}/\mathit{m³}\)

  • Hysteretic damping \(\eta =0.01\)

1.3. Boundary conditions and loads#

We impose a zero displacement on the abscissa face \(y=0.25m\)

To calculate the harmonic response, a vertical point excitation of amplitude \((1+\mathrm{0.5j})/2\) is applied to the coordinate point \((0m\mathrm{,0}.1375m,0.03m)\).