FEM: $4$ Eigen modes

The $2$D frame shown in Figure $3$ represents a two$-$story building fixed at its base. The stiffness of the horizontal

elements $($blue elements representing the decks$)$ is infinitely greater than the stiffness of the vertical ones.

Consider the connections deck$-$element to be perfectly rigid.

Assemble the global Stiffness matrix $K$;

Assemble the global Mass matrix $M$;

Determine the frequencies and the eigen$-$vectors associated only to the horizontal degrees of freedom;

Draw a sketch of the eigen$-$shapes.

Elements type $1$:

Square cross section $6565cm$

Length $600cm$

Concrete $C\frac{25}{30}$

$E=31$GPa

$v=0\mathrm{.}2$

$=2500k\frac{g}{m^3}$

Elements type $2$:

Square cross section $4040cm$

Length $300cm$

Concrete C$25/30$

$E=31$GPa

$v=0\mathrm{.}2$

$=2500k\frac{g}{m^3}$