Damping matrix

In applied mathematics, a damping matrix is a matrix corresponding to any of certain systems of linear ordinary differential equations.

A damping matrix is defined as follows. If the system has n degrees of freedom u_n and is under application of m damping forces.

Each force can be expressed as follows:

$f_{{Di}}=c_{{i1}}{\dot {u_{1}}}+c_{{i2}}{\dot {u_{2}}}+\cdots +c_{{in}}{\dot {u_{n}}}=\sum _{{j=1}}^{n}c_{{i,j}}{\dot {u_{j}}}\,$

It yields in matrix form;

$F_{D}=C{\dot {U}}\,$

where C is the damping matrix composed by the damping coefficients:

$C=(c_{{i,j}})_{{1\leq i\leq n,1\leq j\leq m}}\,$

References

• (fr) Mechanics of structures and seisms