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