MODAL ANALYSIS RESPONSE OF MDOFS MODELS(uncoupled models ) to arbitrary loadsWe consider that the external forces act after the degree of freedom (translation)

Known: M, K, C;

(normalized modal matrix);

One uses the modal transformation :

(1)

Equation of motion:

(2)

Using (1) determine : (3)

Where :

=[]

The system equation is:

Or for i mode of vibration:

Where

Sollution is:

The value of displacement is :

Particular case: harmonical external forces

The sollution of displacements is:

Where:

The displacement will be:

Taken into account the unnormalized forms of vibration we have: