## W. Transient analysis of an in-vacuum Elastic Structure Driven by ExternalForces (TRA1)

In this analysis, known loads (forces F) are applied on the elastic structure. The systemof equations becomes:

where × and ×× denote the first and second time derivative, respectively. w0 is the pulsation at which the materials losses are defined. This differentialequation is solved by an iterative method, taking a constant time step D t. Three methods areimplemented: the Central Difference Method, the Newmark Method and the Wilson-q Method. The method, the time step and the method’sparameters are defined with the TRANSIENT command. Thecode computes the displacement field U for therequested time steps. The problem can be solved only in double precision.