## Y. Transient analysis of an in-vacuum Electrically Driven Piezoelectric or Magnetostrictive Structure (TRA3)

In this analysis, known displacements U, electric potentials f and currents I are applied on the piezoelectric ormagnetostrictive structure. The system of equations becomes:

where × and ×× denotethe 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, theelectrical potential F, the reducedmagnetic potential f and the currents inmagnetic sources I for the requested timesteps, together with reactions to prescribed displacements. The problem can besolved only in double precision.

Important notice: the Central Difference Method algorithm does not accept losses for electric or magnetic degrees of freedom, only for mechanical degrees of freedom. This means that the matrices [K"F], [K"uf], [K"uI], [K"FF], [K"fI], [K"ff] and [K"II] must be zero.