Forward coupling approach to model time periodic piezoelectric problems

Micro electro-mechanical systems (MEMS), such as piezoelectric loudspeakers are widely used for ultrasound applications. Designing advanced MEMS can be challenging, since nonlinear physical effects may have a significant impact. Piezoelectricity couples the mechanical and electrostatic field directly via material law, which is often hysteretic. In many applications, only steady-state solution of interest. The response to periodic forcing found in frequency domain with help harmonic balancing an alternating time scheme. For certain problems boundary conditions it might sufficient assume forward coupling, i.e. one first computes hysteretic then, use resulting electric polarization define piezoelectrically induced strains that excite system. There several ways incorporate into One way constant coupling tensor, Voigt's linear model. We phenomenological model linearly scaling tensor based on magnitude polarization. this model, we neglect depolarization under assumption prevailing stresses small strong applied enforces errors made by estimated compared direct used. result approach agrees well coupled results, needs less computational effort. Due system changes reflects influence electrostatics.