A variational principle for the equations of viscopiezoelectricity

The three-dimensional equations of linear viscopiezoelectricity and an accompanying electromechanical energy theorem are deduced, by the quasielectrostatic approximation, from the equations of viscoelectromagnetism and a generalized Poynting´s theorem, respectively. For a viscopiezoelectric solid of volume V and bounding surface S, the internal energy, kinetic energy, and electric enthalpy densities as well as the variation of work done over S and the variation of energy dissipation in V are defined. A variational principle in terms of the defined functions is presented. It is shown that, from the principle, the equations of viscopiezoelectricity in V and the natural boundary conditions on S are obtained.