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 quasi-electrostatic 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.