Abstract
Our paper deals with a mixed initial-boundary value problem in thermoelasticity of piezoelectric bodies with dipolar structure. It is considered the general case of a thermoelastic body which inhomogeneous and also anisotropic and we add the effect of piezoelectricity. We take into account the main equations and basic conditions of a temperature rate dependent theory which predict the waves propagation with a finite speed. Using some middle conditions imposed on the boundary conditions and initial data, we obtain that our mixed problem admits one solution. A generalized form of the Hamilton's principle is obtained to cover this context.