The constituent equations of piezoelectric heterogeneous bimorphs.

The electromechanical characteristics of a heterogeneous piezoelectric bender subjected to various electrical and mechanical boundary conditions are discussed based on the results of the free bender analysis. The mechanical boundary conditions considered are: a mechanical moment at the end of the bender, a force applied perpendicularly to the tip of the bender, and a uniform load applied over the entire length of the bender. The constituent equations of the bender under these electromechanical influences are derived by calculating the internal energy assuming thermodynamic equilibrium.