Modeling of Piezoelectric Structures- A Hamiltonian Approach

This contribution is dedicated to the geometric description of infinite-dimensional port Hamiltonian systems with in- and output operators. The introduced in- and output maps are defined by linear differential operators. It is shown, that this extension leads in general to additional boundary conditions. The derived theory is applied to the piezoelectric field equations in order to obtain their port Hamiltonian representation. Here the electrical field strength is assumed to act as distributed input. Furthermore it is shown, that distributed inputs, that are in the kernel of the input map act similarly on the system as certain boundary inputs.