Analysis and Comparison of Port-Hamiltonian Formulations for Field Theories - demonstrated by means of the Mindlin plate

TL;DR

This paper compares different port-Hamiltonian formulations for field theories, using the Mindlin plate as an example, highlighting their derivations from variational principles and boundary conditions.

Contribution

It provides a detailed comparison of Stokes-Dirac and bundle-structure-based port-Hamiltonian formulations for systems described by PDEs, exemplified by the Mindlin plate.

Findings

Stokes-Dirac structures effectively model boundary interactions.

Bundle-structure approaches align with variational principles.

Comparison reveals advantages of each formulation in specific contexts.

Abstract

This paper focuses on the port-Hamiltonian formulation of systems described by partial differential equations. Based on a variational principle we derive the equations of motion as well as the boundary conditions in the well-known Lagrangian framework. Then it is of interest to reformulate the equations of motion in a port-Hamiltonian setting, where we compare the approach based on Stokes-Dirac structures to a Hamiltonian setting that makes use of the involved bundle structure similar to the one on which the variational approach is based. We will use the Mindlin plate, a distributed parameter system with spatial domain of dimension two, as a running example.