Partitioned finite element method for the Mindlin plate as a port-Hamiltonian system

Abstract

The port-Hamiltonian framework allows for a structured representation and interconnection of distributed parameter systems described by Partial Differential Equations (PDE)from different realms. Here, the Mindlin-Reissner model of a thick plate is presented in a tensorial formulation. Taking into account collocated boundary control and observation gives rise to an infinite-dimensional port-Hamiltonian system (pHs). The Partitioned Finite Element Method (PFEM), already presented in our previous work, allows obtaining a structure-preserving finite-dimensional port-Hamiltonian system, and accounting for boundary control in a straightforward manner. In order to illustrate the flexibility of PFEM, both types of boundary controls can be dealt with: either through forces and momenta, or through kinematic variables. The discrete model is easily implementable by using the FEniCS platform. Computation of eigenfrequencies and vibration modes, together with time-domain simulation results demonstrate the consistency of the proposed approach.