Interconnection of the Kirchhoff plate within the port-Hamiltonian framework

The Kirchhoff plate model is detailed by using a tensorial port-Hamiltonian (pH) formulation. A structure-preserving discretization of this model is then achieved by using the partitioned finite element (PFEM). This methodology easily accounts for the boundary variables and the finite-dimensional system can be interconnected to the surrounding environment in a simple and structured manner. The algebraic constraints to be considered are deduced from the boundary conditions, that may be homogeneous or defined by an interconnection with another pH system. The versatility of the proposed approach is assessed by means of numerical simulations. A first illustration considers a rectangular plate clamped on one side and interconnected to a rigid rod welded to the opposite side. A second example exploits the collocated output feature of pH systems to perform damping injection in a plate undergoing an external forcing. A stability proof is obtained by the application of the LaSalle's invariance principle.