## 1 Introduction  
**Subject matter, main purpose, and practical application value of this work. ** In the last few decades, the development of control algorithms for nonlinear complex systems has been a productive field of research. To this end, the paradigm of port-Hamiltonian systems (**PHS**) currently provides an elegant and efficient (unifying mathematical) framework to model, couple, and control various complex multiphysics systems such as mechanical, electrical, and thermal systems, while taking into account the effects of energy flows, whether inside the bulk or via the boundary (or _port_) of the interconnected PHS (which, by definition, are each open). The purpose of this paper is merely to apply the PHS formalism to [PERSON]'s (**NR**) shell model in linear elasticity in order to prepare the theoretical background required for the numerical coupling (or interconnection) with an acoustic fluid model and the different types of interactions that can arise among them. Our interest in applying this PHS formalism is also motivated by the fact that its possibilities and limits in structural and continuum mechanics are not yet fully elucidated. Additionally, the proper Hamiltonian/Lagrangian variational principles (or laws of Varying Action) for systematically generating the canonical PHS equations still need to be better understood from this perspective in order to adopt the most-efficient computational methods. **Brief review of the current state-of-the-art of the PHS formalism. ** A basic exposition of what port-Hamiltonian systems are can be found in [1], and the progress in the last twenty years since the pioneering work [2] is given in [3]. In essence, the underlying framework of PHS is based on the variational theory combining the Hamilton(-D'Alembert-Lagrange) principle with the Fenchel-Legendre (Legendre-Young) transformations of the Lagrangian potential. The PHS formalism highlights the ([PERSON]-)Dirac mathematical structure, which guarantees a global (power) balance equation for the Hamiltonian functional [1; 4; 5; 6; 7]. This framework is currently undergoing an enormous progressive evolution for continuous (or again, distributed-parameter) systems with importance for civil, aeronautical, and astronautical engineering, though still less developed compared to the discrete (or lumped-parameter) systems. Indeed, based on the symplectic geometry formalism [5], PHS for distributed-parameter systems were initially introduced by [PERSON] and [PERSON] [2], with the aim to combine the advantages of network theory to model complex systems with those of the geometric Hamiltonian analysis of physical systems to derive better control algorithms based on energy considerations [8; 9]. While going progressively from simple systems to more complex ones, including continuous systems or distributed-parameter systems, recent publications have proven the possibility of applying this formulation to structural models of beams [10; 11; 12; 13] and plates [14; 15; 16; 17; 18] or to unidimensional acoustic fluids [19] and ideal isentropic fluids [20], among other examples. Notably, related to this current work, writing the dynamic equations of plates as a PHS was carried out, for instance, in [14] for thick plates represented by the Reissner-Mindlin model and in [15] for thin plates represented by the Kirchhoff-Love model. Regarding fluid mechanics, some light can be shed on applications involving Navier-Stokes equations, both in [21; 22], just to cite a few works. Besides, as far as multiphysics coupling is concerned, the PHS framework has been proven to be very powerful and well suited to this aim: quite a few examples can be found in [23] for the Allen-Cahn equationand heat, in [24] for elasticity and heat, in [12; 25] for a liquid sloshing in a moving container, in [26] for heat waves, and [27] for thermomagneto-hydrodynamics coupling in tokamaks.