  This article presents a systematic methodology for modeling a class of
flexible multidimensional mechanical structures defined by linear elastic
relations that directly allows to obtain their infinite-dimensional
port-Hamiltonian representation. The approach is restricted to systems based on
a certain class of kinematic assumptions. However this class encompasses a wide
range of models currently available in the literature, such as
${\ell}$-dimensional elasticity models (with ${\ell}$ = 1,2,3), vibrating
strings, torsion in circular bars, classical beam and plate models, among
others. The methodology is based on Hamilton's principle for a continuum medium
which allows defining the energy variables of the port-Hamiltonian system, and
also on a generalization of the integration by parts theorem, which allows
characterizing the skew-adjoint differential operator and boundary inputs and
boundary outputs variables. To illustrate this method, the plate modeling
process based on Reddy's third-order shear deformation theory is presented as
an example. To the best of our knowledge, this is the first time that an
infinite-dimensional port-Hamiltonian representation of this system is
presented in the literature.
