Continuum modelling of a beam-like latticed truss: Identification of the constitutive functions for the contact and inertial actions

Continuum modelling of piezoelectromechanical truss beams: an application to vibration damping

“…A modelling procedure for smart truss beams has been introduced essentially based on an identi®cation in power; both the mechanical truss beam and electric transmission line have been described by continuum models in which PEM constitutive equations are expressed in terms of modular properties (generalizing [4] with method suggested in [2]). …”

“…In [4] truss beams are modelled using a continuum description generalizing the standard Bernoulli-Navier theory. The main result of the cited paper, based on the identi®cation of the mechanical power on the re®ned level with that on the continuum one, allows for the determination of the constitutive equations for the contact and inertial actions explicitly in terms of the mechanical properties in the module.…”

“…The coarse model apt to describe our electromechanical system is a one-dimensional continuum endowed with structure: we assume as model for the mechanical part the standard Euclidean structure used in the theory of Bernoulli-Navier beam (see for a complete discussion [4]), and for the electric part the standard model from the theory of the continuous electrical transmission line. Finally, the electromechanical coupling will be modelled assuming that every used constitutive equation depends on all the electro-mechanical state parameters listed below.…”

“…Therefore, the second one (see for instance [4], [5], [6], [9], [10]) has been proposed: the displacement and rotation ®elds describe a homogenized average displacement and rotation of the generic constituent module.…”

“…This identi®cation procedure was used by [4] in a purely mechanical contest, and has shown its validity in the study of technical problems [9], [10]. Moreover, the results expounded in [2] clearly indicate that, when dealing with the electromechanical coupling phenomena, the most useful tool is given by the method of virtual power: we are con®dent that the identities (32) allow among the possible continuum models the determination of that one which better approximates the discrete re®ned model.…”