The method of virtual power in continuum mechanics: Application to coupled fields

Modal coupling in one-dimensional electromechanical structured continua

“…2 the balance equations for a one-dimensional continua endowed with an affine electro-mechanical structure are derived following the ideas developed in [7]: the mechanical configuration of the beam and the charge distribution in the electric transmission lines are chosen as state variables of the system; the mechanical contact actions, the inertial actions and the electric potential drops are introduced as dual quantities of the generalized velocity and deformation fields; balance equations and boundary conditions are finally obtained by means of the principle of virtual power (see [8]). Section 3 mainly concerns the analytical study of the general linear differential operator of the problem within the partition of the state vector into its mechanical and electrical parts.…”

On some fundamental misunderstandings in the indeterminate couple stress model. A comment on recent papers of A.R. Hadjesfandiari and G.F. Dargush

“…Among higher gradient elasticity models [26,27,3,24,20,25] one of the very first models considered in the literature is the so called indeterminate couple stress model [9,28,42,19] in which the higher gradient contributions only enter through gradients of the continuum rotation, i.e. the total elastic energy can be written as W (∇u, ∇(∇u)) = W lin (sym∇u) + W curv (∇curl u).…”

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

“…In this paper, using the method of virtual power [2], we formulate a continuum description for a piezoelectromechanical truss beam which accounts for its modular structure, and use it to propose a new vibration damping technique. The typical module constituting the considered truss beam is composed: 1) by a pair of¯at rigid diaphragms connected by a number of elastic bars (some of which are piezoelectric) constrained to remain straight and 2) by an electric net connected also with the piezoelectric actuators.…”