Characterization of beam stiffness matrix with embedded piezoelectric devices via generalized eigenvectors

Abstract

a b s t r a c tThe formulation described in this paper leads to the electro-elastic characterization of the sectional properties of elastic anisotropic prismatic beams with embedded piezoelectric devices. The related matrix is derived by analyzing a set of two-dimensional electro-elastic problems defined on the beam section. These problems allow to compute both the so-called beam de Saint-Venant's solutions and the beam deformation field induced by an electric potential difference imposed between the piezoelectric conductive laminae. The results are compared to those obtained with three dimensional finite element models.

Periodic controllers for vibration reduction using actively twisted blades

“…The section properties of the actively twisted blades, on the contrary, have to be computed. An accurate way to compute such properties, still accounting for three-dimensional elastic and piezoelectric constitutive laws, is the semi-analytical approach (19-21) . The three-dimensional continuum is decomposed into the one-dimensional domain of the beam model and the two-dimensional domain of the beam section.…”

Velocity feedback damping of piezo-actuated wings

“…[1,7,8]. Basically the same approach can be used for the characterization of composite beams with piezoelectric patches [9,10]. That said, simplified models such as the one used in this paper are still interesting, as they allow to get a better inside into the dependence of the elastic solution of the beam section parameters.…”

Multiphysics cross-section analysis of smart beams

“…Unlike the former methods following (Giavotto et al, 1983), in (Morandini et al, 2010), the solid beam equation was derived without a-priori separation of nodal displacement into reference section displacement and a wrapping field, and a numerical method was exploited to calculate the generalized eigenvectors corresponding to null eigenvalues of Hamiltonian matrix referring to the second order differential equation hierarchically rather than tightly depend on Hamiltonian matrix. Later the author extended this procedure to smart beams that contains piezoelectric devices (Brillante et al, 2015). Rooting in the symplectic method proposed in (Zhong et al, 1996), a comprehensive framework aiming to solve the de Saint-Venant problem was developed in (Bauchau and Han, 2014;Bauchau, 2015, 2016).…”