Analysis of the deformational behaviour of a bimorph configuration with piezoelectric actuation

Abstract

The stimulation of controlled deformation in lightweight constructions by means of actuator units as an integrated part of the structure currently represents an attractive subject in engineering. A common design uses a piezoelectric film that is bonded to a shell component by an adhesive layer and induces a bending deformation in the structure. A simplified beam design has been used as a test set-up to characterize the actuator performance of a given system under practical conditions. The bimorph configuration consists of an actuator unit, the bonding adhesive and the substrate material from which the lateral bending deflection of the free end, induced by actuation of the piezoelectric film, is measured. An improved theoretical approach is presented that combines a comprehensive composite theory analysis of the bending with a detailed analytical approach for the gradual stress transfer from the edges of the piezoceramic induced by a deformational misfit between the layers. The results are validated by a finite element analysis of the system. They reveal a substantial influence of the assumptions for the transverse (width direction) state of deformation for which free bending appears to be the most realistic for the test geometry. The study is completed by an experimental analysis that investigates the influence of adhesive stiffness and layer thickness on the actuator performance of a system consisting of a steel substrate and a carbon fibre reinforced substrate and a prototypic PZT actuator module. The results are correlated to the model providing a confirmation of the essential trends.

Extension of the Euler–Bernoulli model of piezoelectric laminates to include 3D effects via a mixed approach

“…Some recent papers [26][27][28] pointed out that available beam models overlook some fundamental phenomena. In particular, the 1D theories are based either on a planestress or on a the plane-strain condition where the actual stress and strain states of a layered beam with thickness polarized ceramics are more complex.…”

On models of layered piezoelectric beams for passive vibration control

“…If essential boundary conditions are prescribed on u and w, the beam balance equations and natural boundary conditions(13) and the constitutive equations (19) lead to the complete set of equations for the beam model assuming hypotheses (3)(4)(5)(6) and the weak conditions on transversal stresses (8). When the kinematical hypotheses (3)(4) are assumed, different conditions on the distribution of the generalized stresses (T, D) lead to different constitutive coefficients for the beam constitutive equations (19).…”

“…In a beam model accounting for hypotheses (3)(4)(5)(6), the beam constitutive equations are derived from the three dimensional ones by assuming that, when the beam axis deforms, the cross sections remain rigid along the transversal direction e 2 (hypthesis 3). In order to enforce this constraint, transversal reactive stresses arise and (σ (2) i , ζ (2) i ) are in general different from zero.…”

“…The essential boundary conditions on u and ϕ and the kynematical compatibility equations are included in the definitions of the functional spaces V u and V ϕ . In a beam model accounting for hypotheses (3)(4)(5)(6), the distributions of the three dimensional state fields (u,ϕ, T, D) is uniquely determined by the axial fields (u, w, φ i ,σ…”

“…Although a number of accurate beam models have been presented (see [2] for a review), most of them do not describe the fully coupled electro-mechanical nature of the system (the piezoelectric elements are regarded merely as either actuators [3] or sensors [4]) and neglect transversal interactions between elastic and piezoelectric layers by assuming either pointwise vanishing transversal stress or strain (this issue is discussed in [5]). As a consequence, global properties as the equivalent piezoelectric capacitance are not correctly estimated.…”