A piezoelectric multilamina shell FE developed to model thin walled structures with piezoelectric fibre composites polarized with interdigitated electrodes (PFCPIE) is proposed in this paper. A new scheme for the interpolation of the electric field is presented. The electric field in each lamina lies parallel to the lamina plane and coincides with the poling direction. Each piezoelectric lamina admits an arbitrary poling direction. Based on Reissner–Mindlin assumptions and a multilaminate approach, the element employs a single layer assumption for the mechanical displacements and a layerwise constant electric potential. An MITC strategy is used to avoid shear locking. Two static examples are presented. The first is a cantilever piezoactuated beam and the second a single cell closed box beam with piezoelectric actuators. The results obtained for the cantilever beam with the present formulation are compared with those obtained with native ABAQUS plane stress elements and an analytical solution. For the closed box beam the numerical results were compared with experimental results from the literature. Very encouraging results are obtained in both cases. Finally, for the piezoactuated closed box beam, the FE model is used to obtain a state space model (SS). Based on the SS model, the design of the control system and the assessment of the system performance are carried out. Important systems characteristics are captured by the model, i.e. attenuation levels, frequency response and control voltage levels. This reveals that the proposed FE can be used to model and assess structural behaviour in a relatively simple and efficient way.

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A thin walled single-cell box beam with piezoelectric fiber composite patches bonded to its skin is analyzed. Patch fibers are oriented at ±45 • with respect to the beam's longitudinal axis. Two types of connections are used to supply control signals to the patches. In the first case, upper and lower patches are connected in pairs. The second case involves independent control of each patch.A FE approach is used to model the host structure and the actuators. The analysis is made in the state-space using a state feedback control concept. A LQR control strategy is used.A uniform field material model is used to obtain the effective electromechanical properties of the patches, while the passive host structure material is modeled as isotropic linear elastic.Closed-loop root locus plots show a notable increment in damping ratios introduced by independent actuation with respect to coupled actuation. Frequency responses show the attenuation in tip twist and tip displacement while resonant conditions are investigated. Numerical results reveal that, in contrast to coupled actuation, independent actuation is able to control not only torsional modes but also flexional modes. However, as expected, due to the orientation of the patches, torsional vibration control exhibits a better performance.Finally, a transient analysis is performed and results for open and closed-loop systems are compared. A substantial attenuation of the closed-loop system with admissible voltages is attained.

This paper focuses on the numerical modelling of micro-energy harvesting systems(MEHSs) based on piezoelectric composites polarised with interdigitated electrodes (PCPIE). The system response and the harvested energy are numerically assessed using a multilayer piezoelectric shell finite element (FE) with a uniform fibre aligned electric field (UFAEF) in each active layer. Circuit and compatibility equations are included to take into account the presence of the electrical network. A state-space (SS) model is derived and used to evaluate the effect of electrical impedance on damping and natural frequencies, as well as dissipated energy/power. An energy harvester beam with a piezoelectric macro fibre composite (MFC) patch is first modelled with the developed tools. Numerical results are found to be in good agreement with experimental results reported in the literature. Finally, a MEHS consisting of a closed-box beam equipped with PCPIE devices bonded to its skin is analysed. The structural system is subjected to dynamic loading imposing oscillating displacements and deformations compatibles with those expected during service-life. Numerical results show the influence of the electrical impedance on system response, damping, natural frequencies, and electrical power.