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This paper presents a finite element model for adaptive sandwich beams to deal with either extension or shear actuation mechanism. The former corresponds to an elastic core sandwiched beam between two transversely polarized active surface layers; whereas, the latter consists of an axially polarized core, sandwiched between two elastic surface layers. For both configurations, an electric field is applied through thickness of the piezoelectric layers. The mechanical model is based on Bernoulli-Euler theory for the surface layers and Timoshenko beam theory for the core. It uses three variables, through-thickness constant deflection, and the mean and relative axial displacements of the core's upper and lower surfaces. Augmented by the bending rotation, these are the only nodal degrees of freedom of the proposed two-node adaptive sandwich beam finite element. The piezoelectric effect is handled through modification of the constitutive equation, when induced electric potential is taken into account, and additional electric forces and moments. The proposed finite element model is validated through static and dynamic analysis of extension and shear actuated, continuous and segmented, cantilever beam configurations. Finite element results show good comparison with those found in the literature, and indicate that the newly defined shear actuation mechanism presents several promising features over conventional extension actuation mechanism, particularly for brittle piezoceramics use and energy dissipation purposes.

This paper focuses on the modelling of structures equipped with Macro Fiber Composite (MFC) transducers. Based on the uniform field method under the plane stress assumption, we derive analytical mixing rules in order to evaluate equivalent properties for d 31 and d 33 MFC transducers. In particular, mixing rules are derived for the longitudinal and transverse piezoelectric coefficients of MFCs. These mixing rules are validated using finite element computations and experimental results available from the literature.

Hybrid active-passive damping treatments combine the reliability, low cost and robustness of viscoelastic damping treatments and the high performance, modal selective and adaptive piezoelectric active control. Numerous hybrid damping treatments have been reported in the literature. They differ mainly by the relative positions of viscoelastic treatments, sensors and piezoelectric actuators. Therefore, the present article provides a review of the open literature concerning geometric configurations, modeling approaches and control algorithms for hybrid active (piezoelectric)-passive (viscoelastic) damping treatments of beams. In addition, using a unified finite element model able to represent sandwich damped beams with piezoelectric laminated faces and an optimal control algorithm, the geometric optimization of four hybrid treatments is studied through treatment length and viscoelastic material thickness parametric analyses. A comparison of the performances of these hybrid damping treatments is carried out and the advantages and drawbacks of each treatment are identified. Beside the literature review of more than 80 papers, the present assessment has the merit to present for the first time detailed parametric and comparative analyses for these already known hybrid active (piezoelectric)-passive (viscoelastic) damping configurations. This may be of valuable help for researchers and designers interested in this still growing field of hybrid active-passive damping systems.

This work intends to compare two viscoelastic models, namely ADF and GHM, which account for frequency dependence and allow frequency and time-domain analysis of hybrid active-passive damping treatments, made of viscoelastic layers constrained with piezoelectric actuators. A modal strain energy (MSE) based iterative model is also considered for comparison. As both ADF and GHM models increase the size of the system, through additional dissipative coordinates, and to enhance the control feasibility, a modal reduction technique is presented for the first time for the ADF model and then applied to GHM and MSE ones for comparison. The resulting reduced systems are then used to analyze the performance of a segmented hybrid damped cantilever beam under parameters variations, using a constrained input optimal control algorithm. The open loop modal damping factors for all models match well. However, due to differences between the modal basis used for each model, the closed loop ones were found to be different.