Ayech Benjeddou
Conservatoire national des arts et métiers
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Computers & Structures | 2000
Ayech Benjeddou
This paper makes a first attempt to survey and discuss the advances and trends in the formulations and applications of the finite element modeling of adaptive structural elements. For most contributions, the specific assumptions, in particular those of electrical type, and the characteristics of the elements are precised. The informations are illustrated in tables and figures for helpful use by the researchers as well as the designers interested in this growing field of smart materials and structures. Focus is put on the development of adaptive piezoelectric finite elements only. However, papers on other applications and active systems are also listed for completeness purpose. In total, more than 100 papers were found in the open literature. Taking this number as a measure of research activity, trends and ideas for future research are identified and outlined. 7 2000 Elsevier Science Ltd. All rights reserved.
Journal of Intelligent Material Systems and Structures | 1997
Ayech Benjeddou; Marcelo A. Trindade; Roger Ohayon
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 cores 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.
AIAA Journal | 1999
Ayech Benjeddou; Marcelo A. Trindade; Roger Ohayon
We present the formulation and validation of a new adaptive sandwich-beam finite element, capable of dealing with either extension or shear actuation mechanisms, which is reached by coating an elastic core with piezoelectric sheets or sandwiching a piezoelectric core between two elastic faces. The poling direction is taken parallel to the transversely applied electric field for the first mechanism and in the axial direction for the second one. The sandwich construction is made of asymmetric thin faces (Euler-Bernoulli beams) and a relatively thick core (Timoshenko beam). The obtained two-node finite element has only four mechanical degrees of freedom that are the deflection and its derivative and the mean and relative axial displacements of the faces midplanes. Finite element analysis of segmented and continuous cantilever adaptive sandwich beams with active faces (extension actuated) or core (shear actuated) show good comparisons with results found in the Iiterature, Additional parametric studies (actuators position and thickness, structures stiffness) with the present element indicate that the shear actuation mechanism presents several promising features over the conventional extension actuation mechanism. In fact, the shear actuation mechanism is better than the extension one for stiff structures and thick piezoelectric actuators.
Journal of Vibration and Control | 2002
Marcelo A. Trindade; Ayech Benjeddou
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.
Journal of Vibration and Acoustics | 2000
Marcelo A. Trindade; Ayech Benjeddou; Roger Ohayon
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.
Journal of Intelligent Material Systems and Structures | 2009
Arnaud Deraemaeker; Houssein Nasser; Ayech Benjeddou; André Preumont
This article focuses on the modeling 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 d31 and d33 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.
Mechanics of Advanced Materials and Structures | 2009
Marcelo A. Trindade; Ayech Benjeddou
This work presents a critical analysis of methodologies to evaluate the effective (or generalized) electromechanical coupling coefficient (EMCC) for structures with piezoelectric elements. First, a review of several existing methodologies to evaluate material and effective EMCC is presented. To illustrate the methodologies, a comparison is made between numerical, analytical and experimental results for two simple structures: a cantilever beam with bonded extension piezoelectric patches and a simply-supported sandwich beam with an embedded shear piezoceramic. An analysis of the electric charge cancelation effect on the effective EMCC observed in long piezoelectric patches is performed. It confirms the importance of reinforcing the electrodes equipotentiality condition in the finite element model. Its results indicate also that smaller (segmented) and independent piezoelectric patches could be more interesting for energy conversion efficiency. Then, parametric analyses and optimization are performed for a cantilever sandwich beam with several embedded shear piezoceramic patches. Results indicate that to fully benefit from the higher material coupling of shear piezoceramic patches, attention must be paid to the configuration design so that the shear strains in the patches are maximized. In particular, effective square EMCC values higher than 1% were obtained embedding nine well-spaced short piezoceramic patches in an aluminum/foam/aluminum sandwich beam.
International Journal of Solids and Structures | 2002
Ayech Benjeddou; Jean-François Deü
This work presents a two-dimensional (2D) closed-form solution for the free-vibrations analysis of simply-supported piezoelectric sandwich plates. It has the originality to consider all components of the electric field and displacement, thus satisfying exactly the electric equilibrium equation. Besides, the formulation considers full layerwise first-order shear deformation theory and through-thickness quadratic electric potential. Its independent mechanical and electric variables are decomposed using Fourier series expansions, then substituted in the derived mechanical and electric 2D equations of motion. The resulting eigenvalue system is then condensed so that only nine mechanical unknowns are retained. After its validation on single- and three-layer piezoelectric, and hybrid sandwich plates, the present approach was then used to analyze thickness modes of a square sandwich plate with piezoceramic faces and elastic cross-ply composite core. It was found that only the first three thickness modes are global, thus can be modeled by the mixed equivalent single-layer/layerwise approach, often retained in the literature; the remaining higher thickness modes being characteristic of sandwich behavior; i.e., dominated by the deformations of either the core or the faces. These results, together with presented through-thickness variations of the mechanical and electric variables clearly recommend full layerwise modeling. Several numerical results are provided for future reference for validation of 2D approximate analytical or numerical approaches; in particular, of 2D piezoelectric adaptive finite elements.
Journal of Intelligent Material Systems and Structures | 1999
Marcelo A. Trindade; Ayech Benjeddou; Roger Ohayon
This paper presents a comparative numerical analysis of shear and extension actuation mechanisms for the bending vibrations control of sandwich beams. The extension actuation mechanism denotes the use of through-thickness poled piezoelectric actuators bonded on the surfaces of the structure such that, when submitted to a through-thickness applied electric potential, these actuators produce axial stresses or strains. The shear actuation mechanism, in the contrary, is obtained through an embedded longitudinally poled piezoelectric actuator that, subjected to the same electric potential, produces shear stresses or strains. Theoretical and finite element models of a sandwich beam, capable of dealing with both mechanisms, are presented. The models are based on Bernoulli-Euler assumptions for the surface layers and Timoshenko ones for the core. An optimal state feedback control law is used to maximize the damping of the first four natural modes of the sandwich beam. The influence of important parameters variation, such as actuator thickness and structure/actuator modulus ratio, on the performance of the control system is analyzed under limited input voltage and induced beam tip transverse deflection. Results suggest that shear actuators can be more effective than extension ones for the control of bending vibrations.
Mechanics of Advanced Materials and Structures | 2005
Ayech Benjeddou; Orlando Andrianarison
This work derives, for piezoelectric media, the analog of Reissners mixed variational theorem (RMVT), initially developed for elastic media, by adding the transverse electric field–potential relation as a constraint via a Lagrange multiplier. The latter is shown to be the transverse (normal) electric displacement, for which continuity can now be fulfilled in a natural way as is the case for transverse stresses in the RMVT. Hence, the newly proposed piezoelectric mixed variational theorem (PMVT) will be well suited for layered piezocomposites. Mixed piezoelectric constitutive equations to be used in conjunction with the PMVT are developed and guidelines for their numerical implementation are also given.