Analytical and numerical approaches to piezoelectric bimorph

Abstract We propose an efficient and accurate approach to piezoelectric bimorph based on a refined expansion of the elastic displacement and electric potential. The field approximation of the through-the-thickness variation accounts for a shear correction and a layerwise modelling for the electric potential. A particular attention is devoted to the boundary conditions on the bottom and top faces of the plate as well as to the interface continuity conditions for the electromechanical variables. The continuity condition on the electric potential imposes some restrictions on the approximation of the electric potential. Moreover, the continuity condition on the normal component of the electric induction at the bimorph interface is ensured by a Lagrange multiplier. The equations of the piezoelectric bimorph are obtained by using variational formulation involving the appropriate boundary and continuity conditions. A selection of numerical illustrations is presented for the series and parallel piezoelectric bimorphs simply supported under cylindrical bending conditions. Two types of electromechanical load are considered (i) a surface density of force applied on the top face and (ii) an electric potential applied on the bottom and top faces of the bimorph. The results thus obtained are compared to those provided by finite element computations performed for the full 3D model and by a simplified model without shear effect. At last, the problem of piezoelectric bimorph vibration is also examined for both closed and open circuit conditions. Excellent predictions with low error estimates of the local (profile) and global responses as well as resonant frequencies are observed. The comparisons assess of the effectiveness of the present approach to piezoelectric bimorph.

[1]  E. Crawley,et al.  Detailed Models of Piezoceramic Actuation of Beams , 1989 .

[2]  P. G. Harper,et al.  The piezoelectric bimorph: An experimental and theoretical study of its quasistatic response , 1978 .

[3]  Singiresu S. Rao,et al.  Piezoelectricity and Its Use in Disturbance Sensing and Control of Flexible Structures: A Survey , 1994 .

[4]  P Muralt,et al.  Wide-range, low-operating-voltage, bimorph STM: Application as potentiometer , 1986, IBM J. Res. Dev..

[5]  Junji Tani,et al.  Intelligent Material Systems: Application of Functional Materials , 1998 .

[6]  J. Reddy.  A Simple Higher-Order Theory for Laminated Composite Plates , 1984 .

[7]  Paolo Gaudenzi,et al.  Control of beam vibrations by means of piezoelectric devices: theory and experiments , 2000 .

[8]  Maurice Touratier,et al.  A refined theory of laminated shallow shells , 1992 .

[9]  Amâncio Fernandes,et al.  An accurate modelling of piezoelectric multi-layer plates , 2002 .

[10]  J. G. Smits,et al.  The constituent equations of piezoelectric bimorphs , 1989, Proceedings., IEEE Ultrasonics Symposium,.

[11]  Ai Kah Soh,et al.  Three-dimensional analysis of an antiparallel piezoelectric bimorph , 2000 .

[12]  A. Love.  A treatise on the mathematical theory of elasticity , 1892 .

[13]  D. Saravanos,et al.  Mechanics and Computational Models for Laminated Piezoelectric Beams, Plates, and Shells , 1999 .

[14]  Amâncio Fernandes,et al.  Accurate modelling of piezoelectric plates: single-layered plate , 2001 .

[15]  Nesbitt W. Hagood,et al.  Simultaneous Piezoelectric Sensing/Actuation: Analysis And Application To Controlled Structures , 1994 .

[16]  D. Peters,et al.  Piezoelectric bimorph‐based translation device for two‐dimensional, remote micropositioning , 1989 .

[17]  M. Touratier,et al.  An efficient standard plate theory , 1991 .

[18]  H. F. Tiersten,et al.  Linear Piezoelectric Plate Vibrations , 1969 .

[19]  Jan G. Smits,et al.  The effectiveness of a piezoelectric bimorph actuator to perform mechanical work under various constant loading conditions , 1991 .

[20]  Stefano Vidoli,et al.  Vibration control in plates by uniformly distributed PZT actuators interconnected via electric networks , 2001 .

[21]  Grant P. Steven,et al.  A Review on the Modelling of Piezoelectric Sensors and Actuators Incorporated in Intelligent Structures , 1998 .

[22]  Ai Kah Soh,et al.  Three-dimensional electromechanical responses of a parallel piezoelectric bimorph , 2001 .

[23]  J. Kelly Lee.  Piezoelectric bimorph optical beam scanners: analysis and construction. , 1979 .

[24]  E. Reissner,et al.  On transverse bending of plates, including the effect of transverse shear deformation☆ , 1975 .

[25]  Seiji Chonan,et al.  Soft-handling gripper driven by piezoceramic bimorph strips , 1996 .

[26]  Paolo Bisegna,et al.  Evaluation of higher-order theories of piezoelectric plates in bending and in stretching , 2001 .

[27]  Hwan-Sik Yoon,et al.  Piezoceramic actuated aperture antennae , 1998 .