The electromechanical response of multilayered piezoelectric structures

The constitutive equations of multilayered piezoelectric structures are derived in a new form. In this form, the electromechanical coupling is presented as an additional stiffness matrix. This matrix is a true property of the piezoelectric structure and is independent of specific mechanical boundary conditions that may apply to the structure. A novel model of the electromechanical response of such structures is presented. This model accounts for the three-dimensional (3-D) kinematics of the structure deformation. Solution of example problems using the new model shows excellent agreement with full 3-D finite element simulations. These solutions are also compared to the results of previous two-dimensional (2-D) model approximations presented in literature, and the inaccuracies associated with these previous models are discussed.

[1]  T. Ikeda.  Fundamentals of piezoelectricity , 1990 .

[2]  Michael Krommer,et al.  On the correction of the Bernoulli-Euler beam theory for smart piezoelectric beams , 2001 .

[3]  B. Nogarede,et al.  Optimal dimensioning of a piezoelectric bimorph actuator , 2002 .

[4]  Michael Krommer,et al.  An electromechanically coupled theory for piezoelastic beams taking into account the charge equation of electrostatics , 2002 .

[5]  Alessandra Borrelli,et al.  Saint-Venant's Principle for a Piezoelectric Body , 1998, SIAM J. Appl. Math..

[6]  Paul Muralt,et al.  Ferroelectric thin films for micro-sensors and actuators: a review , 2000 .

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

[8]  S. Timoshenko,et al.  THEORY OF PLATES AND SHELLS , 1959 .

[9]  Roger Ohayon,et al.  A Unified Beam Finite Element Model for Extension and Shear Piezoelectric Actuation Mechanisms , 1997 .

[10]  Hui Li,et al.  Radioactively powered pressure transducer with RF pulse output , 2003, TRANSDUCERS '03. 12th International Conference on Solid-State Sensors, Actuators and Microsystems. Digest of Technical Papers (Cat. No.03TH8664).

[11]  Michael Krommer,et al.  On the influence of the electric field on free transverse vibrations of smart beams , 1999 .

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

[13]  A. Dehe,et al.  Current drive methods to extend the range of travel of electrostatic microactuators beyond the voltage pull-in point , 2002 .

[14]  M. Weinberg.  Working equations for piezoelectric actuators and sensors , 1999 .

[15]  Lucy Edery-Azulay,et al.  Piezoelectric actuation and sensing mechanisms––closed form solutions , 2004 .

[16]  Craig A. Rogers,et al.  Intelligent Material Systems — The Dawn of a New Materials Age , 1993 .

[17]  E. Crawley,et al.  Use of piezoelectric actuators as elements of intelligent structures , 1987 .

[18]  Kazuo Tanaka,et al.  A unified approach to controlling chaos via an LMI-based fuzzy control system design , 1998 .

[19]  J.G. Smits,et al.  The constituent equations of piezoelectric heterogeneous bimorphs , 1991, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[20]  A. Pisano,et al.  Modeling and optimal design of piezoelectric cantilever microactuators , 1997 .