FINITE ELEMENT MODELLING OF STRUCTURES INCLUDING PIEZOELECTRIC ACTIVE DEVICES

Finite element modelling is used to study the response of plate structures on which piezoelectric active devices are mounted. Such devices are typically small in relation to the size of the structure which can be modelled as a plate or shell structure. In modelling the response of such devices, it is necessary to use a detailed model of the device but to do the same for the whole structure is computationally expensive and unnecessary. Full three-dimensional elements are used to model the piezoelectric devices because such devices are anisotropic, couple electric and elastic fields and satisfy boundary conditions independently on the two fields. Shell elements, approximated by many flat-shell elements are used in modelling the structure. Transition elements have been derived to connect the three-dimensional solid elements in the piezoelectric region to the flat-shell elements used for the plate. This approach has merits in terms of accuracy in modelling the piezoelectric device and computational economy for the plate structure. The use of shell elements is preferred for the structure since brick elements lead to unnatural stiffening of the plate and artificially high natural frequencies. The aspect ratio of the transition elements are first optimized through a numerical study and the sensor and actuator performance of the devices is then verified. © 1997 by John Wiley & Sons, Ltd.

[1]  J. Hossack,et al.  Finite-element analysis of 1-3 composite transducers , 1991, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[2]  Ricardo A. Burdisso,et al.  Optimal Placement of Piezoelectric Actuators for Active Structural Acoustic Control , 1994 .

[3]  Xiaoqi Bao,et al.  A complete finite element-eigenmode analysis for a 1-3 type of piezoelectric composite transducer including the effect of fluid loading and internal losses , 1988, IEEE 1988 Ultrasonics Symposium Proceedings..

[4]  Vijay K. Varadan,et al.  Finite element modeling of a finite piezoelectric sensor/actuator embedded in a fluid-loaded plate , 1994, Smart Structures.

[5]  C. K. Lee.  Theory of laminated piezoelectric plates for the design of distributed sensors/actuators. Part I: Governing equations and reciprocal relationships , 1990 .

[6]  J. N. Reddy,et al.  A generalization of two-dimensional theories of laminated composite plates† , 1987 .

[7]  C. Fuller,et al.  Piezoelectric Actuators for Distributed Vibration Excitation of Thin Plates , 1991 .

[8]  B. Auld,et al.  Acoustic fields and waves in solids , 1973 .

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

[10]  Ali H. Nayfeh,et al.  A refined nonlinear model of composite plates with integrated piezoelectric actuators and sensors , 1993 .

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

[12]  Inderjit Chopra,et al.  Structural modeling of composite beams with induced-strain actuators , 1993 .

[13]  Suk-Yoon Hong.  Active vibration control of adaptive flexible structures using piezoelectric smart sensors and actuators , 1993 .

[14]  T. Hughes,et al.  Finite element method for piezoelectric vibration , 1970 .

[15]  R. Lerch,et al.  Simulation of piezoelectric devices by two- and three-dimensional finite elements , 1990, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[16]  Robert L. Clark,et al.  Optimal placement of piezoelectric actuators and polyvinylidene fluoride error sensors in active structural acoustic control approaches , 1991 .

[17]  J. Reddy,et al.  THEORIES AND COMPUTATIONAL MODELS FOR COMPOSITE LAMINATES , 1994 .

[18]  Thomas J. R. Hughes,et al.  A simple and efficient finite element for plate bending , 1977 .

[19]  V. Varadan,et al.  Finite-element modeling of a smart cantilever plate and comparison with experiments , 1996 .

[20]  Thomas Gmür,et al.  Three‐dimensional solid‐to‐beam transition elements for structural dynamics analysis , 1993 .

[21]  Karan S. Surana,et al.  Transition finite elements for three‐dimensional stress analysis , 1980 .

[22]  Gangan Prathap,et al.  An optimally integrated four‐node quadrilateral plate bending element , 1983 .

[23]  H. Saunders,et al.  Finite element procedures in engineering analysis , 1982 .