Quantifying the Local Kinematic Effect in Actuated Plates via Strain Energy Distribution

Abstract

This article examines the distribution of strain energy in the various component materials of actuated plates and investigates the manner in which the strain energy distribution is influenced by the actuated span-to-thickness ratio and the thickness of the adhesive bond layer. Furthermore, the article investigates the effect of modeling choices (e.g., kinematic assumptions and mesh density) on the predicted magnitude and mode of the dominant strain energy form in each component material. These computed parameters can be used to quantify the overall efficiency of an actuated plate in addition to aiding the understanding of the local mechanics that govern the process. The focus problem consists of a square aluminum plate with a single symmetric pair of surface-mounted piezoceramic actuators that are used to produce in-plane extension or bending in the aluminum plate. The behavior of the actuated plate is examined over a range of plate thicknesses and adhesive bond layer thicknesses by using a series of finite element models that feature different levels of kinematic complexity and different levels of two-dimensional (2-D) mesh density. The results of the study emphasize the need for discrete layer kinematics in determining the magnitude and mode of the dominant strain energy form in each constituent material; however, these computed parameters are shown to be rather insensitive to changes in 2-D mesh density. Most importantly, the study confirms the existence and quantifies the magnitude of the local kinematic effect, whereby a portion of the available actuation energy is diverted to the production of localized transverse shear deformation and transverse normal deformation, thus reducing the amount of actuation energy available to produce in-plane deformation in the structural substrate.

Keywords

actuated plates laminate models transverse shear deformation finite elements.

Get full access to this article

View all access options for this article.

References

Chattopadhyay, A. , Li, J. and Gu, H. 1999. ``Coupled Thermo-piezoelectric-mechanical Model for Smart Composite Laminate,'' AIAA Journal, 37(12):1633—1638.

Chopra, I. 2002. ``Review of State of Art of Smart Structures and Integrated Systems,'' AIAA Journal, 40(11):2145—2187.

Gopinathan, S.V. , Varadan, V.V. and Varadan, V.K. 2000. ``A Review and Critique of Theories for Piezoelectric Laminates,'' Smart Materials and Structures, 9:24—48.

Heyliger, P. , Ramirez, G. and Saravanos, D.A. 1994. ``Coupled Discrete Layer Finite Elements for Laminated Piezoelectric Plates,'' Communications in Numerical Methods in Engineering, 10:971—981.

Kim, J. , Varadan, V.V. and Varadan, V.K. 1996. ``Finite Element Modeling of Structures Including Piezoelectric Active Devices,'' International Journal for Numerical Methods in Engineering, 40:1—16.

Lee, C.K. 1990. ``Theory of Laminated Piezoelectric Plates for the Design of Distributed Sensors/Actuators. Part I: Governing Equations and Reciprocal Relationships,'' Journal of the Acoustic Society of America , 87(3):1144—1158.

Lin, C.C. , Hsu, C.Y. and Huang, H.N. 1996. ``Finite Element Analysis on Deflection Control of Plates with Piezoelectric Actuators,'' Composite Structures, 35:423—433.

Miller, S.E. and Abramovich, H. 1995. ``A Self-sensing Piezolaminated Actuator Model for Shells using a First Order Shear Deformation Theory,'' Journal of Intelligent Material Systems and Structures, 6:624—638.

Reddy, J.N. 1987. ``A Generalization of Two-dimensional Theories of Laminated Composite Plates,'' Communications in Applied Numerical Methods , 3:173—180.

10.

Reddy, J.N. 1989. ``On the Generalization of Displacement-based Laminate Theories,'' Applied Mechanics Reviews Part 2, 42(11): S213—S222.

11.

Reddy, J.N. and Robbins, Jr, D.H. 1994. ``Theories and Computational Models for Composite Laminates,'' Applied Mechanics Reviews Part 1, 47(6):147—170.

12.

Robbins, Jr, D.H. and Chopra, I. 2006a. ``The Effect of Discrete Layer Kinematics on the Global Response of Homogeneous and Composite Plates with Multiple Actuator Pairs,'' Journal of Intelligent Material Systems and Structures (accepted for publication in February 2006).

13.

Robbins, Jr, D.H. and Chopra, I. 2006b. ``The Effect of Laminate Kinematic Assumptions on the Global Response of Actuated Plates,'' Journal of Intelligent Material Systems and Structures, 17(4):273—299.

14.

Robbins, Jr, D.H. and Reddy, J.N. 1993. ``Modelling of Thick Composites Using a Layerwise Laminate Theory,'' International Journal for Numerical Methods in Engineering , 36:655—677.

15.

Saravanos, D.A. , Heyliger, P.R. and Hopkins, D.A. 1997. ``Layerwise Mechanics and Finite Element for the Dynamic Analysis of Piezoelectric Composite Plates,'' International Journal of Solids and Structures, 34(3): 359—378.

16.

Tzou, H.S. and Gadre, M. 1989. ``Theoretical Analysis of a Multilayered Thin Shell Coupled with Piezoelectric Shell Actuators for Distributed Vibration Controls,'' Journal of Sound and Vibration, 132(3):433—450.

17.

Zhou, X. , Chattopadhyay, A. and Gu, H. 2000. ``Dynamic Response of Smart Composites Using a Coupled Thermo-piezoelectric-mechanical Model,'' AIAA Journal, 38(10): 1939— 1948.