Active Vibration Control of Laminated Composite Plates Using Piezoelectric Devices: A Finite Element Approach

A finite element formulation is presented for modeling the behavior of laminated composites with integrated piezoelectric sensors and actuators. This model is valid for both con tinuous and segmented piezoelectric elements that can be either surface bonded or embedded in the laminated plate. The present model takes into account the mass and the stiffness of the piezoelectric patches. The formulation is based on the first-order shear deformation theory, which is applicable for both thin and moderately thick plates. An additional feature of the present model is that it does not introduce the voltage as an additional degree of freedom. The charge/current generated by the sensor and the response of the plate to an actuator voltage can be computed independently. These features are then coupled with a constant-gain negative-velocity/positive-position feedback control algorithm to actively control the transient response of the plate in a closed loop. Numerical results are presented which indicate the increase in damping as the feedback gain is increased. The in fluence of stacking sequence and boundary conditions on the controlled transient response of the plate is examined.

[1]  Craig A. Rogers,et al.  Laminate Plate Theory for Spatially Distributed Induced Strain Actuators , 1991 .

[2]  D. H. Robbins,et al.  Analysis of piezoelectrically actuated beams using a layer-wise displacement theory , 1991 .

[3]  Y. Stavsky,et al.  Elastic wave propagation in heterogeneous plates , 1966 .

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

[5]  J. Reddy.  Energy and variational methods in applied mechanics : with an introduction to the finite element method , 1984 .

[6]  T. Bailey,et al.  Distributed Piezoelectric-Polymer Active Vibration Control of a Cantilever Beam , 1985 .

[7]  Kenneth B. Lazarus,et al.  Induced strain actuation of isotropic and anisotropic plates , 1991 .

[8]  Sathya Hanagud,et al.  Modeling issues in the vibration control with piezoceramic actuators , 1991 .

[9]  Robert L. Clark,et al.  Characterization of multiple piezoelectric actuators for structural excitation , 1990 .

[10]  S. Poh,et al.  Performance of an active control system with piezoelectric actuators , 1988 .

[11]  Nesbitt W. Hagood,et al.  Modelling of Piezoelectric Actuator Dynamics for Active Structural Control , 1990 .

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

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

[14]  Craig A. Rogers,et al.  Modeling of Finite-Length Spatially-Distributed Induced Strain Actuators for Laminate Beams and Plates , 1991 .

[15]  Fu-Kuo Chang,et al.  Finite element analysis of composite structures containing distributed piezoceramic sensors and actuators , 1992 .

[16]  Carl H. Gerhold,et al.  Active Control of Flexural Vibrations in Beams , 1987 .

[17]  Sathya Hanagud,et al.  Electronic damping techniques and active vibration control , 1985 .

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

[19]  K. Chandrashekhara,et al.  Thermal buckling of laminated plates using a shear flexible finite element , 1992 .

[20]  C. I. Tseng,et al.  Distributed piezoelectric sensor/actuator design for dynamic measurement/control of distributed parameter systems: A piezoelectric finite element approach , 1990 .

[21]  Satya N. Atluri,et al.  Effects of a Piezo-Actuator on a Finitely Deformed Beam Subjected to General Loading , 1989 .