Static and vibration control of composite laminates integrated with piezoelectric sensors and actuators using the radial point interpolation method

A meshfree model based on the first-order shear deformation theory is presented for the shape and vibration control of laminated composite plates with integrated piezoelectric sensors and actuators. A point interpolation method using radial basis functions (RPIM) is employed to construct shape functions for mechanical and electrical variables, which possess the delta function property and show linear reproduction behavior. The method shows a high convergence rate equivalent to that of the second-order finite elements approach. Comparing, one sees that a very simple nodal topology can be used for the field representation and no element continuity is required. A constant displacement and velocity feedback control algorithm is used for the active control of the static deflection as well as the dynamic response of plates through closed loop control. Numerical results for the static deformation, vibration modes and dynamic responses are in good agreement with those from the finite element method.

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

[2]  Guirong Liu,et al.  A LOCAL RADIAL POINT INTERPOLATION METHOD (LRPIM) FOR FREE VIBRATION ANALYSES OF 2-D SOLIDS , 2001 .

[3]  K. Liew,et al.  Active control of FGM plates with integrated piezoelectric sensors and actuators , 2001 .

[4]  Gui-Rong Liu,et al.  A meshfree formulation of local radial point interpolation method (LRPIM) for incompressible flow simulation , 2003 .

[5]  V. B. C. Tan,et al.  A CONFORMING POINT INTERPOLATION METHOD FOR ANALYZING SPATIAL THICK SHELL STRUCTURES , 2002 .

[6]  K. M. Liew,et al.  A FEM model for the active control of curved FGM shells using piezoelectric sensor/actuator layers , 2002 .

[7]  J. N. Reddy,et al.  A finite-element model for piezoelectric composite laminates , 1997 .

[8]  Michael A. Golberg,et al.  Some recent results and proposals for the use of radial basis functions in the BEM , 1999 .

[9]  I Y Shen.  Bending and torsional vibration control of composite beams through intelligent constrained-layer damping treatments , 1995 .

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

[11]  W. Hwang,et al.  Finite Element Modeling of Piezoelectric Sensors and Actuators , 1993 .

[12]  Holger Wendland,et al.  Error Estimates for Interpolation by Compactly Supported Radial Basis Functions of Minimal Degree , 1998 .

[13]  L. Lucy.  A numerical approach to the testing of the fission hypothesis. , 1977 .

[14]  H. Tzou.  Piezoelectric Shells: Distributed Sensing and Control of Continua , 1993 .

[15]  Wing Kam Liu,et al.  Reproducing kernel particle methods , 1995 .

[16]  Ping Lin,et al.  Numerical analysis of Biot's consolidation process by radial point interpolation method , 2002 .

[17]  Guirong Liu,et al.  A point interpolation method for two-dimensional solids , 2001 .

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

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

[20]  K. Y. Lam,et al.  Active control of composite plates with integrated piezoelectric sensors and actuators under various dynamic loading conditions , 1999 .

[21]  J. Reddy.  Mechanics of laminated composite plates : theory and analysis , 1997 .

[22]  K. Y. Dai,et al.  A radial point interpolation method for simulation of two-dimensional piezoelectric structures , 2003 .

[23]  Guirong Liu.  Mesh Free Methods: Moving Beyond the Finite Element Method , 2002 .

[24]  Guirong Liu,et al.  A point interpolation meshless method based on radial basis functions , 2002 .

[25]  Shaofan Li,et al.  “Smoothed particle hydrodynamics — a meshfree method” , 2004 .

[26]  T. Belytschko,et al.  Element‐free Galerkin methods , 1994 .

[27]  S. Atluri,et al.  A new Meshless Local Petrov-Galerkin (MLPG) approach in computational mechanics , 1998 .

[28]  Junji Tani,et al.  VIBRATION CONTROL SIMULATION OF LAMINATED COMPOSITE PLATES WITH INTEGRATED PIEZOELECTRICS , 1999 .