Vertically Reinforced 1-3 Piezoelectric Composites for Active Damping of Functionally Graded Plates

M ONOLITHIC piezoelectric materials (PZTs) have been widely used as distributed sensors and actuators for developing smart structures with self-monitoring and selfcontrolling capabilities [1–10]. However, their major drawback is low control authority as the magnitude of their electromechanical coefficients is very small. The situation can be improved by using an active constrained layer damping (ACLD) treatment [11,12] which consists of a layer of a viscoelastic material constrained between a host structure and an active constraining PZT layer. When the constraining layer is activated with a voltage applied to the PZT layer, the shearing deformations of the viscoelastic layer are enhanced to improve the damping characteristics of the overall structures. Since its inception, the ACLD treatment has been extensively used for efficient and reliable control of flexible structures [13–17]. Piezoelectric composites, also called piezocomposites, have emerged as a new class of smart materials and have found wide applications as distributed actuators and sensors. A piezocomposite, composed of PZT reinforcements embedded in a conventional epoxy matrix, provides a wide range of effective material properties not offered by existing PZTs, is anisotropic, and has good conformability and strength. We note that laminae of vertically reinforced 1-3 piezocomposites are commercially available [18] and are being effectively used as underwater high-frequency transducers and in medical imaging applications [19,20]. A 1-3 piezocomposite lamina has PZT fibers vertically reinforced in the epoxy matrix across the thickness of the lamina, thefibers are poled along their length, and the top and the bottom surfaces of the lamina are electroded. The effective PZT coefficient (e33) of the 1-3 piezocomposite, which equals the normal stress ( z) along the fiber direction due to a unit electric field applied across the thickness of the piezocomposite lamina, is much larger than the effective coefficients e31 and e32 which signify the induced normal stresses ( x, y) in directions transverse to the fiber. However, very little attention has been paid to using these 1-3 piezocomposites for active vibration control [21]. Until recently, the host structure in a smart system has been considered to be made of a homogeneous and either isotropic or orthotropic material. Recently, functionally graded materials (FGMs) which exhibit smooth variation of material properties in one or more directions have been investigated for developing highperformance smart FG structures [22–27]. We also note that Batra andGeng [12] considered a FGviscoelastic layer but a homogeneous PZT constraining layer and performed the three-dimensional transient analysis of the problem with the finite element method (FEM). However, it appears that the performance of a vertically reinforced 1-3 piezocomposite has not yet been investigated for active control of FG structures. Here, we use a first-order shear deformation plate theory (FSDT) and the FEM to analyze ACLD of FG plates with the objective of investigating the performance of the vertically reinforced 1-3 piezocomposite as the material of the constraining layer.