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Research Papers

Active Damping of Nonlinear Vibrations of Functionally Graded Laminated Composite Plates using Vertically/Obliquely Reinforced 1-3 Piezoelectric Composite

[+] Author and Article Information
Satyajit Panda

Department of Mechanical Engineering,  Indian Institute of Technology, Kharagpur-721302, India

M. C. Ray

Department of Mechanical Engineering,  Indian Institute of Technology, Kharagpur-721302, Indiamcray@mech.iitkgp.ernet.in

J. Vib. Acoust 134(2), 021016 (Jan 26, 2012) (14 pages) doi:10.1115/1.4004604 History: Received October 15, 2009; Accepted January 31, 2011; Published January 26, 2012; Online January 26, 2012

This paper deals with a study on the active constrained layer damping (ACLD) of geometrically nonlinear vibrations of functionally graded (FG) laminated composite plates. The constraining layer of the ACLD treatment is considered to be made of the vertically/obliquely reinforced 1-3 piezoelectric composites (PZCs). The substrate FG laminated composite plate is composed of generally orthotropic FG layers. The generally orthotropic FG layer is a fiber reinforced composite layer in which the fibers are longitudinally aligned in the plane parallel to the top and bottom surfaces of the layer and their orientation angle is assumed to vary in the thickness direction according to a simple power-law in order to make it as a graded layer only in the thickness direction. The constrained viscoelastic layer of the ACLD treatment is modeled by implementing the Golla-Hughes-McTavish (GHM) method. Based on the first order shear deformation theory, the finite element (FE) model is developed to model the open-loop and closed-loop nonlinear dynamics of the overall FG laminated composite plates integrated with a patch of such ACLD treatment. The analysis suggests the potential use of the ACLD treatment with its constraining layer made of the vertically/obliquely reinforced 1-3 PZC material for active control of geometrically nonlinear vibrations of FG laminated composite plates. The effect of piezoelectric fiber orientation in the active 1-3 PZC constraining layer on the damping characteristics of the overall FG laminated composite plates is also investigated.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic diagram of a FG laminated composite plate integrated with a patch of ACLD treatment

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Figure 2

Deformations of any transverse cross-sections of the FG laminated composite plate integrated with the ACLD treatment which are parallel to (a) the xz plane and (b) the yz plane

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Figure 3

FG laminated composite plates (a/h = 100, a = b) composed of (a) two and (b) three generally orthotropic FG layers; (c)-(d) variation of the fiber orientation angle (ϕ) and (e)-(f) the elastic properties (Cij) across the thickness of the FG laminated composite plates

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Figure 4

Variation of nonlinear center deflection of (a) the FG Laminate 1 (b) the FG laminate 2 (a/h = 100, a = b) with the mechanical load; distribution of in-plane normal stresses (σ¯x) across the thickness of (c) the FG Laminate 1 and (d) the FG laminate 2

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Figure 5

Verification of the FE model: (a) the implementation of the GHM method (a/h = 100, a = b, r = 1.0) (b) the numerical integration scheme [7].

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Figure 6

Uncontrolled transient responses at the center of the (a) FG laminate 1 and (b) FG laminate 2 (a/h == 100, a = b, r = 1.0, Q = 150)

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Figure 7

Nonlinear transient responses for (a) the center deflection of the simply-supported overall FG laminate 1 (a/h = 100, a = b, r = 1.0); (b) the corresponding control voltage and (c) the corresponding phase plot (s is the starting point of motion)

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Figure 8

Nonlinear transient responses for (a) the center deflection of the simply-supported overall FG laminate 2 (a/h=100, a=b, r=1.0); (b) the corresponding control voltage; and (c) the corresponding phase plot (s is the starting point of motion)

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Figure 9

The nonlinear transient responses at the center of the simply-supported overall symmetric FG Laminate 1 (a/h = 100, a = b, r = 1.0) integrated with a patch of ACLD treatment (Q = 150)

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Figure 10

Controlled transient responses at the center of the overall (a) FG Laminate 1 and (b) FG laminate 2 (a/h = 100, a = b Q = 150, kd=120).

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Figure 11

Effect of piezoelectric fiber orientation angle (ψ) in the vertically reinforced 1-3 PZC constraining layer on the performance of the ACLD patch for active damping of nonlinear vibrations of the FG laminate 1 (a/h = 100, a = b Q = 150, kd=80)

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Figure 12

Effect of piezoelectric fiber orientation angle (ψ) in the vertically reinforced 1-3 PZC constraining layer on the performance of the ACLD patch for active damping of nonlinear vibrations of the FG laminate 2 (a/h = 100, a = b Q = 150, kd=80)

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