Control of nonlinear vibrations of functionally graded plates using 1-3 piezoelectric composite

Performance of the vectically/obliquely reinforced 1-3 piezoelectric composite material as the constraining layer of the active-constrained-layer damping treatment for controlling geometrically nonlinear vibrations of the functionally graded plates subjected to a temperature field has been investigated. Unlike the existing analyses, the finite element model uses the induced transverse normal stress in the active constraining layer for the active damping of nonlinear vibrations of the overall functionally graded plates. The temperature field is assumed to be uniform over the substrate plate surfaces and varied through the thickness of the host functionally graded plates. The temperature-dependent material properties of the functionally graded substrate plates are assumed to be graded in the thickness direction of the plates according to a power-law distribution, and Poisson's ratio is assumed to be a constant over the domain of the plate. The constrained viscoelastic layer of the active-constrained-layer damping treatment is modeled using the Golla-Hughes-McTavish method. The first-order shear deformation theory and the Green-Lagrange nonlinear strain-displacement relations are used to model the open-loop and closed-loop nonlinear dynamics of the overall functionally graded substrate plates under a thermal environment. The analysis suggests the potential use of the active-constrained-layer damping treatment with its constraining layer made of the vertically reinforced 1-3 piezoelectric composite material for active control of geometrically nonlinear vibrations of functionally graded plates in the absence or presence of the temperature gradient across the thickness of the plates. The analysis also reveals that the active-constrained-layer damping patch is more effective for controlling the nonlinear vibrations of functionally graded plates when it is attached to the softest surface of the functionally graded plates than when it is bonded to the stiffest surface of the plates. The effect of piezoelectric fiber orientation in the active constraining layer on the control authority of the active-constrained-layer damping treatment has also been investigated. DOI: 10.2514/1.38048