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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

Abstract: A closed form solution is obtained for the optimal control of vibrations of simply supported thin functionally graded (FG) plates integrated with a Piezoelectric sensor layer and a piezoelectric [...]

This study deals with the active constrained layer damping (ACLD) of laminated composite plates to demonstrate the performance of piezoelectric fiber-reinforced composite (PFRC) layer as the constraining layer of ACLD treatment. A finite element model is developed for the smart composite plates integrated with the patches of ACLD treatment. The performance of the constraining PFRC layer has been investigated for active damping of thin symmetric and antisymmetric crossply and antisymmetric angle-ply laminated composite plates. The main concern of this study has been focused on investigating the significant effect of variation of piezoelectric fiber orientation in the PFRC layer on enhancing the damping characteristics of the laminated substrate plates, and the fiber angle in the PFRC layer for which the control authority of the patches becomes maximum has been determined.

Static analysis of laminated smart composite plates integrated with a piezoelectric fiber-reinforced composite (PFRC) layer acting as distributed actuators has been carried out by a generalized-energy-based finite element model. A simple first-order shear deformation theory is used for deriving the model. Eight noded isoparametric serendipity elements are used for discretizing the domain. The performance of the PFRC layer has been investigated for both symmetric and antisymmetric cross-ply and antisymmetric angle-ply laminated composite shell substrates. The effect of piezoelectric fiber orientation on the control authority of the PFRC layer has also been studied.

A novel work demonstrates the effect of delamination in smart laminated composite beams on the performance of active constrained layer damping (ACLD) treatment. A finite element model has been derived to formulate the dynamics of the composite beams integrated with a patch of ACLD treatment and a patch of piezoelectric film acting as a distributed sensor with and without the presence of delamination at different locations. Frequency response functions of the beams have been examined to observe the effect of delamination on the performance of ACLD treatment. It has been observed that the ACLD treatment improves the active damping characteristics of the beams, even in the presence of delamination, and that the responses of the beams are sensitive to the variation of the location of delamination. The responses due to active constrained layer damping presented may provide a useful guide to detect the presence of delamination in smart composite beams by the use of the existing numerical techniques.

A simple method for optimal control of vibrations of simply supported thin laminated shells integrated with piezoelectric layers is presented. The piezoelectric layers act as the distributed sensors and actuators. Coupled electromechanical governing equations of motion are derived using Hamilton's variational principle. The algorithm for a linear quadratic regulator with output feedback has been employed to formulate the optimal control problem. Controlled responses for various design parameters are illustrated, and a study of the effect of variation of the central angle subtended by the shell on the performance of the actuator is presented.

The effective coefficients of piezoelectric fiber-reinforced composites (PFRC) have been determined through micromechanical analyzes. The method of cells (MOC) and the strength of materials (SM) approach have been employed to predict the coefficients. A constant electric field is considered in the direction transverse to the fiber direction and is assumed to be the same both in the fiber and the matrix. MOC and SM predictions for the effective piezoelectric coefficient of the PFRC assessing the actuating capability in the fiber direction are in excellent agreement. It has been found for the piezoelectric fibers considered that, when the fiber volume fraction exceeds a critical fiber volume fraction, this effective piezoelectric coefficient becomes significantly larger than the corresponding coefficient of the piezoelectric material of the fiber. The methods also show the excellent matching of the predictions of the effective elastic constants and the dielectric constant of the PFRC in the useful range of fiber volume fraction.

Controlling vibration in thin symmetric laminated plates has been implemented with a closed-form solution with output feedback using distributed piezoelectric sensors and actuators. The plate structure is made up of a special orthotropic laminated plate combined with piezoelectric layers on the top and bottom layers. The top layer functions as an actuator while the bottom layer works as a sensor. The optimal gain is obtained by using the method for constructing the linear quadratic regulator with output feedback.

A finite element formulation for active vibration control of a laminated plate with piezoelectric polymer layers acting as distributed sensors shows a significant reduction in vibrational amplitude due to increased damping through feedback. The increase in damping ratio of thick plate is more than that of thin plate when both experience the same intensity of mechanical load. The substrate is a symmetric graphite-epoxy laminate and the sensor and actuator layers are made of polyvinylidene fluoride.

The precise solutions for static analysis of a simply supported rectangular plate-type intelligent structure were devised. The structure was composed of a laminated substrate of graphite/epoxy-composite combined with distributed sensor and actuator layers of biaxially polarized piezoelectric polymer (PVDF). The actuator layer is responsible for the layers of the substrate to bend. It also causes transverse compression, in-plane shear and transverse shear deformations. The actuator layer becomes more effective when there is a decrease in the length of the thickness ratio of the substrate. The results can be applied to verify solutions of later studies on the intelligent structure.

The effective coefficients of piezoelectric fiber-reinforced composites (PFRC) have been determined through micromechanical analyzes. The method of cells (MOC) and the strength of materials (SM) approach have been employed to predict the coefficients. A constant electric field is considered in the direction transverse to the fiber direction and is assumed to be the same both in the fiber and the matrix. MOC and SM predictions for the effective piezoelectric coefficient of the PFRC assessing the actuating capability in the fiber direction are in excellent agreement. It has been found for the piezoelectric fibers considered that, when the fiber volume fraction exceeds a critical fiber volume fraction, this effective piezoelectric coefficient becomes significantly larger than the corresponding coefficient of the piezoelectric material of the fiber. The methods also show the excellent matching of the predictions of the effective elastic constants and the dielectric constant of the PFRC in the useful range of fiber volume fraction. [ABSTRACT FROM AUTHOR]