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This paper is concerned with the smart constrained layer damping (SCLD) treatment of laminated composite shells with variable thickness undergoing geometrically nonlinear vibrations. Three dimensional fractional derivative model (FDM) has been implemented for modelling the constrained viscoelastic layer of the SCLD treatment. The constraining layer of the SCLD treatment is made of vertically/obliquely reinforced 1–3 piezoelectric composites (PZCs) and acts as the distributed actuator. The strain-displacement relations are based on the simplified Novozhilov nonlinear shell theory to introduce the geometric nonlinearity in the large amplitude vibrations of the variable thickness shells. A three dimensional smart nonlinear finite element (FE) model has been developed for carrying out this analysis. Several numerical results are presented to check the accuracy of the present three-dimensional FDM for analyzing the passive and active control authority of the SCLD patch. Also the efficacy of the activated SCLD patch in controlling geometrically nonlinear vibration is computed for variable thickness shells and compared with shells of constant thickness. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the analysis of active control of vibration of thin laminated composite truncated circular conical shells using vertically and obliquely reinforced 1-3 piezoelectric composite (PZC) materials as the constraining layer of the active constrained layer damping (ACLD) treatment. A finite element model of smart truncated conical laminated shells integrated with the patches of such ACLD treatment has been developed to demonstrate the performance of these patches on enhancing the damping characteristics of thin symmetric and antisymmetric cross-ply and antisymmetric angle-ply laminated truncated conical shells. Velocity feedback control loop has been implemented to activate the patches. The effect of variation of semi-cone angle on the performance of the patches for controlling first few modes of the truncated conical laminated shells has been demonstrated. Emphasis has also been placed on exploring the effect of variation of piezoelectric fiber orientation angle in the constraining layer on the control authority of the ACLD patches. [Copyright &y& Elsevier]

Abstract: This paper deals with the analysis of active constrained layer damping (ACLD) of geometrically nonlinear transient vibrations of doubly curved laminated composite shells. Vertically/obliquely reinforced 1–3 piezoelectric composite (PZC) and active fiber composite (AFC) materials are used as the materials of the constraining layer of theACLD treatment. The Golla–Hughes–McTavish (GHM) method has been implemented to model the constrained viscoelastic layer of the ACLD treatment in time domain. The first-order shear deformation theory (FSDT) and the Von Kármán type non-linear strain displacement relations are used for analyzing this coupled electro-elastic problem. A three dimensional finite element (FE) model of doubly curved laminated smart composite shells integrated with ACLD patches has been developed to investigate the performance of these patches for controlling the geometrically nonlinear transient vibrations of the shells. The numerical results indicate that the ACLD patches significantly improve the damping characteristics of the doubly curved laminated cross-ply and angle-ply shells for suppressing their geometrically nonlinear transient vibrations. It is found that the performance of the ACLD patch with its constraining layer being made of the AFC is significantly higher than that of the ACLD patch with vertically/obliquely reinforced 1–3 PZC constraining layer. The effects of variation of piezoelectric fiber orientation in both the obliquely reinforced 1–3 PZC and the AFC constraining layers on the control authority of the ACLD patches have also been investigated. [Copyright &y& Elsevier]

Abstract: This paper deals with the geometrically nonlinear dynamic analysis of functionally graded (FG) laminated composite plates integrated with a patch of active constrained layer damping (ACLD) treatment. The constraining layer of the ACLD treatment is considered to be made of the piezoelectric fiber reinforced composite (PFRC) material. Each layer of the substrate FG laminated composite plate is made of fiber-reinforced composite material in which the fibers are longitudinally aligned in the plane parallel to the top or bottom surface of the layer and the layer is assumed to be graded in the thickness direction by way of varying the fiber orientation angle across its thickness according to a power-law. The novelty of the present work is that, unlike the traditional laminated composite plates, the FG laminated composite plates are constructed in such a way that the continuous variation of material properties and stresses across the thickness of the plates is achieved. The constrained viscoelastic layer of the ACLD treatment is modeled using the Golla–Hughes–McTavish (GHM) method. Based on the first-order shear deformation (FSDT) theory, a finite element model has been developed to model the open-loop and closed-loop nonlinear dynamics of the overall FG laminated composite plates. Both symmetric and asymmetric FG laminated composite plates are considered as the substrate plates for presenting the numerical results. The analysis suggests the potential use of the ACLD treatment with its constraining layer made of the PFRC material for active control of geometrically nonlinear forced vibrations of FG laminated composite plates. The effect of piezoelectric fiber orientation in the active constraining PFRC layer on the damping characteristics of the overall FG plates is also investigated. [Copyright &y& Elsevier]

Abstract: In this paper, a nonlinear static finite element analysis of simply supported smart functionally graded (FG) plates in the presence/absence of the thermal environment has been presented. The substrate FG plate is integrated with the patches of piezoelectric fiber reinforced composite (PFRC) material which act as the distributed actuators of the plate. The material properties of the FG substrate plate are assumed to be temperature dependent and graded along the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The derivation of this nonlinear thermo-electro-mechanical coupled finite element model is based on the first order shear deformation theory and the Von Karman type geometric nonlinearity. The numerical solutions of the nonlinear equations of the finite element model are obtained by employing the direct iteration method. The numerical illustrations suggest the potential use of the distributed actuator made of the PFRC material for active control of nonlinear deformations of smart FG structures. The effects of volume fraction index of the FG material of the substrate plates and the locations of the PFRC patches on the control authority of the patches are investigated. Emphasis has also been placed on investigating the effect of variation of piezoelectric fiber orientation angle in the PFRC patches on their actuation capability for counteracting the large deflections of FG plates. [Copyright &y& Elsevier]

This paper is concerned with the static analysis of simply supported cross-ply substrate plates integrated with a layer of piezoelectric fiber reinforced composite material undergoing nonlinear deformations. The von Kármán type nonlinear strain displacement relations and first order shear deformation theory are used to formulate the variational model of this electromechanical coupled problem. Subsequently, Galerkin procedure is employed to derive the nonlinear algebraic governing equations which are solved by usingNewton-Raphson method. The results suggest the potential use of PFRC material for distributed control of nonlinear deformations of smart composite structures. The effect of variation of piezoelectric fiber orientation on the actuating capability of the PFRC actuator for counteracting the nonlinear deformations of the smart composite plates has also been investigated. [ABSTRACT FROM AUTHOR]

This paper deals with the analysis of vertically reinforced 1-3 piezoelectric composite materials as the material for the distributed actuator of smart laminated composite plates. A simple micromechanics model has been derived to predict the effective elastic and piezoelectric coefficients of these piezoelectric composites which are useful for the three dimensional analysis of smart structures. The main concern of this study is to investigate the performance of a layer of this vertically reinforced 1-3 piezoelectric composite material as the constraining layer of the active constrained layer damping (ACLD) treatment. A finite element model has been developed for analyzing the active constrained layer damping of laminated symmetric and antisymmetric cross-ply and angle-ply composite plates integrated with the patches of such ACLD treatment. Both in-plane and out-of-plane actuation of the constraining layer of the ACLD treatment have been utilized for deriving the finite element model. The analysis revealed that the vertical actuation dominates over the in-plane actuation. Particular emphasis has been placed on investigating the performance of the patches when the orientation angle of the piezoelectric fibers of the constraining layer is varied in the two mutually orthogonal vertical planes. Also, the effect of different boundary conditions on the performance of the patches has been studied. The analysis revealed that the vertically reinforced 1-3 piezoelectric composites which are in general being used for the distributed sensors can be potentially used for the distributed actuators of high performance light-weight smart structures. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the derivation of a finite element model for the static analysis of functionally graded (FG) plates integrated with a layer of piezoelectric fiber reinforced composite (PFRC) material. The layer of PFRC material acts as the distributed actuator of the FG plates. The Young’s modulus of the FG plate is assumed to vary exponentially along the thickness of the plate while the Poisson’s ratio is assumed to be constant over the domain of the plate. The finite element model has been verified with the exact solutions for both thick and thin plates. Emphasis has been placed on investigating the effect of variation of piezoelectric fiber angle in the PFRC layer on its actuating capability of the FG plates. The finite element solutions also revealed that the activated PFRC layer is more effective in controlling the deformations of the FG plates when the layer is attached to the surface of the FG plate with minimum stiffness than when it is attached to the surface of the same with maximum stiffness. [Copyright &y& Elsevier]

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. [ABSTRACT FROM AUTHOR]

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]

Presents information on a study which obtained a closed-form solution for the optimal control of vibrations of a symmetric thin laminated plate integrated with piezoelectric layers. Information on the plate model; Results; Conclusions.