Active damping of geometrically nonlinear vibrations of laminated composite shallow shells using vertically/obliquely reinforced 1-3 piezoelectric composites

This paper addresses the analysis of active constrained layer damping (ACLD) of geometrically nonlinear transient vibrations of laminated thin composite cylindrical shallow shells using vertically reinforced 1-3 piezoelectric composite (PZC). The constraining layer of the ACLD treatment is considered to be made of this 1-3 PZC material. The Golla–Hughes–McTavish (GHM) method has been implemented to model the constrained viscoelastic layer of the ACLD treatment in time domain. The Von Kármán type non-linear strain displacement relations and the first-order shear deformation theory (FSDT) are used for deriving this electromechanical coupled problem. A three dimensional finite element (FE) model of smart composite shallow shells integrated with a patch of such ACLD treatment has been developed to demonstrate the performance of the patch on enhancing the damping characteristics of thin laminated cylindrical shells, in controlling the geometrically nonlinear transient vibrations. The numerical results indicate that the ACLD patch significantly improves the damping characteristics of the shells for suppressing the geometrically nonlinear transient vibrations of the shells. The effect of variation of fiber orientation in the PZC material on the control authority of the ACLD patch has also been investigated.     

Smart damping of geometrically nonlinear vibrations of composite shells using fractional order derivative viscoelastic constitutive relations

In this article, a three-dimensional fractional order derivative model has been developed for the constrained viscoelastic layer of the active constrained layer damping (ACLD) treatment of laminated composite shells undergoing geometrically nonlinear vibrations. The constraining layer of the ACLD treatment is made of vertically/obliquely reinforced 1–3 piezoelectric composites and acts as the distributed actuator. A three-dimensional smart nonlinear finite element model has been developed. Several numerical results are presented to check the accuracy of the present three-dimensional fractional derivative model of the constrained viscoelastic layer for smart damping of geometrically nonlinear vibrations of laminated composite shells.     

Active control of large amplitude vibrations of smart magneto–electro–elastic doubly curved shells

This paper deals with the analysis of active constrained layer damping (ACLD) of large amplitude vibrations of smart magneto–electro–elastic (MEE) doubly curved shells. The constraining layer of the ACLD treatment is composed of the vertically/obliquely reinforced 1–3 piezoelectric composite (PZC). The constrained viscoelastic layer of the ACLD treatment is modeled by using the Golla–Hughes–McTavish method in the time domain. A three-dimensional finite element model of the overall smart MEE doubly curved shells has been developed taking into account the effects of electro–elastic and magneto–elastic couplings, while the von Kármán type nonlinear strain displacement relations are used for incorporating the geometric nonlinearity. Influence of the curvature ratio, the curvature aspect ratio, the thickness aspect ratio on the nonlinear frequency ratios of the MEE doubly curved shells has been investigated. Effects of the location of the ACLD patches and the edge boundary conditions on the control of geometrically nonlinear vibrations of paraboloid and hyperboloid MEE shells have been studied. Particular attention has been paid to investigate the performance of the ACLD treatment due to the variation of the piezoelectric fiber orientation angle in the 1–3 PZC constraining layer of the ACLD treatment.     

Control of geometrically nonlinear vibrations of skew laminated composite plates using skew or rectangular 1–3 piezoelectric patches

This paper deals with the analysis of active constrained layer damping (ACLD) of geometrically nonlinear transient vibrations of skew laminated composite plates using skew or rectangular patches of the ACLD treatment. The constraining layer of the patch of the ACLD treatment is composed of the vertically/obliquely reinforced 1–3 piezoelectric composite material. The Golla–Hughes–McTavish method has been used to model the constrained viscoelastic layer of the ACLD treatment in the time domain. A coupled electromechanical nonlinear three dimensional finite element model of skew laminated thin composite plates integrated with the skew or rectangular patches of ACLD treatment has been derived. The performance of the patches is investigated for different configurations of their placements on the top surface of the skew substrate plates. The analysis reveals that the ACLD treatment significantly improves the active damping characteristics of the skew laminated composite plates over the passive damping for suppressing their geometrically nonlinear transient vibrations. It is found that even though the substrate laminated plates are skew, a rectangular patch of the ACLD treatment located at the centre of the top surface of the substrate should be used for optimum damping of geometrically nonlinear vibrations of skew laminated composite plates irrespective of their skew angles and boundary conditions. The effects of piezoelectric fiber orientation angle and the skew angles of the substrate plates on the control authority of the ACLD patches have been emphatically investigated.     

Active constrained layer damping of geometrically nonlinear vibrations of smart laminated composite sandwich plates using 1–3 piezoelectric composites

This paper deals with the analysis of active constrained layer damping (ACLD) of geometrically nonlinear vibrations of sandwich plate with orthotropic laminated composite faces separated by a flexible core. The constraining layer of the ACLD treatment is composed of the vertically/obliquely reinforced 1?C3 piezoelectric composites. The Golla?CHughes?CMcTavish method has been implemented to model the constrained viscoelastic layer of the ACLD treatment in time domain. The first-order shear deformation theory and the Von Kármán type nonlinear strain displacement relations are used for analyzing this coupled electro-elastic problem. A three dimensional finite element model of smart laminated composite sandwich plate integrated with ACLD patches has been developed to investigate the performance of these patches for controlling the geometrically nonlinear vibrations of the plates. The numerical results indicate that the ACLD patches significantly improve the damping characteristics of the sandwich plates with laminated cross-ply and angle-ply facings for suppressing their geometrically nonlinear vibrations. Particular emphasis has been placed on investigating the effect of the variation of piezoelectric fiber orientation angle on the performance of the ACLD treatment.     

Active control of geometrically nonlinear transient vibrations of laminated composite cylindrical panels using piezoelectric fiber reinforced composite

This paper addresses the analysis of active constrained layer damping (ACLD) of geometrically nonlinear transient vibrations of laminated thin composite cylindrical panels using piezoelectric-fiber- reinforced composite (PFRC) materials. The constraining layer of the ACLD treatment is considered to be made of the PFRC materials. The Golla–Hughes–McTavish (GHM) method has been implemented to model the constrained viscoelastic layer of the ACLD treatment in time domain. The Von Kármán type-nonlinear strain-displacement relations and a simple first-order shear deformation theory are used for deriving this electromechanical coupled problem. A three-dimensional finite element (FE) model of smart composite panels 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 laminated cylindrical panels in controlling the geometrically nonlinear transient vibrations. The numerical results indicate that the ACLD patches significantly improve the damping characteristics of both symmetric and antisymmetric panels for suppressing the geometrically nonlinear transient vibrations of the panels. The effect of the shallowness angle of the panels on the control authority of the patches has also been investigated.     

Smart damping of geometrically nonlinear vibrations of functionally graded sandwich plates using 1–3 piezoelectric composites

Geometrically nonlinear dynamic analysis of smart functionally graded (FG) sandwich plates integrated with the patches of active constrained layer damping (ACLD) treatment has been carried out by the finite element method. The constraining layer of the ACLD treatment is considered to be made of vertically/obliquely reinforced 1–3 piezoelectric composite while the constrained layer is made of a viscoelastic material, which is modeled using the Golla–Hughes–McTavish method in the time domain. The top and bottom faces of the substrate sandwich plate are composed of the FG isotropic material whose mechanical properties are assumed to vary according to a standard power-law distribution in terms of the volume fractions of the constituents while the core layer may be either a soft honeycomb material or a hard ceramic material. Several FG sandwich plates with different core configurations are studied to evaluate the numerical results. The numerical results indicate that the ACLD patches significantly improve the damping characteristics of the FG sandwich plates for suppressing their geometrically nonlinear vibrations. Effects of metal- or ceramic-rich top and bottom surfaces, the variation of power-law index on the control authority of the ACLD patches have been investigated. Emphasis has also been placed on investigating the effect of the variation of piezoelectric fiber orientation angle on the performance of the ACLD patches.     

Analysis of smart damping of laminated composite beams using mesh free method

This paper is concerned with the development of mesh free model for the performance analysis of active constrained layered damping (ACLD) treatments on smart laminated composite beams. The overall structure is composed of a substrate laminated composite beam integrated with a viscoelastic layer and a piezoelectric layer attached partially or fully at the top surface of the substrate beam. The piezoelectric layer acts as the active constraining layer of the smart beam and the viscoelastic layer acts as the constrained layer. A layer wise displacement theory has been used to derive the models. Both symmetric cross-ply and antisymmetric angle-ply laminated beams are considered for the numerical analysis. It is observed that ACLD treatment significantly improves the active damping properties of the substrate beam. The numerical results also reveal that the triangular ACLD treatment is more effective than the rectangular ACLD treatment of same thickness and volume for active damping of smart composite beams.     

Active damping of geometrically nonlinear vibrations of laminated composite plates using vertically reinforced 1-3 piezoelectric composites

This paper addresses the analysis of active constrained layer damping (ACLD) of geometrically nonlinear transient vibrations of laminated composite plates using vertically reinforced 1-3 piezoelectric composite (PZC) as the material of the constraining layer of the ACLD treatment. The Von Kármán type nonlinear strain-displacement relations and the first-order shear deformation theory (FSDT) are used for deriving the coupled electromechanical nonlinear finite element model. The Golla?CHughes?CMcTavish (GHM) method has been used to model the constrained viscoelastic layer of the ACLD treatment in the time domain. The numerical results indicate that the ACLD patches significantly improve the damping characteristics of the cross-ply and antisymmetric angle-ply plates for suppressing the geometrically nonlinear transient vibrations of the plates.     

Active damping of geometrically nonlinear vibrations of doubly curved laminated composite shells

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.     

Active damping of laminated thin cylindrical composite panels using vertically/obliquely reinforced 1–3 piezoelectric composites

This paper deals with the analysis of active constrained layer damping (ACLD) of laminated thin composite panels using vertically and obliquely reinforced 1–3 piezoelectric composite materials as the material of the constraining layer of the ACLD treatment. A finite element model has been developed for analyzing the ACLD of laminated antisymmetric cross-ply and antisymmetric angle-ply thin composite panels integrated with the patches of such ACLD treatment. Both in-plane and out-of-plane actuations 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. 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 thin composite panels.     

Hybrid damping of smart, functionally graded plates using piezoelectric, fiber-reinforced composites

This paper deals with the investigation of active, constrained layer damping (ACLD) of smart, functionally graded (FG) plates. The constraining layer of the ACLD treatment is considered to be made of a piezoelectric, fiber-reinforced composite (PFRC) material with enhanced effective piezoelectric coefficient that quantifies the in-plane actuating force due to the electric field applied across the thickness of the layer. The Young's modulus and the mass density of the FG plates are assumed to vary exponentially along the thickness of the plate, and the Poisson's ratio is assumed to be constant over the domain of the plate. A finite-element model has been developed to model the open-loop and closed-loop dynamics of the FG plates integrated with two patches of ACLD treatment. The frequency response of the plates revealed that the active patches of ACLD treatment significantly improve the damping characteristics of the FG plates over the passive damping. Emphasis has been placed on investigating the effect of variation of piezoelectric fiber angle in the constraining layer of the ACLD treatment on the attenuating capability of the patches. The analysis also revealed that the activated patches of the ACLD treatment are more effective in controlling the vibrations of FG plates when the patches are attached to the surface of the FG plates with minimum stiffness than when they are attached to the surface of the same with maximum stiffness.     

Active structural-acoustic control of laminated composite plates using vertically/obliquely reinforced 1–3 piezoelectric composite patch

This article deals with the active structural-acoustic control of thin laminated composite plates using vertically reinforced 1–3 piezoelectric fiber-reinforced composite (PFRC) material for constraining layer of active constrained layer damping (ACLD) treatment. A finite element model is developed for the laminated composite plates integrated with ACLD patches and coupled with acoustic cavity to describe the coupled structural-acoustic behavior of the plates enclosing the cavity. 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. The performance of PFRC layers of the patches has been investigated for active control of sound radiated from thin symmetric and antisymmetric cross-ply and antisymmetric angle-ply laminated composite plates into the acoustic cavity.     

Vibration and damping characteristics of beams with active constrained layer treatments under parametric variations

Hybrid damping designs with active piezoelectric materials and passive viscoelastic materials (VEMs) combine the advantages of both active and passive constrained layer damping (ACLD/PCLD) treatments.Researchers have established the standards for the extent and placement of the PCLD treatment for common structures. However for ACLD treatment, such detailed studies are not available. This study is aimed to examine, the effect of parametric variation of active constrained layer on the vibration control of the beams treated with optimally placed active or passive constrained layer damping patches. Finite element model is developed to model the open-loop and close-loop dynamics of active/passive constrained layer damping treated beam. The placement strategies of ACLD patches are devised using the modal strain energy (MSE) approach. Extensive experimentation studies are conducted by making twenty one separate samples of ACLD/PCLD treated beams with variations in viscoelastic material layer thickness, ACLD/PCLD patch coverage and location of the patch. Effects of key parameters, such as control gain, viscoelastic material thickness, coverage and location variation of ACLD patch on the system loss factor have been investigated. The careful analysis of results from partially covered ACLD treated beam suggests that the maximum damping of the first mode can be achieved by attaching the ACLD patch only up to 50% coverage. It also reveals that with proper choice of the control voltage and thickness, the effective loss factor can be almost doubled. The present study suggests the potential use of parametric studies that establish some guide lines for the extent and placement of the ACLD patches on the cantilevered beam.     

Performance of piezoelectric fiber-reinforced composites for active structural-acoustic control of laminated composite plates

This paper deals with the active structural acoustic control of thin laminated composite plates using piezoelectric fiber-reinforced composite (PFRC) material for the constraining layer of active constrained layer damping (ACLD) treatment. A finite element model is developed for the laminated composite plates integrated with the patches of ACLD treatment to describe the coupled structural-acoustic behavior of the plates enclosing an acoustic cavity. The performance of the PFRC layers of the patches has been investigated for active control of sound radiated from thin symmetric and antisymmetric cross-ply and antisymmetric angle-ply laminated composite plates into the acoustic cavity. The significant effect of variation of piezoelectric fiber orientation in the PFRC layer on controlling the structure-borne sound radiated from thin laminated plates has been investigated to determine the fiber angle in the PFRC layer for which the structural-acoustic control authority of the patches becomes maximum.     

Smart control of nonlinear vibrations of doubly curved functionally graded laminated composite shells under a thermal environment using 1–3 piezoelectric composites

This paper addresses the active control of geometrically nonlinear vibrations of doubly curved functionally graded (FG) laminated composite shells integrated with a patch of active constrained layer damping (ACLD) treatment under the thermal environment. Vertically/obliquely reinforced 1-3 piezoelectric composite (PZC) and active fiber composite (AFC) are used as the materials of the constraining layer of the ACLD treatment. Each layer of the substrate FG laminated composite shell 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 shells, the FG laminated composite shells are constructed in such a way that the continuous variation of material properties and stresses across the thickness of the shell is achieved. The Golla-Hughes-McTavish (GHM) method has been implemented to model the constrained viscoelastic layer of the ACLD treatment in time domain. Based on the first-order shear deformation theory (FSDT), a finite element (FE) model has been developed to model the open-loop and closed-loop nonlinear dynamics of the overall FG laminated composite shell under a thermal environment. Both symmetric and asymmetric FG laminated composite doubly curved shells are considered for presenting the numerical results. The analysis suggests that the ACLD patch significantly improves the damping characteristics of the doubly curved FG laminated composite 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 material 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 patch have also been investigated.     

Active constrained layer damping of smart laminated composite sandwich plates using 1–3 piezoelectric composites

This paper deals with the analysis of active constrained layer damping (ACLD) of sandwich plate with laminated composite faces. The constraining layer of the ACLD treatment is composed of the vertically/obliquely reinforced 1?C3 piezoelectric composites. Several honeycomb core materials like HEREX honeycomb and honeycomb with foam fill separated by different facing materials have been studied and a three-dimensional finite element model has been developed considering first order shear deformation theory individually for each layer of the sandwich plate. The effect of the ratio between the face sheet thickness and the core thickness of the sandwich plate on the frequency response has been studied. Particular emphasis has been placed on investigating the effect of the variation of piezoelectric fiber orientation angle on the performance of the ACLD treatment.     

Multiscale design of a rectangular sandwich plate with viscoelastic core and supported at extents by viscoelastic materials

This work presents a multiscale model of viscoelastic constrained layer damping treatments for vibrating plates/beams. The approach integrates a finite element (FE) model of macroscale vibrations and a micromechanical model to include effects of microscale structure and properties. The FE model captures the shear deformation of the viscoelastic core, rotary inertial effects of all layers, and viscoelastic boundaries of the plate. Comparison with analytical and FE results validates the proposed FE model. A self-consistent (SC) model makes the micro to macro scale transition to approximate the effective behavior a heterogeneous core. Modal damping resulting from the presence of voids and negative stiffness regions in the core material is modeled. Results show that negative stiffness regions in the viscoelastic core material, even at low volume fractions, yield superior macroscopic damping behavior. The coupled SC and FE models provide a powerful multiscale predictive design tool for sandwich beams and plates.     

Dynamic analysis and damping of composite structures embedded with viscoelastic layers

In recent years, it has been found that composites co-cured with viscoelastic materials can enhance the damping capacity of a composite structural system with little reduction in stiffness and strength. Because of the anisotropy of the constraining layers, the damping mechanism of co-cured composites is quite different from that of conventional structures with metal constraining layers. This paper presents an analysis of the dynamic properties of multiple damping layer, laminated composite beams with anisotropic stiffness layers, by means of the finite element-based modal strain energy method. ANSYS 4.4A finite element software has been used for this study. The variation of resonance frequencies and modal loss factors of various beam samples with temperature is studied. Some of these results are compared with the closed-form theoretical results of an earlier published work. For obtaining optimium dynamic properties, the effects of different parameters, such as layer orientation angle and compliant layering, are studied. Also, the effect of using a combination of different damping materials in the system for obtaining stable damping properties over a wide temperature range is studied.     

Nonlinear damping and forced vibration analysis of laminated composite beams

The purpose of the present work it to study the damping and forced vibrations of three-layered, symmetric laminated composite beams. In the analytical formulation, both normal and shear deformations are considered in the core by using the higher-order zig-zag theories. The harmonic balance method is coupled with a one mode Galerkin procedure for a simply supported beam. The geometrically nonlinear coupling leads to a nonlinear frequency amplitude equation governed by several complex coefficients. In the first part of the paper, linear and nonlinear damping parameters of laminated composite beams are obtained. In the second part, nonlinear forced vibration analysis is carried out for small and large vibration amplitudes. The frequency response curves are presented and discussed for various geometric and material properties.