Active Constrained Layer Research Articles

Active vibration control of smart beam under parametric variations

Vibration control is one of the prominent factors, especially in lightweight structures in space technology. These structures, due to their low mass and thinness, frequently lose the stability under environmental disturbances. Piezoelectric materials as sensors/actuators have been widely used to control vibrations and mode shapes of such structures. Nowadays, piezoelectric and passive materials like viscoelastic materials have shown combined advantage of hybrid damping (active constrained layer damping) and with different parametric variations in them have shown remarkable property for control authority. This paper presents the details of parametric variations in smart structure using energy methods to demonstrate the utility for further structure design. Finite element model has been implemented using MATLAB software to analyze its effect of various parameters. Different environmental temperatures as thermal loads have been considered, and their effect on damping ratio is investigated. Parameters like percentage coverage of viscoelastic, piezoelectric material patches and the shape of patches on damping characteristics have been demonstrated.

Moment approach to the boundary exact controllability of an active constrained layer beam

Using the moment approach, we consider the boundary exact controllability of an active constrained layer (ACL) beam consisting of three layers, which is modeled as a Rayleigh beam coupled with two wave equations. We convert the controllability problem of the ACL beam into a corresponding moment problem which can be solvable in a Hilbert space ℓ2. Then, we conclude that the ACL beam is exactly controllable when the control time is greater than the maximum value among of the optical lengths of the two waves and the square root of the moment of inertia of the Rayleigh beam. The well-posedness and asymptotic spectral expressions of the ACL beam are also presented.

Performance analysis of smart laminated composite plate integrated with distributed AFC material undergoing geometrically nonlinear transient vibrations

The present work focuses on geometrically nonlinear transient analysis of laminated smart composite plates integrated with the patches of Active fiber composites (AFC) using Active constrained layer damping (ACLD) as the distributed actuators. The analysis has been carried out using generalised energy based finite element model. The coupled electromechanical finite element model is derived using Von Karman type nonlinear strain displacement relations and a first-order shear deformation theory (FSDT). Eight-node iso-parametric serendipity elements are used for discretization of the overall plate integrated with AFC patch material. The viscoelastic constrained layer is modelled using GHM method. The numerical results shows the improvement in the active damping characteristics of the laminated composite plates over the passive damping for suppressing the geometrically nonlinear transient vibrations of laminated composite plates with AFC as patch material.

Vibration control of multiferroic fibrous composite plates using active constrained layer damping

Abstract Geometrically nonlinear vibration control of fiber reinforced magneto-electro-elastic or multiferroic fibrous composite plates using active constrained layer damping treatment has been investigated. The piezoelectric (BaTiO3) fibers are embedded in the magnetostrictive (CoFe2O4) matrix forming magneto-electro-elastic or multiferroic smart composite. A three-dimensional finite element model of such fiber reinforced magneto-electro-elastic plates integrated with the active constrained layer damping patches is developed. Influence of electro-elastic, magneto-elastic and electromagnetic coupled fields on the vibration has been studied. The Golla–Hughes–McTavish method in time domain is employed for modeling a constrained viscoelastic layer of the active constrained layer damping treatment. The von Karman type nonlinear strain-displacement relations are incorporated for developing a three-dimensional finite element model. Effect of fiber volume fraction, fiber orientation and boundary conditions on the control of geometrically nonlinear vibration of the fiber reinforced magneto-electro-elastic plates is investigated. The performance of the active constrained layer damping treatment due to the variation of piezoelectric fiber orientation angle in the 1–3 Piezoelectric constraining layer of the active constrained layer damping treatment has also been emphasized.

Active damping of multiferroic composite plates using 1–3 piezoelectric composites

A layer-wise shear deformation theory is used to analyze the smart damping of multiferroic composite or magneto-electro-elastic (MEE) plates. The intent of this analysis is to investigate the need for incorporating additional smart elements for controlling the vibrations of multiferroic composite plates. Active constrained layer damping (ACLD) treatment has been incorporated to alleviate the vibration of MEE plate. A layer of viscoelastic material is used as constrained layer for the ACLD treatment. The coupled constitutive equations of multiferroic (ferroelectric and ferromagnetic) composite materials along with the total potential energy principle are used to derive the finite element formulation for the overall multiferroic or MEE plate. Maxwell’s electrostatic and electromagnetic relations are used to compute the electric and magnetic potential distribution. Influence of obliquely reinforced piezoelectric fibers in the piezoelectric layer of the ACLD treatment has also been investigated. In order to investigate the importance of using ACLD treatment for an active damping of multiferroic or MEE plate, an active control of MEE plate has also been analyzed by providing the control voltage directly to the piezoelectric layers of the MEE substrate plate without using the ACLD treatment. The present study suggests that for an optimal control of MEE plates, the smartness element such as the ACLD treatment is essentially required.

Control of large amplitude vibrations of doubly curved sandwich shells composed of fuzzy fiber reinforced composite facings

This paper is concerned with the analysis of active constrained layer damping (ACLD) of geometrically nonlinear vibrations of doubly curved sandwich shells with facings composed of fuzzy fiber reinforced composite (FFRC). FFRC is a novel composite where the short carbon nanotubes (CNTs) which are either straight or wavy are radially grown on the periphery of the long continuous carbon fiber reinforcements. The plane of waviness of the CNTs is coplanar with the plane of carbon fiber. The constraining layer of the ACLD treatment is composed of the vertically/obliquely reinforced 1–3 piezoelectric composites (PZCs) while the constrained viscoelastic layer has been sandwiched between the substrate and the PZC layer. The Golla–Hughes–McTavish (GHM) method has been implemented to model the constrained viscoelastic layer of the ACLD treatment in time domain. A three dimensional finite element (FE) model of smart doubly curved FFRC sandwich shells integrated with ACLD patches has been developed to investigate the performance of these patches for controlling the geometrically nonlinear vibrations of these shells. This study reveals that the performance of the ACLD patches for controlling the geometrically nonlinear vibrations of the doubly curved sandwich shells is better in the case of the facings composed of laminated FFRC than that in the case of the facings made of conventional orthotropic laminated composite. The research carried out in this paper brings to light that even the wavy CNTs can be properly utilized for attaining structural benefits from the exceptional elastic properties of CNTs.

Modeling and Controlling an Active Constrained Layer (ACL) Beam Actuated by Two Voltage Sources With/Without Magnetic Effects

A fully dynamic three-layer active constrained layer (ACL) beam is modeled for cantilevered boundary conditions by using a thorough variational approach. The Rao-Nakra thin compliant layer assumptions are adopted to model the sandwich structure, and all magnetic effects for the piezoelectric layers are retained. The piezoelectric layers are activated by two different voltage sources. When there are no "mechanical" boundary forces acting in the longitudinal direction, it is shown that the system with certain parameter combinations is not uniformly strongly stabilizable by the $B^*-$type feedback controller, which is the total current accumulated at the electrodes for the piezoelectric layers. However, as the magnetic effects are ignored (electrostatic assumption), the closed-loop system with all mechanical feedback controllers is shown to be uniformly exponentially stable.

Exponential stability of an active constrained layer beam actuated by a voltage source without magnetic effects

We study the boundary stabilization of an active constrained layer (ACL) beam consisting of a stiff layer, a viscoelastic layer and a piezoelectric layer. The piezoelectric layer is actuated by a voltage source without magnetic effects. The system is modeled as a Rayleigh beam coupled with two wave equations. By using an asymptotic technique, we present the asymptotic expressions for the eigenpairs of the system. We show that the generalized eigenfunctions form a Riesz basis in the state space, and hence the spectrum determined growth condition holds. Finally, the exponential stability of the closed-loop system is established.

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

ABSTRACTIn 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.

A design of active constrained layer damping treatment for vibration control of circular cylindrical shell structure

A new 1-3 viscoelastic composite material (VECM) layer is designed for improved active constrained layer damping (ACLD) treatment of vibration of a functionally graded (FG) circular cylindrical shell. Besides this improved active damping treatment, another objective of this study is to control all the modes of vibration of the shell effectively using the treatment (active constrained layer damping) in layer-form throughout the outer shell-surface. In this design of active constrained layer damping treatment in layer-form, its (active constrained layer damping) necessary conformability with the curved host shell-surface is ensured by the use of a vertically reinforced 1-3 piezoelectric composite (PZC) constraining layer, whereas the effective control of several modes of vibration of the shell is achieved by the use of electrode-patches over the surfaces of the constraining layer. A fruitful strategy in the arrangement of electrode-patches is proposed for effective control of several modes of vibration of the shell using one configuration of the electrode-patches. An electric potential function is assumed for this use of electrode-patches and a geometrically nonlinear coupled electro-visco-elastic incremental finite element model of the overall shell is developed for its analysis in the frequency-domain. The analysis reveals significant improvement of active damping characteristics of the active constrained layer damping layer for the use of the present 1-3 viscoelastic composite material layer instead of the traditional monolithic viscoelastic material (VEM) layer. The analysis also reveals the suitability of the present strategy of arrangement of electrode-patches for achieving aforesaid control-activity of the ACLD layer. The effects of temperature in the host functionally graded shell and different geometric parameters in the design of the 1-3 viscoelastic composite material layer on the damping characteristics of overall shell are also presented.

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

ABSTRACTGeometrically 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.

Active Vibration Control of Smart Functionally Graded Beams

This work is devoted to examine the performance of the constraining layer of the active constrained layer damping (ACLD) treatment made of the active fiber composites (AFC) materials for vibration control of functionally graded (FG) beams. The task of investigating the performance of the active constrained layer damping (ACLD) treatment has been accomplished to demonstrate the use of AFCs as the materials for distributed actuators. Finite Element (FE) model is developed to describe the open loop and closed loop dynamics of the FG beams integrated with the patches of the ACLD treatment. The closed loop frequency response functions computed by the FE models reveal that the ACLD treatment with its constraining layer composed of AFC material significantly enhances the damping characteristics of the FG beams.The performance of the ACLD treatment when the orientation angle of the piezoelectric fibers of the AFC constraining layer is varied has also been investigated. Such variation of piezoelectric fiber orientation angle significantly affects the controllability of the ACLD treatment for active damping of the FG beams. The investigations carried out here may be useful for further experimental verifications and suggest the potential use of AFC materials for developing new distributed actuators of light-weight smart structures.

基于主动约束阻尼层的次镜支撑结构设计

基于主动约束阻尼层的次镜支撑结构设计

基于主动约束阻尼层的次镜支撑结构设计

基于主动约束阻尼层的次镜支撑结构设计

Three-dimensional fractional derivative model of smart constrained layer damping treatment for composite plates

This paper deals with the finite element analysis of active constrained layer damping (ACLD) of laminated composite plates using fractional order derivative constitutive relations for viscoelastic material. The constraining layer of the ACLD treatment is composed of the vertically/obliquely reinforced 1–3 piezoelectric composites (PZCs). The novelty of the present analysis is that the three dimensional fractional derivative model (FDM) of the constrained viscoelastic layer has been derived in time domain. A three-dimensional finite element model has been developed based on the FDM of the viscoelastic layer. Thin laminated plates with various boundary conditions and stacking sequences are emphatically analyzed to investigate the effectiveness of the three-dimensional FDM for both the passive and active control authority of the ACLD patch.

Acoustic radiation from the submerged circular cylindrical shell treated with active constrained layer damping**Project supported by the National Natural Science Foundation of China (Grant Nos. 11162001, 11502056, and 51105083), the Natural Science Foundation of Guangxi Zhuang Autonomous Region, China (Grant No. 2012GXNSFAA053207), the Doctor Foundation of Guangxi University of Science and Technology, China (Grant No. 12Z09), and the Development Project

Based on the transfer matrix method of exploring the circular cylindrical shell treated with active constrained layer damping (i.e., ACLD), combined with the analytical solution of the Helmholtz equation for a point source, a multi-point multipole virtual source simulation method is for the first time proposed for solving the acoustic radiation problem of a submerged ACLD shell. This approach, wherein some virtual point sources are assumed to be evenly distributed on the axial line of the cylindrical shell, and the sound pressure could be written in the form of the sum of the wave functions series with the undetermined coefficients, is demonstrated to be accurate to achieve the radiation acoustic pressure of the pulsating and oscillating spheres respectively. Meanwhile, this approach is proved to be accurate to obtain the radiation acoustic pressure for a stiffened cylindrical shell. Then, the chosen number of the virtual distributed point sources and truncated number of the wave functions series are discussed to achieve the approximate radiation acoustic pressure of an ACLD cylindrical shell. Applying this method, different radiation acoustic pressures of a submerged ACLD cylindrical shell with different boundary conditions, different thickness values of viscoelastic and piezoelectric layer, different feedback gains for the piezoelectric layer and coverage of ACLD are discussed in detail. Results show that a thicker thickness and larger velocity gain for the piezoelectric layer and larger coverage of the ACLD layer can obtain a better damping effect for the whole structure in general. Whereas, laying a thicker viscoelastic layer is not always a better treatment to achieve a better acoustic characteristic.

Active damping of geometrically nonlinear vibrations of sandwich plates with fuzzy fiber reinforced composite facings

This paper is concerned with the analysis of active constrained layer damping (ACLD) of geometrically nonlinear vibrations of sandwich plates with facings composed of fuzzy fiber reinforced composite (FFRC). FFRC is a novel composite where the short carbon nanotubes (CNTs) which are either straight or wavy are radially grown on the periphery of the long continuous carbon fiber reinforcements. The plane of waviness of the CNTs is coplanar with the plane of carbon fiber. The constraining layer of the ACLD treatment is composed of the vertically/obliquely reinforced 1–3 piezoelectric composites (PZCs) while the constrained viscoelastic layer has been sandwiched between the substrate and the PZC layer. The Golla–Hughes–McTavish method has been implemented to model the constrained viscoelastic layer of the ACLD treatment in time domain. A three dimensional nonlinear finite element model of smart FFRC sandwich plates integrated with ACLD patches has been developed to investigate the performance of these patches for controlling the geometrically nonlinear vibrations of these plates. This study reveals that the performance of the ACLD patches for controlling the geometrically nonlinear vibrations of the sandwich plates is better in the case of the facings composed of laminated FFRC than that in the case of the facings made of conventional orthotropic laminated composite. Particular emphasis has been placed on investigating the effect of the variation of piezoelectric fiber orientation angle on the performance of the ACLD treatment. The research carried out in this paper brings to light that even the wavy CNTs can be properly utilized for attaining structural benefits from the exceptional elastic properties of CNTs.

Control of geometrically nonlinear vibrations of functionally graded magneto-electro-elastic plates

This article deals with the analysis of active damping of geometrically nonlinear vibrations of functionally graded magneto-electro-elastic (FGMEE) plates integrated with the patches of the active constrained layer damping (ACLD) treatment. 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 a Golla–Hughes–McTavish (GHM) method in time domain. The material properties of the FGMEE plate are assumed to be functionally graded along the thickness direction according to a simple power-law distribution. Based on the layer-wise shear deformation theory, a three-dimensional finite element (FE) model of the overall smart FGMEE plate has been developed taking into account the effects of coupling between elasticity, electric and magnetic fields, while the von Kármán type nonlinear strain displacement relations are used for incorporating the geometric nonlinearity. Influence of the variation of the power law index, material gradation, edge boundary conditions and the piezoelectric fiber orientation angle in the 1–3 PZC constraining layer of the ACLD treatment on the control of geometrically nonlinear vibrations of the FGMEE plates have been investigated.

Further stabilization and exact observability results for voltage-actuated piezoelectric beams with magnetic effects

It is well known that magnetic energy of the piezoelectric beam is relatively small, and it does not change the overall dynamics. Therefore, the models, relying on electrostatic or quasi-static approaches, completely ignore the magnetic energy stored/produced in the beam. A single piezoelectric beam model without the magnetic effects is known to be exactly observable and exponentially stabilizable in the energy space. However, the model with the magnetic effects is proved to be not exactly observable / exponentially stabilizable in the energy space for almost all choices of material parameters. Moreover, even strong stability is not achievable for many values of the material parameters. In this paper, it is shown that the uncontrolled system is exactly observable in a space larger than the energy space. Then, by using a $B^*-$type feedback controller, explicit polynomial decay estimates are obtained for more regular initial data. Unlike the classical counterparts, this choice of feedback corresponds to the current flowing through the electrodes, and it matches better with the physics of the model. The results obtained in this manuscript have direct implications on the controllability/stabilizability of smart structures such as elastic beams/plates with piezoelectric patches and the active constrained layer (ACL) damped beams/plates.

Effect of carbon nanotube waviness on active damping of laminated hybrid composite shells

In this article, we investigate the effect of carbon nanotube (CNT) waviness on the active constrained layer damping (ACLD) of the laminated hybrid composite shells. In particular, the effect of CNT waviness has been studied for the case of a novel nano-tailored composite—continuous fuzzy fiber-reinforced composite (FFRC). The distinctive feature of the construction of the FFRC is that the uniformly spaced straight or wavy CNTs are radially grown on the circumferential surfaces of carbon fibers. The constraining layer of the ACLD treatment is considered to be made of vertically or obliquely reinforced 1–3 piezoelectric composite material. A three-dimensional finite element model has been developed to study the damping characteristics of the laminated FFRC shells integrated with the patches of ACLD treatment. Our results reveal that (i) the planar orientation of CNT waviness has a significant influence on the damping characteristics of the laminated FFRC shells, (ii) damping characteristics of the symmetric cross-ply, and antisymmetric angle-ply laminated FFRC shells are improved if CNT waviness is coplanar with the longitudinal plane of the carbon fiber, and (iii) for the antisymmetric cross-ply laminated FFRC shells, the performance of the ACLD patches becomes maximum for attenuating the fundamental mode when CNT waviness is coplanar with the transverse plane of the carbon fiber.