Constrained Layer Damping Treatment Research Articles

Active damping of geometrically nonlinear vibrations of smart composite shells using elliptical smart constrained layer damping treatment with fractional derivative viscoelastic layer

In this article, the performance of elliptical smart constrained layer damping treatments on active damping of geometrically nonlinear vibrations of doubly curved smart laminated composite shells is analyzed. The constraining layers of the smart constrained layer damping treatments comprised vertically/obliquely reinforced 1–3 piezoelectric composites, while the constrained layers of isotropic viscoelastic materials are modeled using the three-dimensional fractional order derivative model. A mesh-free model of the smart composite shells is developed for analyzing their nonlinear transient responses within the framework of a layerwise shear and normal deformation theory considering the von Kármán–type geometric nonlinearity. Thin, doubly curved laminated composite shells integrated with elliptical/rectangular smart constrained layer damping patches with different stacking sequences and boundary conditions are considered for presenting the numerical results. The numerical analyses demonstrate the higher effectiveness of the elliptical smart constrained layer damping treatments over the rectangular ones in attenuating the nonlinear vibrations of laminated composite shells.

Vibration analysis of a free moving thin plate with fully covered active constrained layer damping treatment

A comprehensive dynamic model for a free moving thin plate with fully covered active constrained layer damping (ACLD) treatment is developed. The discrete equations of motion of the moving ACLD plate are derived by using Ritz method and Lagrange’s equations. Free vibration analysis of the composite plate undergoing large rotational or translational motions are performed by solving the complex modal eigenvalue problem of the system in open-loop and closed-loop cases. Interesting frequency curve veering, mode shape switching as well as damping ratio jumping phenomena are observed and discussed for the plate rotating around two different axes. It is demonstrated that the flexible plate undergoing rigid motions can not only generate dynamic stiffening effect but also dynamic softening effect. Effects of parameters such as angular velocity, acceleration, and control gain on the modal and damping characteristics of the ACLD plate are also investigated.

Influence of active constrained layer damping on the coupled vibration response of functionally graded magneto-electro-elastic plates with skewed edges

This article makes the first attempt in assessing the influence of active constrained layer damping (ACLD) treatment towards precise control of frequency responses of functionally graded skew-magneto-electro-elastic (FGSMEE) plates by employing finite element methods. The materials are functionally graded across the thickness of the plate in terms of modest power-law distributions. The principal equations of motion of FGSMEE are derived via Hamilton’s principle and solved using condensation technique. The effect of ACLD patches are modelled by following the complex modulus approach (CMA). Additionally, distinctive emphasis is laid to evaluate the influence of geometrical skewness on the attenuation capabilities of the plate. The accuracy of the current analysis is corroborated with comparison of previous researches of similar kind. Additionally, a complete parametric study is directed to understand the combined impacts of various factors like coupling fields, patch location, fiber orientation of piezoelectric patch in association with skew angle and power-law index.

Comparative study on performance of controlling geometric nonlinearity of laminated smart composite plate using piezoelectric fiber reinforced composite & active fiber composite material

The present work highlights on comparative investigation for the performance of active constrained layer damping treatment using PFRC and AFC patch material for controlling the nonlinear transient vibrations of laminated composite plate. In this case for making the constraining layer of the ACLD treatment for PFRC and AFC patch material is used. For modelling of ACLD in the time domain Golla-Hughes-McTavish (GHM) method is used. The Von Karman type non-linear strain displacement relations along with a simple first-order shear deformation theory are used for deriving this electromechanical coupled problem. A finite model in 3-dimensions has been developed for smart composite plate integrated with the ACLD treated patches of PFRC and AFC. The results of both the cases have been compared and it has been found that the improved performance of AFC patch over the PFRC in subsiding the transient nonlinear vibrations of symmetric cross ply laminated composite plate.

Comparative investigation on nonlinear transient vibrations of laminated composite shallow shell with active constrained layer damping treatment using PFRC and AFC patch material

Here, the comparative investigation for the performance of active constrained layer damping treatment using PFRC and AFC patch material for controlling the nonlinear transient vibrations of laminated composite shallow shell is carried out. The patch material used in this case for making the constraining layer of the ACLD treatment is PFRC and AFC. For modelling of ACLD in the time domain Golla-Hughes-McTavish (GHM) method is used. The Von Kármán type non-linear strain displacement relations along with a simple first-order shear deformation theory are used for deriving this electromechanical coupled problem. A finite model in 3-dimensions have been developed for smart composite shallow shell integrated with the ACLD treated patches of PFRC and AFC. The results of both the cases have been compared and it has been found that the improved performance of AFC patch over the PFRC in subsiding the transient nonlinear vibrations of symmetric cross ply laminated composite shallow shell.

Active Control of Nonlinear Transient Vibration of Laminated Composite Beams Using Triangular SCLD Treatment With Fractional Order Derivative Viscoelastic Model

Abstract This paper is concerned with the analysis of the effectiveness of triangular shaped smart constrained layer damping (SCLD) treatment in attenuating geometrically nonlinear transient vibrations of laminated composite beams. The SCLD treatment is comprised of an advanced vertically reinforced 1–3 piezoelectric composite (PZC) as the constraining layer and an isotropic viscoelastic layer as the constrained layer, which is modeled using a two-dimensional fractional order derivative (FOD) model with Grünwald definition of the FODs. A nonlinear meshfree model of the smart composite beam is developed for analyzing its nonlinear transient response within the framework of a layerwise shear and normal deformation theory considering von Kármán type geometric nonlinearity. Cantilever type composite beams having different lamination sequences integrated with regular rectangular/triangular type of SCLD treatments are considered for presenting the numerical results. For comparison purpose, a geometrical constraint has been imposed such that both the rectangular and triangular shaped SCLD treatments will cover the equal area on the top surface of the beam. The numerical analyses demonstrate the effectiveness of the triangular shaped SCLD patches over the rectangular SCLD treatment in controlling the nonlinear vibration of laminated composite beams. The two-dimensional FOD model of the viscoelastic material has been efficiently implemented for the active damping analysis of smart composite beam.

Dynamic modeling and vibration control of a rotating space flexible arm with enhanced active constrained layer damping treatment

In this paper, an active-passive control technology called as enhanced active constrained layer damping (EACLD) is applied to structural vibration suppression of a rigid-flexible coupled hub-beam system. The longitudinal shortening of the beam caused by the transverse deformation is considered so that the high-order geometrically nonlinear terms are obtained. By using the Euler-Bernoulli beam theory and describing the VEM with a complex shear modulus, and using the assumed mode method together with Lagrange’s equations, the discrete high-order dynamic equations of the system with EACLD treatment are derived in the closed-loop case with a PD controller. Based on the new dynamic model, the dynamic behavior of the rotating EACLD beam is described in the time domain. The effects of coverage ratio of the control patch, mass of edge element, control gain and edge element location on the dynamic responses of the system are investigated. The results obtained show that the influences of edge element stiffness and mass can be helpful to designs of structural vibration control.

Dynamic modeling and vibration analysis of rotating beams with active constrained layer damping treatment in temperature field

A new rigid-flexible coupled dynamic model considering temperature variation is developed for rotating beams with active constrained layer damping (ACLD) treatment in closed-loop and open-loop cases. By solving the corresponding linearized vibration equations of the smart system, the thermal vibration characteristics of the system in the two cases are analyzed. Influences of parameters, such as the angular velocity, the temperature, the gains of PD control, on the modal frequencies and damping ratios of the smart beam are discussed. Simulation results show that the variation of temperature can strongly affect the modal frequencies and damping performance of the ACLD beam, and there are critical temperatures that can change the damping performance of the ACLD beam in both open-loop and closed-loop cases. Research in this paper will be helpful for the dynamics of high speed rotating blades operating under thermal environment.

Passive vibration control of plate using nodal patterns of mode shape

Passive constrained layer damping (PCLD) is nowadays a general method for reducing vibrations. Constrained layer damping (CLD) is a very good technology in terms of reducing vibration energy. This paper deals with optimal damping of first three modes of a thin square cantilever plate by constrained viscoelastic layers which are positioned according to the nodal patterns of the mode. In essence, the CLD patches are cut according to the nodal patterns and then applied on to the bare plate. Thus, this approach uses prior information of the deformation patterns of the plate. The ABAQUS finite element analysis software was used to create viscoelastically damped plate models subjected to forced vibration. The direct steady-state dynamic analysis was used to obtain the frequency response functions from which the resonance frequencies of the models were derived. Vibration control using nodal pattern CLD patches is a better way to apply CLD treatment to a plate. This is because the mode shapes give good predictions of where the maximum strains are in the plate as well as the design and size of the damping patches required. It is believed that the methodology proposed in this research work is capable of providing good results.

Vibration Control of an Aero Pipeline System with Active Constraint Layer Damping Treatment

In this paper, vibration control of an aero pipeline system using active constrained layer damping treatment has been investigated in terms of the vibration and stress distribution. A three-dimensional finite element model of such a pipeline with active constrained layer damping (ACLD) patches is developed. The transfer of the driving force under harmonic voltage is analyzed based on the finite element model. The vibration control of the pipeline with active constrained layer damping treatment under different voltages is computed to analyze the influence of control parameters and structural parameters on the control effect. An experiment platform is developed to validate the above relations. Results show that the performance of the active constrained layer damping treatment is affected by the elastic modulus and thickness of the viscoelastic layer, control voltage and structure size. The performance increases significantly with the rising of the control voltage and cover area of ACLD patches among these parameters.

Dynamic modeling and analysis of rotating beams with partially covered enhanced active constrained layer damping treatment

A new dynamic model for vibration analyses of rotating flexible beams with partially covered enhanced active constrained layer damping (EACLD) treatment is developed. To improve the previous EACLD beam modeling method that only considers the edge element stiffness, the edge element of the EACLD patch is modeled as an equivalent spring with attached point mass so that the mass effect of the two added edge elements are included. The discrete rigid-flexible coupled dynamic equations of the hub-beam systems with EACLD treatment in the open-loop and closed-loop cases are derived by using the assumed mode method and Lagrange's equations. The effect of the angular velocity, edge element stiffness, edge element mass, and coverage ratio of the EACLD on the vibration characteristics of the system are investigated. Simulation results show that the edge element stiffness will increase the natural frequencies of the system and make the system become stiffer, while the edge element mass will decrease the natural frequencies of the system. Results from the traditional ACLD beam model, the EACLD beam model without edge element mass and the present EACLD beam model with edge element mass are also compared with each other. It is indicated that the mass effect of the added edge elements should be considered in practical applications and it could even play a positive role in stiffness or damping regulation of systems in conjunction with the vibration controller design.

Finite element simulation of controlled frequency response of skew multiphase magneto-electro-elastic plates

The linear frequency response of skew multiphase magneto-electro-elastic composite plate embedded with active constrained layer damping treatment has been studied. The volume fraction of piezoelectric fibres embedded in the piezomagnetic matrix significantly affects the coupling characteristic of this multiferroic material, and hence, the frequency of the skew multiphase magneto-electro-elastic plate is drastically altered. This study emphasizes on evaluating the influence of different volume fraction of barium titanate (BaTiO3) and cobalt ferrite (CoFe2O4) on the frequency characteristics of skew multiphase magneto-electro-elastic. In this regard, a finite element formulation has been proposed to assess the damped response of such skew multiphase magneto-electro-elastic plates. Incorporating the complex modulus approach, the constrained viscoelastic layer of the active constrained layer damping patch is modelled. In addition, the effect of geometrical skewness has also been investigated. Meanwhile, an exhaustive parametric study is carried out to analyse the influence of control gain, patch position and fibre orientation angle of piezoelectric composite.

Active control of doubly curved laminated composite shells using elliptical smart constrained layer damping treatment

In this paper, performance of the smart constrained layer damping (SCLD) treatment with elliptical geometrical plan form is investigated for controlling the vibrations of various types of doubly curved composite shells. The SCLD treatment is composed of a viscoelastic layer and an advanced constraining piezoelectric composite (PZC) layer attached at the top surface of the composite shell. A mesh free (MF) model of the smart composite shell has been developed based on the element free Galerkin approach to study its dynamic behaviour within the framework of a mixed layerwise displacement field theory considering transverse extensibility. Spherical, paraboloid and hyperboloid type composite shells with antisymmetric/symmetric cross-ply as well as general angle-ply lamination sequences are considered for the analysis. The numerical results demonstrated that the elliptical SCLD patches are more efficient in attenuating the vibration of the spherical and paraboloid laminated shells while the regular rectangular/square plan form patches are effective for the hyperboloid shells. The numerical results also indicate that the elliptical patches are having higher performance index in enhancing the active damping characteristics of the composite shells. Investigations are also carried out to analyze the effect of the variation in orientation of the piezoelectric fibers in the active PZC layers in attenuating the vibration of shells.

Effect of carbon nanotube waviness on smart damping of geometrically nonlinear vibrations of fuzzy-fiber reinforced composite plates

In this article, we present a finite element model for the three-dimensional analysis of smart constrained layer damping of geometrically nonlinear vibrations of laminated fuzzy-fiber reinforced composite plates. The three-dimensional fractional derivative constitutive relation is implemented for the viscoelastic layer. The constraining layer of the smart constrained layer damping treatment is composed of the vertically/obliquely reinforced 1–3 piezoelectric composites. The von Kármán–type nonlinear strain–displacement relations are used to incorporate the geometric nonlinearity in the model. The main aim of this article is to numerically investigate the effect of carbon nanotube waviness on the nonlinear smart damping. Several thin laminated substrate fuzzy-fiber reinforced composite plates with straight carbon nanotubes and wavy carbon nanotubes with different waviness in different planes are considered with various boundary conditions and stacking sequences to numerically compute their effect on smart damping. The performance of the obliquely reinforced 1–3 piezoelectric composites is discussed and the efficacy of the present smart finite element model in terms of active control authority is also presented.

Active control of laminated composite plates using elliptical smart constrained layer damping treatment

In this article, performance of the elliptical patches of smart constrained layer damping (SCLD) treatment is investigated for controlling vibrations of smart laminated composite plates. A three dimensional mesh free model (MFM) has been implemented for the first time based on the element free Galerkin (EFG) method and layer wise displacement theory for studying the dynamic behavior of the composite plates integrated with the SCLD treatments. Symmetric/antisymmetric cross-ply and general angle-ply laminates are considered for the substrate of the smart composite plates. Circular and regular rectangular type patches are also considered for the analysis. It is observed that the elliptical SCLD patches are more efficient in attenuating the amplitude of vibration in the laminated composite plates as compared to the circular and square type patches. The results from numerical analysis also reveal that the elliptical patches have the maximum performance index followed by the circular and the square type SCLD patches in enhancing the active damping characteristics of smart composite plates. The performance of the elliptical patch is sensitive to the piezoelectric fiber orientation angle and becomes maximum if the piezoelectric fiber orientation is vertical irrespective of the types of SCLD patches considered as well as the lamination sequence.

Constrained Layer Damping Treatment: Analysis of multi-strip application on thin plates

This paper focuses on analysing the effects of using multiple strips of Constrained Layer Damping (CLD) treatments to cover entirely a thin aluminium plate and assess the vibration performance for various strips orientation. In particular, for a fixed type of CLD treatment, three strips orientation are considered: (i) parallel to the long axis of the plate, (ii) perpendicular to the long axis, and (iii) 45º to the long axis. By using both experimental and Finite Element (FE) modelling, it is shown that depending on the mode shape curvature and corresponding nodal line positions, the strip orientation would strongly affect the amount of energy that can be dissipated at one particular resonance. An approximate topology optimisation technique is investigated to target the first bending mode of the structure and is validated experimentally. This technique involves optimising a uniform CLD topology for maximum stiffness (using a topology optimization feature of a FE commercial software) and then manually locating optimal strip placement by taking into account orientation effects.

Nonlinear model reduction for control of an active constrained layer damper

One technique to reduce vibrations of low-damped structures is the application of constrained layer damping (CLD) treatments. A unique extension of the CLD is a compressible constrained layer damping (CCLD) where the usually stiff viscoelastic layer is replaced by a compressible one. Due to the adaptable deformation kinematics, as well as compression-dependent material properties, the dynamic behavior of the whole considered structure can be optimized during the operation. One challenge for this application is to determine the optimal compression levels in order to adapt the dynamic behaviour of the component with CCLD to the excitation characteristics. Through the application of finite element model such optimal control strategies can be extensively studied and the dynamics of actuation principle can be included. Herein, low computation times are highly desired, especially for applications where the CCLD undergoes large deformations. This contribution shows how nonlinear model reduction can be applied to accelerate the solution of such finite element models.

Interface finite elements for the modelling of constrained viscoelastic layers

Viscoelastic treatment has traditionally been used in industrial applications to reduce structural noise and vibration by dissipating part of the strain energy. Constrained-layer damping (CLD) treatments usually dissipate more energy than free-layer damping treatment (FLD), but its design must be integrated in the design process of the structure to be damped. Parametric studies are then necessary to determine the optimal viscoelastic material forming the CLD treatment, and the optimal placement and thickness of the layer. For structures with complex geometry, 3D finite elements are required and a change in the thickness or the placement of the viscoelastic layer implies a complete remeshing of the structure, which represents a significant additional computational cost in the parametric study. The goal of this work is to present a new strategy to model efficiently thin constrained viscoelastic layers. Two interface finite elements, based on a surface representation of the damping layer, are proposed. The first one is a joint element using relative displacements at the interface, and the second one is an original zero-thickness element which makes use of a volumetric integration. These elements are validated by comparison with 3D finite elements. Results show that the proposed interface elements allow a good representation of the damping layer’s behaviour, especially for thin layers. Moreover, this modelling approach can be efficiently used in the context of parametric optimisation.

Free vibration and damping characteristics study of doubly curved sandwich shell panels with viscoelastic core and isotropic/laminated constraining layer

Abstract In this work, a shear deformable viscoelastic sandwich shell element is proposed for doubly curved sandwich shell panels with passive constrained layer damping (PCLD) treatment. The transverse displacements of the constraining layer and base layer are considered to be independent, besides the in-plane displacements . The transverse and in-plane displacements of the viscoelastic core are considered to be varying linearly through the thickness. Shear as well as normal deformations of the core are included in the analysis. The equation of motion of the doubly curved sandwich shell panel under free vibration is derived via Hamilton's principle . The modal frequencies and modal loss factors of the Isotropic elastic-Viscoelastic-Isotropic elastic (IVI) sandwich shell panel and Laminated elastic-Viscoelastic-Laminated elastic (LVL) sandwich panel are obtained from numerical solutions, using finite element method in conjunction with Hamilton's principle. Parametric studies are carried out to ascertain the effects of shell geometries, aspect ratio, orthotropicity of the skins, core layer thickness, constraining layer thickness, core loss factor on the natural frequencies and system loss factors under different boundary conditions.

Smart damping of large amplitude vibrations of variable thickness laminated composite shells

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.