Constrained Layer Damping Research Articles

Free Vibration and Damping of Rotating Composite Shaft with a Constrained Layer Damping

The free vibration and damping characteristics of rotating shaft with passive constrained layer damping (CLD) are studied. The shaft is made of fiber reinforced composite materials. A composite beam theory taking into account transverse shear deformation is employed to model the composite shaft and constraining layer. The equations of motion of composite rotating shaft with CLD are derived by using Hamilton’s principle. The general Galerkin method is applied to obtain the approximate solution of the rotating CLD composite shaft. Numerical results for the rotating CLD composite shaft with simply supported boundary condition are presented; the effects of thickness of constraining layer and viscoelastic damping layers, lamination angle, and rotating speed on the natural frequencies and modal dampings are discussed.

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.

High Damping Characteristics of an Elastomer Particle Damper

Research testing has led to the development of an Elastomer Particle Damper (EPD), which can add considerable damping to a structure by directing the vibration to a set of interacting elastomer particles through a rigid connection. This vibration treatment presents highly nonlinear behavior that is strongly dependent on both the vibration amplitude and frequency. Curves of damping loss factor (DLF) of an EPD system with vertical motion as a function of frequency and acceleration are reported herein. The results show that the elastomer particle damper has two distinct damping regions. The first region is related to the fluidization state of the particles, as described in the literature, obtained when the damper is subjected to vertical acceleration close to 1 g and frequencies below 50 Hz. The second region presents high values of DLF to acceleration values lower than 1 g, and the frequency range is dependent upon the stiffness of the particles. A high degree of effectiveness is achieved when the working frequency of the elastomer particle dampers is tuned to a natural frequency of a plate and when they are strategically located at points having large displacement. The performance of EPDs was compared with that of a commercial constrained layer damping installed in an aircraft floor panel. The EPDs achieved an acceleration level attenuation in the aircraft floor panel similar to that of the commercial constrained layer damping system.

Influence of Sandwich-Type Constrained Layer Damper Design Parameters on Damping Strength

This paper presents a theoretical study of the parameters that influence sandwich-type constrained layer damper design. Although there are different ways to reduce the noise generated by a railway wheel, most devices are based on the mechanism of increasing wheel damping. Sandwich-type constrained layer dampers can be designed so their resonance frequencies coincide with the wheel’s resonant vibration frequencies, and thus the damping effect can be concentrated within the frequency ranges of interest. However, the influence of design parameters has not yet been studied. Based on a number of numerical simulations, this paper provides recommendations for the design stages of sandwich-type constrained layer dampers.

Topology optimization of PCLD on plates for minimizing sound radiation at low frequency resonance

Topology optimization of passive constrained layer damping (PCLD) treatment patched on thin plates with respect to sound radiation at low frequency resonance is investigated. An extended solid isotropic material with penalization (SIMP) model is described using an interface finite element model for viscoelastic layer. Then the given FE mesh for base structure can remain the same during the optimization process. The objective function, radiated sound power, is simplified by using sound radiation mode and modal strain energy method, the merit of which is the complex dynamic equations of the composite plate need not to be solved and only modal analyses for the associated undamped modal equations are required. Numerical and experimental results show that significant reductions of the sound power are achieved. Two optimal topologies of the PCLD patches are analyzed. It's shown that to minimize the sound radiation power at low frequency, not only the structural damping but also the volume velocity should be concerned.

A general vibration theory for constrained layer damping-treated thick sandwich structures

The vibration equations of a thick sandwich structure with a viscoelastic material core were derived. The host layer was assumed thick and the top layer could be thin or thick. This type of structures may apply to various cases and the particular application for which it fit is that of constrained layer damping treatment for vibration attenuating. The governing differential equations contained nine displacements for thick–thick surface layers. For cases of thin–thick, the number of displacement was significantly reduced to only five, which were one transverse displacement, two in-plane displacements, and two layer rotation angles, all associated with the host layer. The derived theory was general, and it could be not only specialized for many commonly seen structures such as beams, plates, and cylindrical shells but also degenerated into one- or two-layer structures. Specialization for a sandwich cylindrical shell was extensively illustrated, and numerical results of natural frequencies and damping were compared to those of thin shell theory. How each layer's thickness influenced the frequency and damping of the sandwich shell were particularly discussed.

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.

Modal Analyses of a Thin Shell with Constrained Layer Damping (CLD) Based on Rayleigh-Ritz Method

Foreign Object Debris (FOD) is debris or article alien, which may This paper presents analytical results of natural frequencies and loss factors of node-diameter and node-circumferential modes of a thin shell treated with constrained layer damping (CLD) based on Rayleigh-Ritz method. General differential equations of motion of the thin CLD shell are derived firstly by following the Donnell-Mushtari shell theory. By taking the beam characteristic functions as the admissible functions, the Rayleigh-Ritz method is employed to deduce the higher degree equations of natural frequencies of the thin CLD shell under different boundary conditions. It is confirmed that the present method is accurate and convenient so that it is applicable to the thin CLD shell compared with classic analytic method or transfer matrix method. Several examples are achieved and compared to illustrate the effects of the viscoelastic material (VEM) and constrain layer’s thickness ratios on the natural frequencies and modal loss factors, besides the effect of boundary conditions. The results show that the thickness ratio of VEM affects sensitively the modal frequencies and the total damping capacity of the thin CLD shell.

An experimental comparison between existing damping solutions for railway wheels

The acoustic reductions achieved with the current damping solutions for railway wheels that appear in the state of the art were obtained with different railway wheel designs, under different measurement scenarios (laboratory and on track), under different testing conditions, making it impossible to compare these damping solutions in a straightforward manner. The aim of this paper is to analyse, measure and estimate the behaviour of damping solutions installed on the same railway wheel and under the same testing conditions. Experimental measurements were carried out in the laboratory on wheels that are currently in use in metro lines. Damping solutions that were evaluated are ring damper, friction damper and sandwich-type constrained layer damper. Results show that ring and friction dampers are dependent on the applied preload and that they can only dissipate energy at high frequencies. Sandwich-type constrained layer dampers are the only damping solution that can add damping at low frequencies, but it is essential that they be properly designed in order to significantly increase the final wheel damping.

Boring bar with constrained layer damper for improving process stability

Boring is one of the most common operations to enlarge or finish predrilled deep holes and is usually conducted in low spindle speed ranges. Due to low dynamic performances of conventional boring bar, boring operation is often hindered by drastic vibration. In this paper, a design and optimization method of a special boring cutter with constrained layer damping (CLD) bar is developed based on the CLD beam theory and finite element method (FEM). The boring cutter designed is composed of four modules: cutting head, substrate layer, damping layer, and constrained layer, which can greatly improve the dynamic performances in boring process. Meanwhile, the effectiveness and capability of boring cutter with CLD bar for forced- and chatter-vibration suppression are presented based on experimental and numerical methods. The results show that (1) the method for restraining forced vibration is different from that for chatter suppression. The former can be greatly avoided by shifting the natural frequency of boring system, e.g., changing dynamic stiffness. The latter, due to its complexity in low spindle speed range, on the other hand, cannot be entirely avoided and can only be eliminated by reducing the possibility of occurrence, e.g., increasing damping. (2) The boring cutter with CLD bar developed can change dynamic stiffness through constrained layer and improve damping performance through damping layer. So, it can avoid forced vibration and eliminate chatter to some extent. In the presented parameter domains, the capability of CLD bar for chatter suppression is improved five times corresponding to that of conventional bar.

Microstructural topology optimization of viscoelastic materials for maximum modal loss factor of macrostructures

The geometric layout and physical properties of a viscoelastic damping material have a significant influence on the damping performance of a passive constrained layer damping (PCLD) structure. This paper presents a two-scale optimization method and aims to find the optimal microstructural configuration of the viscoelastic material (i.e., the optimal effective properties of the material) with maximum modal loss factors of the macrostructures. The modal loss factor is obtained by using the Modal Strain Energy (MSE) method. The material microstructure is assumed to be homogeneous in the macro-scale, i.e., the macrostructure is composed of periodic unit cells (PUC). In the optimization formulation, the relative densities are introduced as the design variables for the material microstructure design, based upon the idea of the Solid Isotropic Material with Penalization (SIMP) method of topology optimization. The modal loss factor of the structure is assigned as the objective function. All the sensitivities of the modal loss factor with respect to the design variables are derived analytically and the optimization problem is solved by Method of Moving Asymptote (MMA) method. Several examples of the design optimization of viscoelastic cellular materials are presented to demonstrate the validity of the method. The effectiveness of the design method is illustrated by comparing a solid and an optimized cellular viscoelastic material as applied to a cantilever beam with the PCLD treatment.

Optimum design of grain sieve losses monitoring sensor utilizing partial constrained viscoelastic layer damping (PCLD) treatment

Grain sieve losses has been an important dominant factor for automatic adjustment of the major working parameters of combine harvesters such as cylinder speed, concave clearance, fan speed and vehicle forward speed. To monitor grain sieve losses real-timely in the working processing of combine harvester, a grain sieve losses monitoring sensor, which utilizing YT-5 type piezoelectric ceramic as sensing material developed. To accelerate grain sieve losses monitoring sensor's detecting speed, theoretical analysis was performed from view of structural vibration and a partial constrained viscoelastic layer damping (PCLD) treatment was carried out on the surface of the grain sieve losses monitoring sensor. On the basis of analyzing the mechanical relationships among each layer of the sandwich in depth, an optimal position to past the viscoelastic layer was found. Grain collision experiment results found that grain collision signal attenuate time was shortened to about 2–3ms after treated with PCLD in places with relative larger modal deformation, namely, the developed sensor could identify more than 300–500 grains within 1s in theory, which verified that the sensor's detecting speed was significantly improved. To test the performance of the developed sensor, calibration experiments carried out in the laboratory, and analysed the influence of moisture content (MC), sensor mounts height and angle on measurement accuracy. At last, installed grain sieve losses monitoring sensor on a combine harvester field experiments took place; experimental results showed that the largest measurement relative error was 4.48% when harvesting rice.

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.

Damped leaf flexure hinge.

Flexure-based mechanism like compliant actuation system embeds complex dynamics that will reduce the control bandwidth and limits their dynamic positioning precision. This paper presents a theoretical model of a leaf flexure hinge with damping layers using strain energy method and Kelvin damping model. The modified loss factor of the damped leaf flexure hinge is derived, and the equivalent viscous damping coefficient of the damped leaf hinge is obtained, which could be used to improve the pseudo-rigid-model. The free vibration signals of the hinge in three different damping configurations are measured. The experimental modal analysis also is performed on the three kinds of damped leaf flexure hinges in order to evaluate their 1st order bending natural frequency and vibration-suppressing effects. The evaluation of modified loss factor model also is performed. The experimental results indicate that the constrained layer damping can enhance the structure damping of the hinge even if only single damping layer each side, the modified loss factor model can get good predicts of a damped leaf flexure hinge in the frequency range below 1st order natural frequency, and it is necessary that the dimensional parameters of the damping layers and basic layer of the hinge should be optimized for simplification at the mechanism's design stage.

A unified method for the vibration and damping analysis of constrained layer damping cylindrical shells with arbitrary boundary conditions

In this paper, an accurate solution is developed for the vibration and damping characteristics of a three-layered passive constrained layer damping (PCLD) cylindrical shell with general elastically restrained boundaries. In this formulation, characteristic equations of the system are derived by using the modified Fourier–Ritz method in conjunction with Donnell shell assumptions and linear viscoelastic theory. Regardless of boundary conditions, the displacements of each layer are expanded as the linear combination of a standard Fourier series and closed-form functions introduced to eliminate all the relevant discontinuities with the displacements and derivatives at the edges. This method can be universally applicable to all classical boundaries, elastic boundaries and their combinations without any special change in the solution procedure. It provides an effective way to investigate the influence of restraints from different directions on the vibration and damping performance of PCLD shells. New results for elastic restraints and intermediate ring supports are presented, which may serve as benchmark solutions. Furthermore, the detailed effects of thickness of layers and shear parameter on natural frequencies and loss factors are also illustrated.

A numerical and experimental study on viscoelastic damping of a 3D structure

Structural vibrations often cause problems in high precision instruments, which may be solved by introducing passive damping. In this paper, different ways of introducing passive damping via viscoelastic materials (VEM) are discussed. Discrete damping elements and constrained layer (CL) configurations are selected and used to efficiently damp an open aluminum box. For the constrained layer configurations, a distinction is made between full and partial coverage of the structure. The steady-state dynamics of the box are simulated using a finite element (FE) model, which includes frequency dependent VEM properties. This model is used to find a design that possesses high damping while taking into account design constraints. The simulation results are experimentally validated using both modal parameters and frequency response functions (FRFs). For the computation of model based FRFs, a new method based on Interpolated Modal Parameter Superposition (IMPS) is proposed. Model based results and experimental results show good resemblance, even without updating the model with deviations in the realized structure. The local dampers add most damping to a limited number of modes. Partially covering the box with CL dampers is found to be more effective than full coverage of the structure with the same mass addition.

Method to characterize the damping behavior of thin passively constrained layer laminates using dynamic mechanical analysis (DMA) in shear mode

In order to characterize the damping behavior of thin passively constrained layer damping (CLD) loudspeaker membranes, usually the whole loudspeaker has to be built. Therefore, a method was established to characterize the damping performance of these membranes with thicknesses below 50 μm at the film level using dynamic mechanical analysis (DMA).Since in the CLD design damping is provided via shear deformation of the middle damping layer, a test was set up to determine the mechanical loss factor tan δ (f,T) in DMA shear mode. Subsequently, results from 1-200 Hz were extrapolated to application-relevant frequencies of up to 1000 Hz via time-temperature superposition. Finally, the damping behavior was rated by the frequency dependent integrated average of the mechanical loss factor tA¯.Furthermore, in experiments with different constraining and damping layers, it was found that the damping performance was maintained as long as the adhesion between them was sufficiently strong.

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.