Constrained Layer Damping Research Articles

Topology optimization of constrained layer damping plates with frequency- and temperature-dependent viscoelastic core via parametric level set method

Frequency- and temperature-dependent properties of viscoelastic materials have a significant effect on vibration characteristics of constrained layer damping (CLD) structures. In this article, parametrized level set method (PLSM) is extended to solve the topology optimization problem of CLD plates, in which the viscoelastic material with frequency- and temperature-dependent characteristics is employed as damping core. The single/weighted modal loss factors, which are solved by an iterative method, are defined as objective functions, and topology optimization problem is formulated based on the finite element model for CLD plates which are described by combining parametric level set (PLS) functions. The sensitivities of objective functions with respect to expansion coefficients in PLS are calculated by the use of adjoint vector method. As the optimized results with complex constant shear modulus for viscoelastic core indicates, the proposed method is effective for topology optimization of CLD structures and insensitive to initial design. Numerical examples with the consideration of frequency- and temperature-dependent characteristics for “soft” and “hard” viscoelastic core are implemented. Through comparing the optimal results with different models for viscoelastic core, the influences of frequency- and temperature-dependent characteristics for viscoelastic core on natural frequencies, modal loss factors and optimized layouts are analyzed. Similarity indices are defined for distinguishing the difference among optimized layouts and initial design induced by modal strain energy contour. The optimal design dependence on layer thicknesses is further discussed with additional mass of CLD materials unchanged.

Dynamic modelling and analysis of smart carbon nanotube-based hybrid composite beams: Analytical and finite element study

In this work, the carbon nanotube-based hybrid carbon fibre-reinforced composite smart beam constraining the layer of an active constrained layer damping treatment is investigated using an in-house finite element model based on first-order shear deformation theory. The effect of in-plane and transverse-plane actuation of the integrated active constrained layer damping treatment layer on the damping characteristics of the novel smart cantilever hybrid carbon fibre-reinforced composite beam is considered. The parameters affecting the damping characteristics of the hybrid carbon fibre-reinforced composite substrate beam such as the volume fraction of both carbon nanotubes and carbon fibre, and the aspect ratio are also studied. Besides, the micromechanical model based on the mechanics of materials approach is developed to estimate the effective elastic coefficient of novel hybrid carbon fibre-reinforced composite lamina. The effective properties of hybrid carbon fibre-reinforced composite are predicted quantitatively by considering non-bonded interaction formed between carbon nanotubes and the polymer matrix. It is revealed that due to the incorporation of carbon nanotubes into the epoxy matrix, the effective longitudinal, transverse and shear properties of the hybrid carbon fibre-reinforced composite lamina are significantly enhanced. Our outcomes explore that the damping performance of the laminated hybrid carbon fibre-reinforced composite smart beam considering the incorporation of carbon nanotubes shows substantial improvement as compared to the base composite. To bring more clarity, the quantitative relative performance of hybrid carbon fibre-reinforced composite and base composite is presented. Our fundamental analysis sheds the light on the opportunities of developing efficient, high-performance and lightweight carbon nanotubes-based micro-electro-mechanical systems smart structures such as sensors, actuators and distributors.

A framework of flexible locally resonant metamaterials for attachment to curved structures

Locally resonant metamaterials (LRMs) have been extensively investigated for their superior attenuation performance in the band gap frequencies despite not resulting in a large mass increase, comparatively. However, for their application on actual industrial structures, there exist limitations, the most important of which is the flexibility of the LRM structure. Several studies have succeeded in attaching LRMs to curved surfaces, but if the curvature changes, the unit structure must be redesigned. In this paper, a flexible LRM design independent of curvature is proposed, and numerical simulations illustrate the implementation of the band gap in a beam. Proof of concept of the flexible LRM has been shown through modal experiments on various curved surfaces. Excellent attenuation characteristics of the flexible LRM are demonstrated via a comparison with a constrained layer damping treatment, which are typically considered in noise, vibration and harshness (NVH) area. As the proposed flexible LRM can be attached to various curvatures without restriction or redesign, it differentiates itself as a practical alternative to other LRM designs and expected to be explored in diverse applications.

Smart control of laminated plates using Murakami zig-zag functions

The study aims at vibration control of laminated plates by the active constraining layer damping (ACLD) treatment incorporating the Murakami zig-zag function (MZZF) while deriving the displacement fields. The control is achieved by activating the ACLD patches by supplying the control voltage. The ACLD patch has two component layers, namely 1–3 piezoelectric composite (PZC) constraining material layer and the viscoelastic constrained material layer. The complete ACLD plate system is modelled as a three layered structure using a MZZF in the displacement fields of the individual layers, and the FE model is obtained by the virtual work principle. A MATLAB FE code has been developed considering the closed loop feedback system for the control of the input parameters. The present method of modelling the ACLD system has proven to be accurate and cost effective for damping the vibrations of the composite plates. Also, the change in piezo fiber orientation angle on the control and performance of the ACLD patches has been effectively studied in detail.

Damping ratio maximization in thickness direction using viscoelastic and structural materials based on constrained layer damping

Constrained layer damping (CLD) is a typical application known to exhibit high damping. However, the damping ratio generally attains its maximum value when the applied surface is fully covered with the damping material. In this study, a method is proposed of topology optimization in the thickness direction using viscoelastic and constrained materials based on CLD in order to obtain a higher damping ratio. A mathematical formulation is proposed of the material interpolation functions of the store elastic modulus, loss elastic modulus, Poisson's ratio and density. As a result of the optimization using a cantilever beam, the damping ratio obtained in the optimal layout is 1.44 times higher than that in conventional CLD. The higher damping in the optimal layout can be attributed to compression of the viscoelastic material by the slits, and a decrease in the flexural rigidity caused by the taper and the longitudinally extending part of the slits.

Smart damping of skew composite plates using Murakami zig-zag function

The present work is aimed at deriving a finite element model for active constraining layer damping treatment (ACLD) of layered skew plates by incorporating zig-zag behaviour using a Murakami zig-zag function (MZZF). The ACLD in skew patch form comprises of 1–3 PZC material and viscoelastic material in the layer form placed on substrate skew plate. The overall skew substrate ACLD system deformation kinematics are derived using MZZF and the equations of motion for the same are derived by virtual work method. A MATLAB subroutine for the overall skew plate ACLD system has been developed to present the closed loop frequency responses by successful implementation of closed-loop feedback system. The substrate skew plates with different lamination schemes namely symmetric/antisymmetric cross-ply and antisymmetric angle-ply are considered to assess the damping behavior of the skew plates undergoing ACLD. Also, the piezo-fiber angle (obliquely reinforced) variation of the PZC layer on the damping responses of the skew plates have been thoroughly examined.

Vibration and Damping Analysis of Pipeline System Based on Partially Piezoelectric Active Constrained Layer Damping Treatment.

Pipelines work in serious vibration environments caused by mechanical-based excitation, and it is thus challenging to put forward effective methods to reduce the vibration of pipelines. The common vibration control technique mainly uses the installation of dampers, constrained layer damping materials, and an optimized layout to control the vibration of pipelines. However, the passive damping treatment has little influence on the low frequency range of a pipeline system. Active control technology can obtain a remarkable damping effect. An active constrained layer damping (ACLD) system with piezoelectric materials is proposed in this paper. This paper aims to investigate the vibration and damping effect of ACLD pipeline under fixed support. The finite element method is employed to establish the motion equations of the ACLD pipeline. The effect of the thickness and elastic modulus of the viscoelastic layer, the laying position, and the coverage of ACLD patch, and the voltage of the piezoelectric material are all considered. The results show that the best damping performance can be obtained by selecting appropriate control parameters, and it can provide effective design guidance for active vibration control of a pipeline system.

Vibration Reduction Design of Torpedo Engine Based on Modal Contribution Method

Aiming at improving the structure of torpedo engine, the damping technology based on modal contribution method was proposed. Based on the results of the linear combination analysis of the modal participation factors, the vibration control method of the constrained damping layer was designed to control the dominant modes with large contribution. Firstly, the dynamic model of torpedo engine support structure is built, and the modal frequency, modal displacement and normalized modal stiffness are obtained. The dominant modes in the target frequency band are calculated, and the first 24 modes are analyzed. According to the mode shape of dominant mode, the constrained damping layer is designed for the engine. The optimized structure was verified by numerical simulation and the corresponding experimental results. The results showed that the damping technology based on modal participation factor can significantly reduce the vibration response of the engine support structure. This method creatively combines the dynamic design with the damping design, and obtains an effective damping method for engineering, especially for the military industry field with narrow space and strict weight requirements.

Topological optimization design on constrained layer damping treatment for vibration suppression of aircraft panel via improved Evolutionary Structural Optimization

Light-weight panel structures are commonly used in inlets of the Auxiliary Power Unit (APU) of aircraft. In this paper, a study on topological optimization design of constrained layer damping (CLD) treatment for vibration suppression of aircraft panel based on improved Evolutionary Structural Optimization (ESO) is presented. In the analysis, the volume fraction of CLD material is selected as the constraint condition, and the maximization of modal loss factor is considered as the objective function to enhance damping in the topology optimization model of the structure with CLD treatment, Modal Strain Energy (MSE) method is adopted to deduce the sensitivity of the objective function to design variables, using mesh-independent filter method to solve the checkerboard pattern and the mesh-dependent problem, the ESO with improved evolutionary rate is proposed to search the optimal layout of CLD material, and the correctness and effectiveness of the optimization results are demonstrated through the numerical examples. Compared with conventional ESO, the improved ESO can not only increase the calculation efficiency but also obtain a more reasonable optimized topology geometry. The vibration suppression of the optimized panel is compared with those of the original panel, stiffened panel, and full cover CLD material damping panel and verified by experiments. The results show that the optimized damping panel has a better vibration reduction effect.

Vibration suppression of a rotating functionally graded beam with enhanced active constrained layer damping treatment in temperature field

This paper investigates the vibration control of a rotating functionally gradient material (FGM) beam under thermal environment by using an enhanced active constrained layer damping (EACLD) treatment. The present model is extended from a newly developed dynamic model for composite EACLD beams. The difference is that the base beam is composed of temperature-dependent FGM that was widely used in the aerospace industry as advanced heat-resisting composite and the temperature dependence of viscoelastic material in the constrained layer is also considered. The active piezoelectric layer has edge elements at both ends, which are modeled as equivalent springs and mass points. The Lagrange’s equation is used to derive the dynamic equations of the system and the deformation of the beam is described by the assumed-mode method. Based on the rigid-flexible coupling dynamic theory, the dynamic responses of the rotating FGM beam with various temperature differences are investigated. Simulation results show that the vibration suppression performance of the EACLD beam is better than the ACLD beam. The equivalent springs have more significant influences on the structural vibration suppression effect than the mass points. The larger the temperature difference is, the larger the thermal induced flutter of the structure is. The influences of VEM damping layer thickness, rotating speed, and control gain on the vibration of the structure with EACLD treatment are also discussed.

Effect of multi-layered IIR/EP on noise reduction of aluminium extrusions for high-speed trains

Damping treatment is effective for noise and vibration control. However, there is a lack of research on the relationship between the fabrication and mechanical property characterisation of damping materials and the vibroacoustic characteristic analysis after damping materials are applied to actual composite structures. We performed such a study. First, modified butyl rubber (IIR) with high damping performance was prepared, and its frequency-dependent elastic modulus and loss factor were identified. Second, the vibration and damping characteristics of the modified IIR used in multi-layered constrained-layer damping (MLCLD) were investigated via cantilever-beam experiments and simulations. Third, the noise reduction (both sound radiation and sound insulation) effects of the MLCLD on aluminium extrusions were examined using prediction models, which were validated according to acoustic laboratory tests. The results indicated that the structural vibroacoustic characteristics are affected by not only the number of layers but also the application objects, structural parameters, and material properties. The final lightweight optimisation design of the aluminium extrusion using the MLCLD reduced the radiated sound power level by 2.7 dB, improved the sound insulation level by 3.0 dB, and reduced the total mass by 14.4%.

Istraživanje stabilnosti kod unutrašnje obrade struganjem pomoću vretena bušilice sa pasivnim prigušivanjem ograničavajućim slojem

The vibrations produced in a boring tool in internal turning deteriorate the machined surface quality and reduce the tool life, which results in a massive noise during the machining. Therefore, unwanted vibrations are necessary to be eliminated by improving the boring bar's dynamic stiffness and damping capacity. This paper investigates a passive constrained layer damping (CLD) boring bar with a hybrid damping layer to study the internal turning system's stability. Initially, the dynamic models of the conventional and CLD tools are thoroughly studied using Euler-Bernoulli beam theory (EBT) and validated them with finite element modelling (FEM). The frequency response functions (FRFs) obtained from the impact hammer tests are used to estimate the modal parameters. With modal parameters, the semi-analytical stability lobe diagrams (SLDs) are plotted for the boring system with the conventional and CLD boring bar. Tool-tip responses for various cutting conditions are simulated numerically to validate and to study stability. The cutting experiments with traditional and CLD boring bar are conducted for stability analysis and compared tool-tip responses with numerical results. It is observed that both the numerical and experimental results agree with the selected cutting conditions from SLDs. It is also observed that the CLD boring bar with a hybrid damping layer reduced the vibration displacements by five times compared to the conventional one.

Vibration suppression analysis and experimental test of additional constrained damping layer in space science experiment cabinet

Aiming at the problem that the vibration of the space science experimental cabinet is too large during the launch phase of the rocket, the viscoelastic constrained damping layer is used to suppress the vibration. Firstly, to explore the vibration suppression mechanism of the constrained damping layer, the dynamic model of the constrained damping layer is established and the modal loss factor is calculated. Secondly, the influence of the modulus, material thickness, and the position and the area of the damping layer on the loss factor of the structure is analyzed. Finally, the simulation and experiment methods are used to calculate and verify the space science experiment cabinet with additional constrained damping layer. The results show that the viscoelastic constrained damping can effectively reduce the vibration level of the space science experiment cabinet, and the acceleration response in the resonance region is reduced by more than 56%. The viscoelastic constrained damping structure is simple and easy to realize, which can suppress the vibration of the space payload design is of great significance.

Noise simulation and low noise design of skinned panel structure of scientific experiment rack

The noise of the scientific experiment rack radiates into the space station through the skinned structure, which directly affects the safety and health of astronauts in orbit for a long time, so it is necessary to carry out low-noise design. Firstly, the finite element model of the panel structure is established, and the correctness of the model is verified by modal test. Secondly, select a point as the vibration excitation point on the finite element model of the plate structure to simulate the vibration input of the excitation source, obtain its vibration response through the modal superposition method, take the vibration response as the boundary condition of the acoustic boundary element, use the modal acoustic transfer vector technology to calculate the radiation noise of the plate structure, and verify it through the noise test in the half anechoic chamber. Then, the acoustic pressure contribution analysis of the radiated noise from the skinned panel structure is carried out, and the panel area which can reduce the radiated noise of the target is determined. The constrained damping layer is applied in this area. The results show that the radiated noise at the target position is significantly reduced.

Topology optimization of partial constrained layer damping treatment on plate for maximizing modal loss factors

Constrained layer damping treatment is widely used to suppress the vibration and noise of thin-walled structures. However, full coverage of constrained damping layer will increase unnecessary additional mass, resulting in material waste and cannot effectively improve the damping performance of the composite structure. In this article, a topology optimization approach is proposed to realize the optimal distribution of constrained damping layer. The design objective is to maximize modal loss factors solved by the modal strain energy method under the constraint of volume. Taking the relative density of the finite element of the constrained damping layer as design variable, the solid isotropic material with penalization method is used to realize the optimal topological distribution of the damping material on the surface of the metal substrate. Then the moving asymptote method is adopted as an optimizer to search the optimal layout of the constrained damping layer. Based on a modified modal superposition method, the sensitivities of the objective function with respect to the design variables are obtained. Numerical examples and experiments are presented for illustrating the validity and efficiency of this approach. The results show that the objective function converges to the optimal value smoothly, and the optimized modal loss factors have been significantly improved. The layouts of the constrained damping layer after optimization are clear and reasonable, and its distributions are affected by both the damping layer and the constraining layer. Each part of the constrained damping layer after optimizing can greatly improve the damping performance of the structure.

NLMS Feedback Vibration Control of Open Cylindrical Shells With Active Constrained Layer Damping

A novel partial active constrained layer damping (ACLD) structure was proposed to reduce the vibration of thinwalled open cylindrical shells. Based on the Sanders thinshell theory and the Lagrange equation, the dynamic model for open cylindrical shells with the partial ACLD structure was established. According to the system state space form, an adaptive feedback controller was developed based on the normalized least mean square (NLMS) adaptive filter algorithm and the linear quadratic programming algorithm (LQR) to study the effects of control parameters on the open cylindrical shell midpoint dynamic characteristics and the control voltage. The numerical results demonstrate that, the NLMS feedback control method can ensure the effectiveness of the vibration attenuation of the open cylindrical shell under different control voltage frequencies, different filter orders and different adaptive step sizes. Increasing the adaptive step size and the filtering order can effectively improve the damping decrement but raise the control voltage overshoot, while increasing the filtering order and the frequency control voltage can reduce noise and disturbance to obtain better damping effects.

Nonlinear vibration analysis of smart functionally graded plates

Abstract This paper presents the damping characteristics of nonlinear vibrations of functionally graded (FG) plates utilizing piezoelectric composite material. For this analysis the active fiber composite (AFC) is taken as piezoelectric composite material. Finite element (FE) models are made for the FG plates combined with active constrained layer damping (ACLD) patches made of AFC material. Von Karman strain–displacement equations considering the displacement fields and satisfactory boundary conditions are used. The working of the ACLD patches for nonlinear vibration damping of FG plates is explored where AFC is used for the constraining layer of the ACLD patches. The Golla-Hughes-McTavish method is used for modeling the constrained layer of ACLD patch which is considered to be made of a viscoelastic material. Simulation models are also developed using ANSYS software for smart FG plates for validating the FE model. The contribution of ACLD patches for the nonlinear vibration control of the FG plates is investigated.

Extension of an analytical solution of a unified formulation to the frequency response of composite plates with viscoelastic layers

AbstractResulting from their high stiffness and low weight, lightweight structures made from fiber reinforced polymers are usually prone to vibrations. The inclusion of viscoelastic interlayers can provide a viable mean to passively damp these structures due to constrained layer damping. For the modeling of such structures, a layerwise approach based on the Generalized Unified Formulation has previously been proven suitable for static load cases.This contribution presents an analytical procedure to determine the frequency response and vibration characteristics of such heterogeneous laminates incorporating viscoelastic layers. Specifically, simply supported plates modeled by the Generalized Unified Formulation are considered and solved using Navier type solutions. The approach is validated by comparison with 3D finite element models. Particular focus is put on the order of expansion in thickness direction needed to accurately predict the frequency response of the laminate.

Damping Material for Stabilization of Panel Flutter at High Supersonic Speed

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Enhancing Vibration Reduction on Lightweight Lower Control Arm

This paper describes the design procedure to enhance the damping properties of a multimaterial lightweight suspension arm for a C-segment vehicle. An innovative viscoelastic material has been used to join carbon fiber with steel that has a function of passive constrained layer damper and adhesive simultaneously. Therefore, the hybrid technology applied has been focused on reducing the LCA mass, diminishing the steel thickness, and adding a CFRP tailored cover without compromising the global mechanical performance. Particular attention has been paid to the investigation of the dynamic response in terms of vibration reduction, especially in the range of structure-borne frequencies of 0–600 Hz. Two different viscoelastic materials have been evaluated in such a way to compare their stiffness, damping, and dynamic properties. The experimental test results have been virtually correlated with a commercial FEM code to create the respective material card and predict the real behavior of the LCAs (original and hybrid). The experimental modal analysis has been performed and compared on both the arms highlighting a very good correlation between virtual and experimental results. In particular, the hybrid LCA allows an interesting improvement of damping ratio, about 3,5 times higher for each eigenmode than in the original solution.