Constrained Layer Damping Treatment Research Articles

Vibration control of piezoelectric beams with active constrained layer damping treatment using LADRC algorithm

Active constrained layer damping (ACLD) treatment has become an important smart structure for vibration suppression due to its ability to achieve enhanced damping effects through real-time control. The control algorithm is a critical factor that determines the damping performance of the ACLD treatment. In this work, we utilize the linear active disturbance rejection control (LADRC) algorithm for the first time in the vibration suppression of beams with the ACLD treatment by compensating for the disturbance. To optimize vibration suppression, we also propose an efficient parameter tuning approach by analyzing the effects of controller bandwidth, control gain, and observer bandwidth on vibration suppression performance. Firstly, the dynamic model of elastic beams with the ACLD treatment is established and the LADRC algorithm is designed. Subsequently, the accuracy of the model is verified by comparing it with open literature and experiments. Then, the influences of the control parameters and different positions of the ACLD treatment on the vibration suppression performance are studied. Finally, the vibration suppression effects of LADRC and traditional PID algorithms are compared. The results indicate that the vibration suppression performance of the ACLD treatment is better than that of the passive constrained layer damping (PCLD) treatment. Setting the controller bandwidth to a small value and then adjusting other control parameters can effectively reduce the difficulty of parameter tuning while achieving superior vibration suppression performance. Appropriately increasing the observer bandwidth or reducing the control gain is beneficial for enhancing the suppression efficiency. The parameter tuning approach in this study provides vital guidance for the application of the LADRC algorithm in structural vibration suppression.

Efficacious constrained layer damping of carbon black‐reinforced nitrile butadiene rubber‐polyvinyl chloride blend vulcanizates: A comprehensive study

AbstractWe report efficacious vibration damping of carbon black reinforced nitrile butadiene rubber‐polyvinyl chloride blend (NVC) vulcanizates in a constrained layer damping (CLD) configuration. The objective is to compare numerical simulations using finite element method (FEM) and the widely used Ross‐Kerwin‐Ungar (RKU) model with the experimental results. NVC blend (50:50 by weight), was compounded with carbon black as reinforcing filler and vulcanized using a sulfur‐based curative system. Significant reinforcement and toughening were observed for the carbon black reinforced vulcanizates compared to the pristine blend. The viscoelastic properties of the vulcanizates were assessed using dynamic mechanical analysis (DMA), exploring their behavior concerning temperature variations and different frequencies to generate the Prony series coefficients for input in FEM analysis. Vibration damping experiments were conducted using the Oberst beam method in a single cantilever mode, with steel as the vibrating substrate, aluminum as the constraining layer, and the NVC vulcanizates as viscoelastic materials (VEM). Numerical simulations were performed using FEM to analyze mode shapes and frequency response function (FRF), and the RKU model was employed to quantify CLD system loss factors (SLF). The salient finding of this study was the observed SLF values in the range of 0.08–0.20 in the frequency regime of 200–2000 Hz. These values qualify the studied material as effective VEMs for CLD treatment of structural vibrations. This study supports design optimization efforts in a wide range of engineering applications where effective vibration damping is critical.Highlights Enhancement of NVC blend properties through carbon black reinforcement. Detailed analysis of viscoelastic behavior using DMA. Validation of findings through experimental modal analysis. Promising results in terms of system loss factors for CLD applications.

Dynamic Modeling and Vibration Suppression of a Rotating Flexible Beam with Segmented Active Constrained Layer Damping Treatment

This paper uses high-order approximate coupling (HOAC) dynamics equations for the hub–beam system with segmented active constrained layer damping treatment (SACLD). To improve the damping characteristics of traditional active constrained layer damping (ACLD), the viscoelastic damping layer, and the piezoelectric constraining layer are cut at the same position. The damping characteristics of the structure are enhanced by increasing the shear strain of the viscoelastic damping layer. The finite element method is used to discretize the SACLD beam. The discontinuity of the SACLD beam element-to-element displacement achieves the notch. Based on the theory of rigid–flexible coupling dynamics, the dynamic responses of the SACLD rotating beam under different cases are studied. The results show that the segmentation method is not always effective. A SACLD beam provides better vibration suppression than an ACLD beam only when appropriate material and dimensional parameters are used. The influences of base-layer thickness, piezoelectric constraining layer thickness, viscoelastic damping-layer thickness, angular velocity, the viscoelastic damping-layer loss factor, and control gains on the vibration of the rotating flexible beam with SACLD treatment are also discussed.

A multi-physical coupling isogeometric formulation for nonlinear analysis and smart control of laminated CNT-MEE plates

This paper presents a novel and comprehensive numerical approach for nonlinear analysis and smart damping control in laminated functionally graded carbon nanotube reinforced magneto-electro-elastic (FG-CNTMEE) plate structures, taking into account multiple physical fields. The approach employs a multi-physical coupling isogeometric formulation based on Non-Uniform Rational Basis Spline (NURBS) to analyze the behavior of laminated FG-CNTMEE plate structures. It incorporates a refined zig-zag theory to accurately capture the Von Kármán nonlinear strain–displacement relationship, as well as the magneto-electro-elastic coupling properties of laminate layers. To achieve nonlinear damped responses, the smart constrained layer damping (SCLD) treatment is applied. Furthermore, to enable smart control of structures using the time-dependent passive/semi-active damping mechanism of viscoelastic materials, the formulation is transformed into the Laplace domain using the Golla–Hughes–McTavish model. The results are then converted back to the time domain through inverse techniques. The proposed approach has been rigorously validated through verification work and demonstrated its effectiveness in simulating and controlling FG-CNTMEE plates in two numerical examples.

Damping performance and its influencing factors of wind turbine towers with constrained layer damping treatment

Constrained layer damping (CLD) is proposed as an energy dissipation measure for vibration control of offshore monopile wind turbine towers (OMWTT). The damping performance and influencing factors of OMWTT with CLD treatment are studied in this paper. First, a theory for calculating the first-order modal loss factor provided by CLD for composite structures is derived using the modal strain energy (MSE) method; second, the error of the theoretical formulation is analyzed using the finite element method; and finally, the influence of each parameter of the CLD on the first-order modal loss factor is discussed. The modal loss factor’s temperature dependence is described with the theory’s aid. The modal damping calculation theory proposed in this paper can rapidly determine the optimal design of CLD, considering the influence of multiple parameters and a complex environment, which could be helpful in the efficient vibration reduction of OMWTT.

Damping contribution of viscoelastic core on airborne sound insulation performance of finite constrained layer damping panels at low and middle frequencies

The airborne sound insulation performance of finite sandwich panels is often significantly worsened by resonant transmission components in low and middle frequencies. In this paper, damping contribution of viscoelastic core on sound transmission loss (STL) of finite constrained layer damping (CLD) panels is studied in narrow frequency bands. A fully coupled layer-wise approach is used with a generalized high-order shear deformation hypothesis that accounts for all types of deformations in the core. The influence of several parameters is investigated extensively. Results show that the adverse impact of the first-three odd-odd order modes, namely (1,1), (3,1), and (1,3) modes, as well as some higher-order modes on STL cannot be disregarded. The constrained viscoelastic core plays a crucial role in enhancing, or even eliminating, dips of STL spectrum at resonant frequencies. Additionally, it can considerably counterbalance a relatively broadband reduction of STL caused by the inter-modal coupling in middle frequencies. The damping mechanism can be divided into two aspects: (i) the reduction of modal amplitude by vibration energy dissipation, and (ii) the change of bending modal shapes. CLD treatment is a concise and effective way to achieve stable sound insulation performance.

Topological optimization design on constrained layer damping treatment for vibration suppression of thin-walled structures via improved BESO method

In this paper, an improved bi-directional evolutionary structural optimization (BESO) technique is proposed, to investigate topological optimization design on constrained layer damping (CLD) treatment for vibration suppression of experiment rack backplane. First, the optimization model for vibration reduction of CLD treated backplane is established, with volume fraction of CLD material as constraint condition, and the maximization of weighted value of the first four order modal loss factors of the structure as objective function. An improved evolutionary rate considering the CLD element sensitivity coefficient of variation of each iteration is presented to increase optimization efficiency. Then, the BESO with improved evolutionary rate is utilized to search the optimal CLD layout of the experiment rack backplane. CLD layouts of three optimization schemes with different volume fraction of CLD material are obtained, and are highly consistent with the stress distribution of the backplane viscoelastic layer, which verifies the rationality of the optimization results. Visualization of iterative optimization process, including elements removal/addition and dynamic change of CLD elements sensitivity in each iteration, is demonstrated, respectively. Further, the effect of improved evolutionary rate on optimization process is discussed. Compared with the conventional BESO method, the improved BESO technique can not only obtain a more reasonable optimized CLD layout, but also improve the optimization efficiency and accuracy. Finally, the validity of the optimized CLD layout is analyzed from three following aspects: natural frequency, modal loss factor and vibration response under order excitation. Numerical and experimental results show that the proposed BESO technique is effective and efficient in the application of CLD material, and the small amount of CLD material can be retained under the premise of ensuring damping.

Dynamic modeling and vibration analysis of planar pipeline with partial constrained layer damping treatment: Theoretical and experimental studies

As an important portion of pipeline systems, the vibration suppression analysis of the plane pipeline is of great significance for life prediction and vibration control. To reduce pipeline vibration by attaching constrained layer damping (CLD), the vibration characteristics of the Z-shaped pipeline (taking a Z-shaped pipeline in the planar pipeline as an example) with partial CLD treatment are investigated, and a modeling method is proposed. Based on the Timoshenko beam theory, the energy formulas of laminated straight pipeline with CLD and curved pipeline are developed. Artificial springs are introduced to establish the coupling between pipeline segments and consider the clamp constraint. Four kinds of polynomials are compared to expand the displacement functions, and the dynamic equitation is derived by employing the Lagrange equation. The rationality of the model is verified by a FE model and by in-plane and out-of-plane experimental test systems of the Z-shaped pipeline before and after CLD treatment. In addition, the results show that a change in the geometrical parameters of the pipeline can cause frequency alternation. The influence law of CLD thickness on the Z-shaped pipeline in-plane and out-of-plane is inconsistent. The modeling method can further provide a basis for nonlinear vibration analysis of pipeline systems.

Modelling of thin constrained layer damping treatment applied to composite floor beams

The Vibration Serviceability Limit State (VSLS) due to human dynamic loading is increasingly becoming the sizing criterion for long-span composite floors. To meet this requirement, structural designers usually tend to increase the stiffness or the mass of the floor. This paper studies a damping technology applicable to these floors since the design stage for improving their dynamic behaviour by increasing their damping capacity and avoiding thus over-sizing the floor structure to meet the VSLS. The studied technology is based on a Constrained Layer Damping (CLD) treatment made of a thin viscoelastic (VE) layer integrated between the concrete slab and the steel profile of the floor, along a percentage of the beam length near the supports. Thus, this paper proposes a simplified Finite Element (FE) approach to model this treatment based on using simple SPRING elements for the VE layer and a corrected version of the modal strain energy method for damping estimation, avoiding thus the use of complex modal analysis. The proposed approach is used to assess the additional damping ratio provided by the CLD treatment. The accuracy of this approach has been validated by comparing it with detailed FE models and widely accepted analytical formulations considering different percentages of the beams’ length treated with CLD. Finally, an application example has been performed with CLD-treated and untreated single-spanning composite floors, showing: i) CLD-treated floors have a better dynamic performance, and ii) CLD technology enables reducing the amount of steel needed to design lightweight floors especially sensitive to vibration.

Active damping of multiscale composite shells using Sinus theory incorporated with Murakami’s zig-zag function

This article is divided into two main sections, the focus of the first is to develop a finite element model using the in-house MATLAB codes, implementing the sinusoidal shear deformation theory incorporating Murakami’s zig-zag function to encounter the inherent zig-zag effects of the laminated structures. The focus of the second is to investigate the active damping behavior of laminated multiscale hybrid fiber-reinforced composite (HFRC) smart shells via active constrained layer damping (ACLD) treatment using the proposed theory. The ACLD treatment layers comprise a constrained layer of viscoelastic material and an advance constraining layer of 1–3 piezoelectric composite material with vertically/obliquely oriented piezo-fibers, responsible for the active control. The computed numerical results of the laminated HFRC shell are analyzed and compared with the laminated base composite shell for symmetric/anti-symmetric cross-ply and anti-symmetric angle-ply. Moreover, we investigated the effect of carbon nanotube waviness and piezo-fibers orientation on the damping performance of the laminated HFRC/ACLD smart shell system. The analysis shows that the damping behavior of laminated HFRC shells improved due to the waviness of carbon nanotubes and that the orientation of piezo-fibers greatly influenced the effectiveness of the ACLD treatment patches. The proposed laminated multiscale HFRC/ACLD shell system with straight and wavy carbon nanotubes can be extensively used in structural health monitoring applications to actively control the mechanical vibrations induced in structures.

Nonlinear active control of thermally induced pyro-coupled vibrations in porous-agglomerated CNT core sandwich plate with magneto-piezo-elastic facings

In this article, the damped nonlinear transient response of a smart sandwich plate (SSP) comprising of agglomerated CNT-reinforced porous nanocomposite core with multifunctional magneto-piezo-elastic (MPE) facesheets, subjected to the thermal environment, is numerically investigated. The synergistic influence of agglomeration, porosity and pyro-coupling on vibration control is studied for the first time under the finite element framework. The attenuation of the vibrations is caused by active constrained layer damping (ACLD) treatment. The kinematics of the plate is based on the layer-wise shear deformation theory and von-Karman’s nonlinearity. The viscoelastic properties of the ACLD patch and CNT agglomeration of the core are mathematically modelled using Golla–Hughes–McTavish and Eshelby–Mori–Tanaka methods, respectively. A comprehensive examination of the inter-related effects of different agglomeration states, porosity distributions and thermal loading profiles has been performed. The new insights on controlling pyro-coupled induced vibrations of smart sandwich plates by supplying control voltage directly to the MPE facesheets without ACLD treatment have been discussed thoroughly. The numerical analysis confirms the significant effects of pyro-coupling associated with active vibration control response of SSP.

Structural Optimization of Lightweight Composite Floors with Integrated Constrained Layer Damping for Vibration Control

Due to current architectural trends, contemporary public buildings are becoming open-plan spaces with much less weight and damping. Consequently, Vibration Serviceability Limit State (VSLS) due to human-induced vibrations has become an increasing concern for structural engineers, especially when designing offices, hospitals, or gymnasiums. When dealing with resonant vibrations, a slight increase in the floor-damping enables decreasing considerably the vibration level. The damping strategy studied in this work is usually known in the literature as Constrained Layer Damping (CLD) and consists of a viscoelastic layer constrained between the concrete slab and the steel beam of a lightweight composite floor. In this paper, a complete structural checking methodology has been developed for analyzing all the limit states that determine the final sizing of a steel–concrete composite floor treated with CLD, including a detailed analysis of the VSLS. The methodology has been used for setting a structural optimization problem for floors with and without CLD treatments. Thus, it has been demonstrated that the integration of CLD treatments at the design stage of the building allows the development of lighter floor structures with a smaller embodied carbon (EC) footprint, especially for long-span schemes with restrictive vibration limitations.

Synergistic effect of flexural wave broadband attenuation in beam with periodic-parallel constrained layer damping (P-PCLD)

The efficient suppression of broadband flexural waves is an important area of research. Owing to the multi-bandgap behaviors of parallel beams and the broadband wave attenuation characteristics of the constrained layer damping (CLD) treatment, their interaction mechanism might improve the flexural wave attenuation efficiency. Hence, in this study, a beam with a periodic parallel constrained layer damping (P-PCLD) was formed using Euler and sandwich beam parallel coupling. The wave propagation constant of the P-PCLD was derived based on the infinite periodic structure theory and evaluated using the finite element method. The practical benefit of the P-PCLD was first evaluated by studying the enhancement of the flexural wave suppression in sandwich beams (SBs) by adding parallel Euler beams. Further, the performance difference between the P-PCLD and constrained layer damping (CLD) treatments with a similar material weight was compared. The results showed that a reasonably designed P-PCLD could achieve better flexural wave attenuation performances than SBs or an equivalent weight CLD in both the low-frequency bandgap and passband range.

Viscoelastic damping design – A novel approach for shape optimization of Constrained Layer Damping treatments at different ambient temperatures

Passive damping plays an important role in the vibration mitigation of aeronautic structures. In contrast to active systems, passive damping systems do not require any energy supply. Thus, their readiness is independent, which reduces the failure probability compared to active systems. Constrained Layer Damping (CLD) has become an established treatment for damping bending vibrations. Unlike other passive systems such as shock-mounts, CLD can be compactly integrated into an existing structure as an add-on solution. However, the design scope is limited by mass constraints and the optimal design for maximum damping must be found by optimization. For this purpose, a novel optimization approach is presented. The layer widths of the core and face layers of a CLD structure are treated as design parameters. Compared to the strategy of placing CLD patches on vibration antinodes, the proposed approach provides up to 52 % higher damping. The optimal design of a generic beam structure is determined considering different modes, viscoelastic material stiffnesses and ambient temperatures. Furthermore, the simulated damping is experimentally verified for a shape-optimized beam. The analyses show that the optimal design depends significantly on the viscoelastic material stiffness and is therefore temperature dependent. As a consequence, a generalized design guideline for CLD treatments cannot be derived.

Dynamical analysis and vibration estimation of a flexible plate with enhanced active constrained layer damping treatment by combinatorial neural networks of surrogates

The effective estimation of the vibration of spacecrafts are frontier issues in the aerospace industry. But the vibration of aerospace components such as space solar panels and flexible manipulators under large overall rotating motion is usually very complex due to strong nonlinearity and often requires a lot of repetitive and burdensome calculations. Artificial neural network (ANN) is composed of interconnected neurons, and a surrogate model can be established to effectively predict the mechanical characteristics. In addition, the computational efficiency will be greatly improved if the object is changed from the model that is established by commercial finite element method (FEM) software or numerical calculations to the surrogates. However, the stochasticity of the estimation by single neural network is inevitable, and some neural networks much rely on the initial weight and threshold. This paper will implement a new combinatorial strategy that relies on multiple neural network models, which have different activation functions and regression feedback processes based on reasonable selection of sample points. To solve the elongated training time led by comparing these neural networks, genetic algorithm (GA) is used to optimize the iteration speed of one neural network when finding the optimal output value. Thus, better estimation accuracy will be achieved by designing an algorithm to combine these combinatorial neural networks of surrogates (CNNS). Based on the proposed method, the vibration estimation of a rotating flexible plate with enhanced active constrained layer damping (EACLD) treatment, and the vibration suppression capacity of the composite structure under various operating conditions will be investigated.

A smoothed finite element formulation using zig-zag theory for hybrid damping vibration control of laminated functionally graded carbon nanotube reinforced composite plates

The paper presents an efficient numerical approach to deal with the hybrid damping vibration control of laminated functionally graded carbon-nanotube reinforced composite plates (FG-CNTRC) structures. In order to evaluate the damped response, a smoothed finite element model has been derived to simulate the laminated FG-CNTRC plate integrated with active constrained layer damping (ACLD) treatment patches consisting of 1-3 piezoelectric composite (1-3 PZC) layer and a viscoelastic layer. The constrained layer of the ACLD patch is modeled as viscoelastic materials by using the complex modulus. In order to enhance the efficiency of the numerical approach, the proposed framework integrates the zig-zag theory into the cell-based smoothed discrete shear gap method (CS-DSG3) to help increase the accuracy and reduce the computational cost. The accuracy and reliability of the present study are validated by comparing its numerical results to those of other available numerical methods. Moreover, the effect of CNT distribution, nanotube volume fraction, and CNT orientation on the damping behavior of FG-CNTRC plates are investigated. Additionally, the influence of symmetrical and asymmetrical damping treatment configuration for controlling the vibration is also examined in detail. • An efficient numerical approach for the hybrid damping of FG-CNTRC plates is proposed. • Proposed framework helps increase the accuracy and reduce computational cost. • Effects of CNT distribution, volume fraction, and orientation on the damping behavior are examined. • Influence of symmetrical and asymmetrical configuration is examined.

Augmented active constrained layer damping of beams using graphite reinforced viscoelastic composite material

This paper deals with the use of viscoelastic composite material (VECM) for the constrained layer of an active constrained layer damping (ACLD) treatment for enhanced damping characteristics due to contributions of extensional strains in addition to transverse shear strain. The proposed VECM layer is composed of graphite fibers reinforced in a conventional viscoelastic matrix. The bending analysis of the overall beam is carried out and contributions of extensional and shear strains for damping behavior are found out. The effects of changing various geometric parameters of the present VECM layer on the control performance of the ACLD treatment have also been evaluated and presented.

Active control of nonlinear coupled transient vibrations of multifunctional sandwich plates with agglomerated FG-CNTs core/magneto-electro-elastic facesheets

This article investigates the controlled nonlinear transient response of sandwich plates made of magneto-electro-elastic (MEE) facesheets and agglomerated carbon nanotube (ACNT) core. The control is achieved by active constrained layer damping (ACLD) treatment which consists of piezoelectric (PE) and viscoelastic (VE) layers. The agglomeration is mathematically modelled using the Eshelby–Mori–Tanaka approach. The governing equations are derived under the framework of finite element (FE) methods using Hamilton’s principle and condensation technique. The VE patch of the ACLD treatment is modelled through the Golla–Hughes–McTavish method. This evaluation has considered two states of agglomerations, such as complete and partial agglomeration. The proposed FE model facilitates the integration of the three-field (magnetic, electric and elastic) coupling with the agglomeration and electromagnetic circuit effects, which makes this work interesting. It acts as a ready tool for the realistic design of a smart structure and system. In addition, the computational efforts and efficiency of the proposed FE model prove to be better than the commercial numerical software. Extensive numerical examples are solved to assess the influence of CNT distributions, electromagnetic circuits, coupling, mechanical boundary conditions, thickness configuration and ACLD patch position. This work serves as a novel benchmark solution for further research on the active control of agglomerated CNT structures.

Effect of orientation of CNTs and piezoelectric fibers on the damping performance of multiscale composite plate

The present work deals with the study of active constrained layer damping treatment of multiscale carbon nanotube-based hybrid carbon fiber-reinforced composite plates. The distinctive feature of novel multiscale hybrid carbon fiber-reinforced composites is that the wavy/straight carbon nanotubes are distributed uniformly in the matrix phase of hybrid carbon fiber-reinforced composites, and the waviness of carbon nanotubes is considered to be coplanar with two mutually orthogonal planes. Firstly, the effective elastic properties of hybrid carbon fiber-reinforced composites are estimated using the Mori-Tanaka method. The outcomes of the Mori-Tanaka method suggest that the transverse effective elastic properties of hybrid carbon fiber-reinforced composites containing wavy carbon nanotubes are better than those of hybrid carbon fiber-reinforced composites with straight carbon nanotubes. Secondly, a finite element model using the layer-wise first-order shear deformation theory is developed to study the damping performance of hybrid carbon fiber-reinforced composite plates integrated with the active constrained layer damping treatment. The constraining layer of active constrained layer damping treatment is a 1–3 piezoelectric composite layer with vertically/obliquely-oriented piezo-fibers. The piezo-fibers make an angle [Formula: see text] with the vertical plane of a layer coplanar with the xz- or yz-plane. The effect of the orientation of piezo-fibers angle on the control authority of active constrained layer damping treatment patches is investigated. Our results reveal that the performance of multiscale hybrid carbon fiber-reinforced composite plates has improved due to the incorporation of wavy carbon nanotubes, and the orientation angle of piezo-fibers has a major impact on the control authority of active constrained layer damping patches. The proposed multiscale composite with the combination of wavy carbon nanotubes and active constrained layer damping patches can be actively used in the aerospace and transport industries to control the mechanical vibrations of structures.

Concurrent Topology Optimization for Maximizing the Modal Loss Factor of Plates with Constrained Layer Damping Treatment.

Damping performance of the plates with constrained layer damping (CLD) treatment mainly depends on the layout of CLD material and the material physical properties of the viscoelastic damping layer. This paper develops a concurrent topology optimization methodology for maximizing the modal loss factor (MLF) of plates with CLD treatment. At the macro scale, the damping layer is composed of 3D periodic unit cells (PUC) of cellular viscoelastic damping materials. At the micro scale, due to the deformation of viscoelastic damping material affected by the base and constrained layers, the representative volume element (RVE) considering a rigid skin effect is used to improve the accuracy of the effective constitutive matrix of the viscoelastic damping material. Maximizing the MLFs of CLD plates is employed as the design objectives in optimization procedure. The sensitivities with respect to macrodesign variables are formulated using the adjoint vector method while considering the contribution of eigenvectors, while the influence of macroeigenvectors is ignored to improve the computational efficiency in the mesosensitivity analysis. The macro and meso scales design variables are simultaneously updated using the Method of Moving Asymptotes (MMA) to find concurrently optimal configurations of constrained and viscoelastic damping layers at the macro scale and viscoelastic damping materials at the micro scale. Two rectangular plates with different boundary conditions are presented to validate the optimization procedure and demonstrate the effectiveness of the proposed concurrent topology optimization approach. The effects of optimization objectives and volume fractions on the design results are investigated. The results indicate that the optimized layouts of the macrostructure are dependent on the objective mode and the volume fraction on the meso scale. The optimized designs on the meso scale are mainly related to the objective mode. By varying the volume fraction on the macro scale, the optimized designs on the meso scale are different only in their detailed size, which is reflected in the values of the equivalent constitutive matrices.