Viscoelastic Composite Structures Research Articles

Dynamic topology optimization of two-phase viscoelastic composite structures considering frequency- and temperature-dependent properties under random excitation

This article proposes an efficient optimum design method of constrained layer damping (CLD) plates characterized by non-proportional damping subjected to random excitation. Considering frequency and temperature dependence, a two-phase viscoelastic composite material composed of stiffness-phase and damping-phase materials is used as the damping layer. The pseudo excitation and hybrid expansion methods are adopted to compute the random responses at the specified frequency intervals as the objective functions. The sensitivity analysis is performed through the adjoint vector method. The similarity index is defined to distinguish the various optimal layouts quantitatively. Several numerical examples clearly demonstrate the robustness and effectiveness of the proposed method, highlighting a remarkable improvement of over 60% in computational efficiency. Furthermore, it is proved that, when subjected to broadband random excitation, the damping materials' temperature- and frequency-dependent properties are critical factors in obtaining accurate vibration responses and desirable optimal layouts. The effects of the layer thicknesses and volume fractions of composite structures on topology optimization are also discussed. The results indicate that both layer thickness and volume fraction can change the mechanical properties of the composite structure and further affect the distribution characteristics of the damping material.

A material–structure-wave integrated hydro-viscoelastic model for floating composite structure with generalized boundary

A floating viscoelastic composite structure with generalized elastic constraints, in which the material–structure-wave interaction induces energy dissipation, is analyzed with a novel cross-scale integrated hydro-viscoelastic model. A double-level three-dimensional (3D) representative volume element model coupling mesoscale reinforced particles to a macroscale composite structure is established to obtain the structure's viscoelastic dynamic equation. Therefore, a hydro-viscoelasticity analytical model for floating composite structures with arbitrary elastic constraints under wave action is developed in the context of potential flow theory. In the process of solving the velocity potential, the dispersion equation of the water covered by the composite structure is derived. The hydrodynamic and mechanical behaviors of the floating composite structure, including the reflection coefficient, transmission coefficient, dissipation coefficient, deflection, shear force, and bending moment, are comprehensively calculated, which depend on the cross-scale integrated effects of wave action, structural features, material characteristics, and constraint combinations. This material–structure-wave integrated model would be useful to elucidate the hydro-viscoelastic dissipation mechanism of marine structures.

Wave Propagation in the Viscoelastic Functionally Graded Cylindrical Shell Based on the First-Order Shear Deformation Theory.

Based on the first-order shear deformation theory (FSDT) and Kelvin-Voigt viscoelastic model, one derives a wave equation of longitudinal guide waves in viscoelastic orthotropic cylindrical shells, which analytically solves the wave equation and explains the intrinsic meaning of the wave propagation. In the numerical examples, the velocity curves of the first few modes for the elastic cylindrical shell are first calculated, and the results of the available literature are compared to verify the derivation and programming. Furthermore, the phase velocity curves and attenuation coefficient curves of the guide waves for a functionally graded (FG) shell are calculated, and the effects of viscoelastic parameters, material gradient patterns, material volume fractions, and size ratios on the phase velocity curves and attenuation curves are studied. This study can be widely used to analytically model the wave propagating in inhomogeneous viscoelastic composite structures and present a theoretical basis for the excellent service performance of composite structures and ultrasonic devices.

Impact of imperfectness on the love-type wave propagation in a viscoelastic composite structure with couple stress

The present paper is intended to frame-out the analytical approach to study the transference of Love-type waves in a viscoelastic sandy layer sandwiched between a size-dependent consistent couple stress to take care of earth’s interior microstructural nature and an orthotropic viscoelastic half-space. An additional parameter termed as characteristic length which is used to investigate the internal microstructural structure of the earth’s interior, which provides us the deeper insights of the analysis of wave propagation aspects. With the help of analytical variable separable technique, the closed version of dispersion equation for the Love-type waves has been derived. The impacts of different material parameters like characteristic length (l), sandy parameter ( η 2 ′ ) , viscoelastic parameters (F1, F2, F3), thickness ratio (H3), and imperfectness parameter (σ1, σ2) which are involved in this study are encapsulated by means of graphs on the phase velocity of Love-type waves. Finally, the obtained result is well match up with the classical Love wave equation. This approach of employing micro continuum theories to analyze seismic waves can bring some useful adjustments to previously established facts about seismic waves, as well as improve the applications of micro continuum theories in the field of seismology.

Dynamic response of fractionally damped two-layered viscoelastic plate

The vibration response of the plates attached with the free viscoelastic damping layer is investigated to predict the performance of free surface damping treatment. The frequency-dependent dynamic properties of the viscoelastic layer are expressed by fractional Kelvin-Voigt model. A simple and efficient identification approach based on the gradient-based optimization principle is employed to evaluate the viscoelastic model parameters from the experimental data. Both classical and fractional Kelvin-Voigt models are employed to describe the viscoelasticity, and the corresponding model parameters are identified. Further, the application of these identified parameters in the modeling and analyzing of real viscoelastic composite structures is demonstrated through quantitative examples. Step load-induced transient responses of the viscoelastic structures modeled using the classical and fractional model parameters are investigated and compared, to demonstrate the consequences of unknowingly using the classical Kelvin-Voigt model. The effects of the viscoelastic layer thickness on the transient response of the two-layered plate are also studied.

Prediction of frequency and spatially dependent attenuation of guided waves propagating in mounted and unmounted A380 parts made up of anisotropic viscoelastic composite laminates

Monitoring damage in composite structures using guided wave-based techniques is particularly effective due to their excellent ability to propagate over relatively long distance and hence to cover a large area with few testing time and equipment. The industrialization of this method is highly tributary of the number and placement of the active elements. Yet, the optimal sensorization of a structure relies on the decrease in amplitude of guided waves over propagation distance. A reliable prediction of attenuation of guided waves is still a challenge especially for anisotropic viscoelastic composite materials which exhibit complex changes of attenuation with propagation direction and thus a spatial dependency of attenuation. In this paper, the damped global matrix method (dGMM), having stable and efficient merits, is developed to predict the frequency and spatially dependent attenuation of waves propagating in anisotropic composite materials. dGMM integrates three damping models (Hysteretic, Kelvin-Voigt, and Biot models) into the conventional undamped GMM to consider viscoelasticity of composite laminates. The proposed dGMM is first theoretically validated by numerical comparison with the semi-analytical finite element method. In addition, two industrial case studies, parts of an A380 nacelle at scale one, are employed to experimentally validate the proposed attenuation prediction method. The first one is a fan cowl structure and the second one is an inner fixed structure, both either unmounted or mounted on an actual instrumented A380 plane. This makes the validation extremely valuable for both the scientific and industrial communities. The proposed attenuation prediction method thus paves the way to optimally deploy sensor network for structural health monitoring of anisotropic viscoelastic composite structures.

Mixed-hybrid and mixed-discontinuous Galerkin methods for linear dynamical elastic–viscoelastic composite structures

Abstract We introduce and analyze a stress-based formulation for Zener’s model in linear viscoelasticity. The method is aimed to tackle efficiently heterogeneous materials that admit purely elastic and viscoelastic parts in their composition.We write the mixed variational formulation of the problem in terms of a class of tensorial wave equation and obtain an energy estimate that guaranties the well-posedness of the problem through a standard Galerkin procedure. We propose and analyze mixed continuous and discontinuous Galerkin space discretizations of the problem and derive optimal error bounds for each semidiscrete solution in the corresponding energy norm. Finally, we discuss full discretization strategies for both Galerkin methods.

Modal parameter calculation for viscoelastic composite structures from reduced order models

The moduli and loss factors of viscoelastic materials are frequency-dependent, which brings difficulty to solve the eigenvalue problems. In this note, an estimation method for resonance frequencies and loss factors of viscoelastic composite structures from reduced order models is presented. The reduced order model could be constructed from calculated or measured forced vibration data, and there is no need to know the specific structural matrices or to solve the eigenvalue problem of the vibration system directly. Thus, the difficulties caused by frequency-dependent behaviors of moduli and loss factors of viscoelastic materials are avoided. Numerical examples are presented to illustrate and validate the method.

Vibrational analysis of Love waves in a viscoelastic composite multilayered structure

A unified procedure is presented to investigate the dispersion and damping behavior of Love waves in a double-layered structure. The double-layered structure is comprised of a viscoelastic fiber-reinforced medium (Medium I) embedded between a viscoelastic sandy layer (Medium II) and a viscoelastic porous semi-infinite medium (Medium III). The displacement vectors for the respective medium have been obtained using analytical techniques. Using the separation of variables method and admissible boundary conditions at the free surface and the interfaces, the complex frequency equation is obtained in closed form. The substantial impact of all material parameters involved in the considered model on the phase velocity as well as damped velocity has been observed numerically and shown by graphical illustrations. The outcomes from this analysis may serve as a dynamic tool in various fields including geophysics, geotechnical, and earthquake engineering.

Transient thermomechanical responses of multilayered viscoelastic composite structure with non-idealized interfacial conditions in the context of generalized thermoviscoelasticity theory with time-fractional order strain

Nowadays, a multilayered viscoelastic composite structure stands as one of the most representative active/passive vibration isolator and high-efficient damper to avoid unwanted vibrations in civil and ocean engineering, which is commonly applied in harsh non-uniform temperature environment (e.g., high heat-flux, drastic changes of temperature, etc.). In such a case, thermoviscoelastic response analysis is of great importance for the safety design of viscoelastic composites, and so a thorough and comprehensive study on this issue is imperatively needed. This work aims to conduct an analytical study of transient thermomechanical responses of multilayered viscoelastic composite structure under time-dependent heating loads. In the context of generalized thermoviscoelasticity theory with time-fractional order strain, a composite laminated viscoelastic plate is chosen as the analytical model while governing equations of each homogeneous layer accounting for non-idealized interfacial conditions are systematically formulated. Then, a semi-analytical approach via Laplace transform is adopted to deal with the problem. The effects of fractional order parameters and material constants’ ratio on the structural dynamic responses are fully discussed to provide new insights and basic guidelines for vibration control and thermal management of viscoelastic composites, especially for the surface coating at the interface between any two adjacent viscoelastic layers.

A hierarchical asymptotic homogenization approach for viscoelastic composites

Effective properties of non-aging linear viscoelastic and hierarchical composites are investigated via a three-scale asymptotic homogenization method. In this approach, we consider the assumption of a generalized periodicity in the different structural levels and their characterization through the so-called stratified functions. The expressions for the associated local and homogenized problems, and the effective coefficients are derived at each level of organization by using the correspondence principle and the Laplace-Carson transform. Considering isotropic components and a perfect contact at the interfaces between the constituents, analytical solutions, in the Laplace-Carson space, are found for the local problems and the effective coefficients are computed. An interconversion procedure between the effective relaxation modulus and the effective creep compliance is carried out for obtaining information about both viscoelastic properties. The numerical inversion to the original temporal space is also performed. Finally, we exploit the potential of the approach and study the overall properties of a hierarchical viscoelastic composite structure representing the dermis.

Parameter determination for the Mini-Oscillator Model of the Viscoelastic Material

The viscoelastic composite structure is widely used in the vibration and noise suppression of thin-walled components. The vibration analysis of viscoelastic composite structures must involve the constitutive equation of viscoelastic materials. The form of the constitutive equation of viscoelastic material has a decisive influence on the dynamic analysis process of viscoelastic composite structures. Since the constitutive relation of the viscoelastic material changes with time, frequency and temperature, the analysis of the dynamic characteristics of the viscoelastic composite structure is greatly complicated. The mini-oscillator model considers the frequency-dependent properties of viscoelastic materials. Therefore, it is widely used in the dynamic analysis of composite structures. Aims at the need of viscoelastic material passive vibration control for viscoelastic composite structures, a method for determining the parameters of mini-oscillator model is proposed. The method obtains the viscoelastic material mini-oscillator model parameters by parameter fitting by the measured viscoelastic material complex modulus data in the frequency domain or other viscoelastic material damping model expressions obtained from experimental data. The results are compared with fractional derivative model. The results show that the mini-oscillator model can correctly describe stress-strain relationship of viscoelastic material and the parameter fitting method proposed in this paper is accurate and effective.

SH-wave propagation in linearly varying fiber-reinforced viscoelastic composite structure uninitial stress

The paper studies the behavior of horizontally polarized shear wave (SH-wave) in an initially stressed fiber-reinforced viscoelastic composite structure, where the elastic parameters vary linearly along the depth of the crustal layer. The displacements in each media have been calculated analytically and closed form dispersion equation has been derived with the help of intrinsic boundary conditions. The dispersion equation thus obtained is a complex valued function, whose real part contains the phase velocity and the imaginary part contains the damped velocity. To demonstrate the effect of various parameters, numerical simulations have been conducted and graphs have been plotted for the phase velocity and the damped velocity against the wave number. Furthermore, a comparative study has been undertaken by means of graphical illustrations to explain its remarkable effects.

Elastic–Viscoelastic Composite Structures Analysis With an Improved Burgers Model

Composite structures integrated with viscoelastic materials are becoming more and more popular in the application of vibration suppression. This paper presents a comprehensive approach for analyzing this class of structures with an improved Burgers model, from material constitutive modeling, finite element formulation to solution method. The refined model consists of a spring component and multiple classical Burgers components in parallel, where the spring component converts the viscoelastic fluid model to a viscoelastic solid model and the multiple Burgers components increase the accuracy. Through the introduction of auxiliary coordinates, the model is applied to the finite element formulation of composites structures with viscoelastic materials. Consequently, a complicated Volterra integro-differential equation is transformed into a standard second-order differential equation and solution techniques for linear elastic structures can be directly used for elastic–viscoelastic composite structures. The improved Burgers model is a second-order mini-oscillator model, in which every mini-oscillator term has four parameters. The model parameters determination is performed by optimization algorithm. By comparison of model fitting results for a typical viscoelastic material, the refined model is better in accuracy than Golla–Hughes–McTavish (GHM) model and original Burgers model. Finally, several numerical examples are presented to further verify the effectiveness of the improved Burgers model.

Analysis of the Effects of Frequency Dependent Characteristic on the Vibration of Viscoelastic Composite Structure

Analysis of the Effects of Frequency Dependent Characteristic on the Vibration of Viscoelastic Composite Structure

Analysis of frequency-domain vibration response of thin plate attached with viscoelastic free layer damping

ABSTRACTTo predict the vibration response of viscoelastic composite structure, two key issues need to be conducted, one is introducing the constitutive model of viscoelastic material into the analysis model and the other is describing the real damping behavior of viscoelastic composite structure. The emphasis of this study is to obtain the effects of frequency dependence on the vibration response of viscoelastic composite structure and the method of introducing two kinds of damping (viscoelastic material damping and remaining equivalent viscous damping). Vibration response analysis in frequency domain was investigated for viscoelastically damped plate. A cantilever plate attached with the ZN_1 viscoelastic free layer damping (FLD) was chosen to demonstrate the developed method. Frequency-domain response of the composite plate were solved and the obtained results were compared with the experimental values for the purpose of assessing the rationality of the proposed method. In addition, in order to obtain the effects of viscoelastic material parameters on vibration response of viscoelastic composite structure, a detailed parametric analysis was performed. This study shows that the frequency dependent characteristic of viscoelastic material has significant influence on the vibration response in the resonant region and acceptable results can be achieved in the non-resonant region if frequency dependent parameters are substituted by average values of the viscoelastic parameters reasonably in the analysis process.

Improved layer-wise optimization algorithm for the design of viscoelastic composite structures

To combine lightness and rigidity in passive damping, elastic faces of visco-elastic sandwich structures are often made of laminates. These laminates are usually cross-ply, angle-ply, special orthotropic, anti-symmetric or balanced laminates which are commonly called classical laminates. In the design of visco-elastic sandwich structures, one often seeks to maximize the loss factor of the structure and its rigidity. To achieve this, computations are often made for several combinations of laminate fibers’ orientation angles. In this paper, the optimal design of composite laminates regarding the orientation angles is carried out by an improved layer-wise optimization algorithm (ILOA) by coupling a parametric non-linear eigenvalue problem resolution method (PANLER) with the so-called layer-wise optimization algorithm (LOA) to determine maximal frequencies and loss factors. The results are checked against a classical optimization algorithm.

Numerical method for nonlinear complex eigenvalues problems depending on two parameters: Application to three-layered viscoelastic composite structures

ABSTRACTThe design of high-damping composite viscoelastic sandwich structures (CVSS) requires continuous study of damping properties according to some parameters. The common design parameters that directly affect the damping properties of CVSS are the fibers' orientation and the thicknesses of the composite layers. However, until now there has been no method for continuously studying the influences of any design parameter on the damping properties of CVSS. Also, to study the influence of a design parameter on the damping properties of CVSS, computations are made for various discrete values of this parameter. These calculations are qualified incrementally, and are very expensive in computation time and do not allow to follow continuously the effects of the parameter on the damping properties of CVSS. In order to tackle these problems, we propose in this article a numerical method for studying the damping properties variation of CVSS according to a chosen modeling parameter, through the resolution of a generic, residual, complex nonlinear eigenvalues problems having frequency dependence and a modeling parameter that describes a study interval. This method is based on the asymptotic numerical method, automatic differentiation, homotopy technique and continuation. An application is performed to study the variation of the damping properties of a three-layered symmetric viscoelastic sandwich plates according to the fibers orientation of their orthotropic faces layers.

Stochastic vibration suppression analysis of an optimal bounded controlled sandwich beam with MR visco-elastomer core

To control the stochastic vibration of a vibration-sensitive instrument supported on a beam, the beam is designed as a sandwich structure with magneto-rheological visco-elastomer (MRVE) core. The MRVE has dynamic properties such as stiffness and damping adjustable by applied magnetic fields. To achieve better vibration control effectiveness, the optimal bounded parametric control for the MRVE sandwich beam with supported mass under stochastic and deterministic support motion excitations is proposed, and the stochastic and shock vibration suppression capability of the optimally controlled beam with multi-mode coupling is studied. The dynamic behavior of MRVE core is described by the visco-elastic Kelvin-Voigt model with a controllable parameter dependent on applied magnetic fields, and the parameter is considered as an active bounded control. The partial differential equations for horizontal and vertical coupling motions of the sandwich beam are obtained and converted into the multi-mode coupling vibration equations with the bounded nonlinear parametric control according to the Galerkin method. The vibration equations and corresponding performance index construct the optimal bounded parametric control problem. Then the dynamical programming equation for the control problem is derived based on the dynamical programming principle. The optimal bounded parametric control law is obtained by solving the programming equation with the bounded control constraint. The controlled vibration responses of the MRVE sandwich beam under stochastic and shock excitations are obtained by substituting the optimal bounded control into the vibration equations and solving them. The further remarkable vibration suppression capability of the optimal bounded control compared with the passive control and the influence of the control parameters on the stochastic vibration suppression effectiveness are illustrated with numerical results. The proposed optimal bounded parametric control strategy is applicable to smart visco-elastic composite structures under deterministic and stochastic excitations for improving vibration control effectiveness.

Model uncertainties in computational viscoelastic linear structural dynamics

This paper deals with the analysis of the propagation of uncertainties in computational linear dynamics for linear viscoelastic composite structures in the presence of uncertainties. In the frequency domain, the generalised damping matrix and the generalised stiffness matrix of the stochastic computational reduced-order model are random frequency-dependent matrices. Due to the causality of the dynamical system, these two frequency-dependent random matrices are statistically dependent and their probabilistic model involves a Hilbert transform. In this paper, a computational analysis of the propagation of uncertainties is presented for a composite viscoelastic structure in the frequency range.