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In this paper, the stress wave propagation and attenuation laws in heterogeneous materials such as rock and concrete are investigated by equating these materials to periodic materials through the viscoelastic analogy method. Firstly, the relaxation functions and stress response curves of the periodic materials are obtained by using a novel numerical inverse transformation method based on the viscoelastic analogy theory. Then, an experimental study of stress wave propagation in slender concrete rods was carried out on a Hopkinson pressure rod platform. The results show that there is a significant attenuation trend of the stress wave during 10 times of reflections. Comparison of the numerical inverse transform results with the experimental results shows that the decay rate in the experiment is faster than that predicted by simple viscosity. Finally, the effects of geometric dispersion and frictional dissipation of energy are considered in ABAQUS finite element simulations. The finite element analysis results show that inherent viscosity in heterogeneous materials can partially explain the stress wave attenuation in concrete. The viscoelastic simulation method effectively predicts stress wave attenuation in heterogeneous materials and provides theoretical insights for engineering applications. [ABSTRACT FROM AUTHOR]

Viscoelastic materials have been widely used for the purpose of passive vibration mitigation in various types of mechanical systems, including, industrial machinery, civil structures and vehicles. In this paper, the use of those materials in aeroelastic systems is investigated, with emphasis placed on the influence of the viscoelastic behavior on the flutter speeds of two-degree-of-freedom typical section models, in which viscoelastic elements are introduced in addition to elastic elements associated to heave and pitch motions. The equations of motion of the aeroelastic system are modified to account for the dependence of the viscoelastic behavior on frequency and temperature, by using the concepts of complex modulus and shift factor. The aerodynamic forces and moments in subsonic regime are modeled according to Theodorsen's method. Numerical simulations are conducted to evaluate the influence of the addition of viscoelastic elements on the flutter speed and elucidate the separated influences of stiffness and damping additions. An experimental wind tunnel setup consisting of a rigid wing supported by flexible elements in pitch and plunge motions has been modified to enable the introduction of viscoelastic elements in parallel to those flexible elements. For various configurations of viscoelastic additions, the flutter instability is characterized from vibration measurements performed for increasing flow speeds in the vicinity of the stability boundary. The experimental results are used to validate the numerical model derived for the aeroviscoelastic system and confirm both qualitatively and quantitatively the predictions of the simulations, especially the possibility of increasing the flutter speed by the inclusion of viscoelastic materials. [ABSTRACT FROM AUTHOR]

Experimental and numerical methods to identify the linear viscoelastic properties of flax fibre reinforced polymer (FFRP) composite are presented in this study. The method relies on the evolution of storage modulus and loss factor as observed through the frequency response. Free-free symmetrically guided beams were excited in the dynamic range of 10 Hz to 4 kHz with a swept sine excitation focused around their first modes. A fractional derivative Zener model has been identified to predict the complex moduli. A modified ply constitutive law has been then implemented in a classical laminates theory calculation (CLT) routine. Overall, the Zener model fitted the experimental results well. The storage modulus was not frequency dependant, while the loss factor increased with frequency and reached a maximum value for a fibre orientation of 70°. The damping of FFRP was, respectively, 5 and 2 times higher than for equivalent carbon and glass fibres reinforced epoxy composites. [ABSTRACT FROM AUTHOR]

Composite and sandwich structures are appealing to many engineering fields. Despite the increased rate of application, their cost remains higher compared to traditional engineering materials. One of the reasons is the necessary use of experimental characterization and validation of materials and structures respectively. One way to reduce costs is to increase predictive capabilities of simulation software. With this respect, finite element analysis is a powerful tool. However, the finite element modelling of composites and sandwich structures requires dedicated strategies in order to account for their non-homogeneity and anisotropy. This paper presents a C 0 -continuous beam element based on the RZT which is employed to predict the dynamic response of composite and sandwich structures. In particular, structures with viscoelastic layers for vibrations reduction will be considered. The damping modelling will also be addressed. The main objective is to assess the capabilities of the RZT for both dynamic response and damping predictions of laminates and sandwiches. [ABSTRACT FROM AUTHOR]

This paper investigates the nonlinear mechanics of layered composites that include a stiff elastic constituent and a soft viscoelastic constituent. Layered composites buckle with an infinite wavelength at small compressive strains in the case of a high volume fraction of the stiff constituent (the non-dilute case). An iterative algorithm is derived for the finite deformation of viscoelastic non-dilute layered composites with neo-Hookean phases. After validation by comparison to nonlinear finite element simulations, we analyze the effect of initial layer direction, strain rate, and prestrain on the response to time-dependent prescribed compressive strains. Interestingly, these composites have both a very high stiffness prior to buckling and a large energy dissipation capacity in the postbuckling regime. When these composites are subjected to cyclic strains of small amplitude, the effective stiffness and damping properties can be tuned by orders of magnitude by adjusting the prestrain. [ABSTRACT FROM AUTHOR]

The main focus of this paper is the experimental comparative analysis of the viscoelastic properties of acrylic- and silicon-based viscoelastic materials. These materials are widely used in the aeronautic industry for structural and/or damping applications. It is therefore required to determine their viscoelastic properties such as shear modulus and loss factor following their integration to aircraft composite structures. The influence of material thickness, bonding quality, curing and cocuring with composite material was evaluated using dynamic mechanical analysis machine in plan shear configuration. This comparative analysis in the 0–600 Hz frequency range provides useful information that should be taken into consideration when designing bonded joints for structural and/or damping applications. The small variation of the acrylic-based material loss factor over a wide range of frequencies suggests that this material is a good candidate for damping applications at room temperature in metallic structures where no curing is required. However, cocuring of acrylic-based material with composite laminae increases its shear modulus up to six times with respect to the uncured material whereas its loss factor is reduced by about 20%. On the other hand, the silicon-based material remains stable after thermal treatment (curing and cocuring) suggesting that it is well suited for in situ damping treatment involving laminate composite structure. However, at room temperature its shear modulus after cocuring is lowered by almost 25% due to poor bonding quality, which depends on the nature of the substrate. [ABSTRACT FROM AUTHOR]

The behaviour of dynamical systems is modified by the use of viscoelastic materials. In order to lead realistic complex eigenvalues analysis on dynamical systems, one need to model the behaviour of viscoelastic materials. The experiments show that the stiffness and the damping of such materials are frequency dependent. A large number of models often used are not able to describe this dependence; this is why the generalised Maxwell's model has been chosen. This paper describes a method based on modulus and angle curves to identify the parameters of this model. Between all the different formulations of generalized Maxwell, the pole-zero formulation is the most suited to lead the identification. However, some formulas allow to find the parameters of others formulations like the Prony one. The identification method presented here is based on the asymptotic curves of generalised Maxwell's model. This identification is led in two step, first parameters are initialised and second they are optimised. This method is confronted to others ones. If several viscoelastic materials have to be modelled in the same dynamical system, the size of the finite element model grows as quick as the number of poles. A way to reduce this size consists in constraining the poles to be equal for all materials. The method presented in this paper allows to perform the identification by taking this new constraint into account. [ABSTRACT FROM AUTHOR]

Hysteretic damping is often modeled by means of linear viscoelastic approaches such as “nearly constant attenuation” models (e.g. NCQ model). These models do not take into account nonlinear effects either on the stiffness or on the damping, which are well known features of soil dynamic behavior. The aim of this paper is to propose a mechanical model involving nonlinear viscoelastic behavior for isotropic materials under dynamic excitations. This model simultaneously takes into account nonlinear elasticity and nonlinear damping. On one hand, the shear modulus is a function of the excitation level; on the other, the description of viscosity is based on a generalized Maxwell body involving nonlinearity. This formulation (X-NCQ) is implemented into a one-dimensional finite-element approach for a dry soil. The validation of the model shows its ability to retrieve low amplitude seismic ground motion. For larger excitation levels, the analysis of seismic wave propagation in a nonlinear soil layer over an elastic bedrock leads to results which are physically satisfactory (lower amplitudes, larger time delays, higher frequency content). [ABSTRACT FROM AUTHOR]

In the context of brake system simulation, the highlight of phenomenon like squeal needs specific methods. We will focus on stability analysis by complex modal analysis. The use of damping system called shims for squeal noise reduction implies that simulations take into account the damping of materials. To do this, we use parametric viscoelastic models and particularly the generalised Maxwell model. Work consisted in tools choice and validation (viscoelastic models, finite elements formulations, ...) and in simulation method implementation. It was divided in several steps. In a first step, we have selected, among several mathematical models able to describe viscoelasticity, the best for damping modelisation in brake systems. We studied the complex modulus model, the Kelvin-Voigt model and the generalised Maxwell model. In a second step, we sought a formulation of the finite element problem adapted to the modal analysis. We then used a state space model formulation. A capital hypothesis on the equality of the pole of the generalised Maxwell model permits to reduce the size of the model and in the same time to simplify its formulation. Finally, the developed methods have been applied to simulate a pad and a full brake system. The influence of the number of modes used in model reduction and the order of the Maxwell model has been quantified in parametric studies. In the pad case, we performed a complex modal analysis with friction material considered as viscoelastic. The objective was to update the pad frequencies and damping according to FRF measures. In the brake case, we performed a complex modal analysis with the two friction materials and one shim considered as viscoelastic. This model has also been used to exhibit the link between the strain energy distribution in the brake and the damping level obtained by complex modal analysis. To conclude, we developed a simulation method using Abaqus® and Matlab® for the complex modal analysis with viscoelasticity effects and Python to make data exchange between Abaqus® and Matlab® possible. This method permits to perform stability analysis with several viscoelastic materials, on large models, without degradation of computation time. [ABSTRACT FROM AUTHOR]

Viscoelastic dampers are being used in structures to mitigate dynamic effects. The models of varying complexities from simple maxwell element to differential models with fractional and complex order derivatives have been used to represent their frequency-dependent force deformation characteristics. More complex models are able to capture the frequency dependence of the material properties better, but are difficult to use in analyses. However, the classical models consisting of assemblies of Kelvin and/or Maxwell elements with an adequate number of parameters can be formed to capture the frequency dependence as accurately as the more sophisticated fractional derivative models can do. The main advantage in adopting these classical models is a simpler and smaller system of equations, which can be conveniently analyzed for nonlinear and linear systems. In this study, the two classical mechanical models consisting of Kelvin chains and Maxwell ladder are used. It is shown that these mechanical models are as effective as the fractional derivative model in capturing the effect of the frequency dependence of the material properties in response calculations and are more convenient to use in dynamic response analyses. [ABSTRACT FROM AUTHOR]

Models of varying complexities are being used to represent the frequency-dependent dynamic force deformation characteristics of viscoelastic dampers. More sophisticated models with real or complex fractional derivatives can definitely capture the frequency-dependent properties better. However, since these advanced models add complexity in the analysis of structures, the use of two classical models—a Kelvin chain and a Maxwell ladder—consisting of usual dashpots and springs is suggested. In this technical note, we provide explicit steps and necessary formulas to calculate the parameters of these two proposed models to provide desired frequency-dependent characteristics represented by the storage and loss moduli. [ABSTRACT FROM AUTHOR]

The present work extends the multicoated micromechanical model of Lipinski et al. (2006, "Micromechanical Modeling of an Arbitrary Ellipsoidal Multi-Coated Inclusion," Philos. Mag., 86(10), pp. 1305-1326) in the quasistatic domain to compute the effective material moduli of a viscoelastic material containing multicoated spherical inclusions displaying elastic or viscoelastic behavior Losses are taken into account by introducing the frequency-dependent complex stiffness tensors of the viscoelastic matrix and the multicoared inclusions. The advantage of the micromechanical model is that it is applicable to the case of nonspherical multicoated inclusions embedded in anisorropic materials. The numerical simulations indicate that with proper choice of material properties, it is possible to engineer multiphase polymer system to have a high-loss modulus (good energy dissipation characteristics) for a wide range of frequencies without substantially degrading the stiffness of the composite (storage modulus). The numerical analyses show also that with respect to the relative magnitudes of the loss factors and the storage moduli of the matrix, inclusion and coating, the overall properties of the viscoelastic particulate composite are dominated by the properties of the matrices in some frequency ranges. The model can thus be a suitable tool to explore a wide range of microstructures for the design of materials with high capacity to absorb acoustic and vibrational energies. [ABSTRACT FROM AUTHOR]

In this paper, the possibility of reducing pressure surges in a quasi-rigid pipe network by replacing one of the pipes of the network by a viscoelastic one is examined. The mathematical model consists of a system of two hyperbolic, partial differential equations which are resolved by the method of characteristics using linear interpolation. The calculation at the network junctions is realised by resolving a linear system of equations including the manner various boundary conditions are introduced into the solution. The behaviour law of the viscoelastic pipe is described by the Kelvin-Voigt model. In order to simplify calculations, only the elastic element of this model is considered. For the applications, a constructed computer progrmn written in FORTRAN language is elaborated. The numerical results show the effect of the pipe wall elasticity on the damping of the pressure waves in the networks. [ABSTRACT FROM AUTHOR]

The need to take into account the oscillation of a system is a special feature in the linear problem of the stability of a cantilevered rod under a follower force. Involvement of viscoelastic materials leads to damping of the oscillation hence to overestimation of critical loads. This new problem is solved here by means of an additional term introduced into the constitutive equation and proportional to the fractional time derivative with complex order--besides the inertial one. The effects contributed by the damping ratio, the real part of the order and the corrective role of its imaginary part on the shape of the bifurcation line, on its maximum and on the disposition of the inflection and maximal deflection points on the centerline of the deformed rod during the secondary loss of stability, are discussed. [ABSTRACT FROM AUTHOR]

In the context of control of sound and vibration of mechanical systems, the use of viscoelastic materials has been regarded as a convenient strategy in many types of industrial applications. Numerical models based on finite element discretization have been frequently used in the analysis and design of complex structural systems incorporating viscoelastic materials. Such models must account for the typical dependence of the viscoelastic characteristics on operational and environmental parameters, such as frequency and temperature. In many applications, including optimal design and model updating, sensitivity analysis based on numerical models is a very usefull tool. In this paper, the formulation of first-order sensitivity analysis of complex frequency response functions is developed for plates treated with passive constraining damping layers, considering geometrical characteristics, such as the thicknesses of the multi-layer components, as design variables. Also, the sensitivity of the frequency response functions with respect to temperature is introduced. As an example, response derivatives are calculated for a three-layer sandwich plate and the results obtained are compared with first-order finite-difference approximations. [ABSTRACT FROM AUTHOR]

Abstract: The task of providing lightly-damped shells with an enhanced modal damping is encountered in many applications. This paper explores the use of a standoff-layered viscoelastic damping treatment for cylindrical shells requiring a minimal distribution area and low added weight. It is shown that partial distribution of the treatment as damping patches can be more beneficial than using full coverage, provided the patches are located in regions of high modal strain energy, as determined from strain energy intensity distribution maps derived for the purpose. The analysis uses the finite element method, and a suitable curved shell element is formulated for the add-on damping treatment. Numerical studies show that the combination of partial coating and a standoff layer can offer a viable approach for achieving optimal damping in the presence of space and weight constraints. [Copyright &y& Elsevier]

In this article we examine an evolution problem, which describes the dynamic contact of a viscoelastic body and a foundation. The contact is modeled by a general normal damped response condition and a friction law, which are nonmonotone, possibly multivalued and have the subdifferential form. First we derive a formulation of the model in the form of a multidimensional hemivariational inequality. Then we establish a priori estimates and we prove the existence of weak solutions by using a surjectivity result for pseudomonotone operators. Finally, we deliver conditions under which the solution of the hemivariational inequality is unique. [ABSTRACT FROM AUTHOR]

Abstract: In this note, one considers a 1-d.o.f. oscillator consisting of a mass and a viscoelastic spring, the rheology of which is represented by a generalized so-called Biot''s model with parameters. It is proved that its independent eigenmotions are of the following nature: two eigenmotions damped with or without oscillations (as in the case of classical viscous damping) and n eigenmotions damped without oscillations which are induced by the viscoelastic rheology. To cite this article: P. Muller, C. R. Mecanique 333 (2005). [Copyright &y& Elsevier]

In the present study, the steady-state response to a sinusoidally varying concentrated force acting at the center of a rectangular point-supported orthotropic elastic plate is analyzed. The equation of the plate is represented by finite-difference expressions. By using the ordinary finite-difference technique, the problem is reduced to the solution of a system of algebraic equations. The influence of mechanical properties of the plate material on the vibration modes and the steady-state response of the plate is investigated numerically. Also, the effect of location of the point supports is studied. The problems considered are solved within the framework of the Kirchhoff-Love hypothesis. [ABSTRACT FROM AUTHOR]