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Natural rubber (NR) composites have been widely applied in damping products to reduce harmful vibrations, while rubber with only a single composition barely meets performance requirements. In this study, rubber blend composites including various ratios of NR and styrene butadiene rubber (SBR) were prepared via the conventional mechanical blending method. The effects of the rubber components on the compression set, compression fatigue temperature rising and the thermal oxidative aging properties of the NR/SBR blend composites were investigated. Meanwhile, the dynamic mechanical thermal analyzer and rubber processing analyzer were used to characterize the dynamic viscoelasticity of the NR/SBR blend composites. It was shown that, with the increase in the SBR ratio, the vulcanization rate of the composites increased significantly, while the compression fatigue temperature rising of the composites decreased gradually from 47 °C (0% SBR ratio) to 31 °C (50% SBR ratio). The compression set of the composites remained at ~33% when the SBR ratio was no more than 20%, and increased gradually when the SBR ratio was more than 20%. [ABSTRACT FROM AUTHOR]

Following the principle of constrained-layer damping (CLD), fiber-metal-elastomer laminates (FMELs) offer a high potential for damped lightweight structures, overcoming the undesirable vibration characteristics of conventional lightweight materials. While proven to be versatile and efficient, the damage-tolerance of such laminates is unexplored. This study for the first time in literature addresses the damage-tolerance of this efficient damping mechanism using a combined experimental and numerical approach. Results of experimental low-velocity impact tests on different configurations of FMELs are presented. In subsequent numerical modal analyses, different types of damage, namely delaminations, intra-ply damage and permanent deformation, are modeled and their influence on the vibrational behavior is investigated. While all types of damage influence the natural frequencies and modal damping ratios with a strong mode dependency, all laminates retain a high amount of modal damping with losses typically not higher than 15%. The results obtained reveal, that CLD is an efficient intrinsic damping measure in FMELs even in the presence of different types of damage. The key contributions of this paper include the thorough experimental characterization of low-velocity impact damages in different configurations of FMELs as well as the numerical assessment of those in frequency-domain simulations. • Low-velocity impact experiments reveal intra-ply damage, delaminations and permanent deformation as predominant damage modes. • Simulations of damaged laminates in numerous configurations reveal the influence of laminate damage on vibration behavior. • The constrained-layer damping mechanism proves to be tolerant towards impact damage. • The effects of damage on damping properties are highly mode dependent. [ABSTRACT FROM AUTHOR]

The free vibrations of cantilever slender beams of polymers, which are viscoelastic materials, are theoretically described using the simple Euler--Bernoulli assumption. The comparison between the theory and the experimental data collected for a thermoplastic elastomer, polyether block amide, shows very satisfactory results. Consequently, the theory is used for a thoughtful analysis of the impact of the material parameters and the beam geometry on its free vibration. Finally, the comparison of the dynamic behaviors of two polymers, using the free vibration test and a simple uniaxial tension/relaxation test, is discussed. Résumé. Les vibrations libres d'une poutre encastrée de polymère, mesurées expérimentalement sont reproduites théoriquement à l'aide de l'hypothèse des poutres d'Euler--Bernoulli, une fois le comportement viscoélastique du matériau identifié classiquement. La théorie permet alors de simplement faire varier les paramètres matériaux et géométriques de la poutre afin de tester leurs impacts sur le test de vibration libre. En utilisant l'analyse théorique et en observant la réponse de deux matériaux lors d'un essai simple de traction/ relaxation, il est possible de prédire leur comportement relatif en vibration libre. [ABSTRACT FROM AUTHOR]

This paper presents a two-variable refined plate theory for free vibration of functionally graded material (FGM) plates lying on viscoelastic Winkler–Pasternak foundations. The present work aims to examine the vibrations by a higher-order shear deformation theory including a new function of warping. The governing equations are derived from the principle of virtual displacements. Some illustrative examples are given in an attempt to solve the free vibration problem of a rectangular plate with various boundary conditions. The effects of damping on free vibrations, considering various parameters, are examined in detail. In the end, it is concluded that the present results with the new shear shape function of viscoelastic foundation are found to be in good agreement with other available results and the proposed method can easily be used to solve free vibration problems of the FGM plates. [ABSTRACT FROM AUTHOR]

Highlights • A 3-D formulation for vibration and damping analysis of sandwich shallow shells is presented. • Arbitrary boundary conditions including elastic ones are considered. • Frequency dependent viscoelastic models are discussed for various temperatures and boundary conditions. • New results for sandwich plate, spherical, cylindrical and hyperbolic paraboloidal shells are calculated. • 3-D modal shapes are depicted for the sandwich shallow shells. Abstract In this paper, we present an accurate three-dimensional formulation for the vibrations of the laminated and sandwich shallow shells. The sandwich structure is characterized by a thick viscoelastic core and two thin composite faces. Frequency dependent viscoelastic models are introduced in the sandwiches. Without any change in solution procedure, the formulation makes it quite easy to change the boundary conditions. The solution can be obtained by means of Rayleigh–Ritz process combined with the three-dimensional modified Fourier series which are actually assumed displacement functions. These functions, without need to meet the boundary conditions in advance, take the form of the three-dimensional Fourier series with several closed-form auxiliary functions which are supplemented to deal with the discontinuities at the boundaries in terms of displacements and its derivatives. Besides, only three assumed displacement variables are employed in the formulation which effectively reduces the computation cost. The reliability and accuracy of the method are demonstrated by numerical comparisons and examples with the constant viscoelastic models as well as the frequency dependent ones. Modal analysis and parametric studies are conducted to examine the influences of the boundary condition, dimension, lamination scheme, temperature and frequency dependence of the materials. [ABSTRACT FROM AUTHOR]

This paper focuses on the thrust ripple reduction in permanent magnet synchronous linear motors (PMSLMs), which are applied to laser cutting machines. To meet the high-precision performance requirements of laser cutting machines, a novel auxiliary suppression device, tuned viscoelastic damper (TVD), is designed to reduce the thrust ripple of PMSLM. First, TVD is designed with the structure and motion characteristics of PMSLM. The PMSLM with TVD is an integrated structure. Then, the equivalent magnetization method is used to analyze the PMSLM thrust, which is the excitation of TVD. Under the excitation of the PMSLM thrust, the damping force of TVD is expressed by the Kelvin model and validated by finite-element analysis (FEA). Subsequently, the thrust of PMSLM with TVD is obtained by adding the PMSLM thrust and TVD damping force. Finally, the thrust ripple rate is selected as a performance index of TVD in reducing the thrust ripple. Simulation is performed to confirm the theoretical analysis. A prototype of PMSLM with TVD is manufactured and experiments are conducted to validate the effectiveness of the proposed auxiliary suppression device. [ABSTRACT FROM AUTHOR]

In this communication, we propose a nonlocal fractional viscoelastic model of a nanobeam resting on the fractional viscoelastic foundation and under the influence of the longitudinal magnetic field and arbitrary number of attached nanoparticles. Size effects are taken into account using the differential form of the nonlocal constitutive relation together with the fractional Kelvin-Voigt model. The governing equation for the free vibration of a nanobeam is derived, where Maxwell’s equations are used in order to represent the effect of the longitudinal magnetic field. We propose an analytical solution of the problem based on the Laplace transform, Mellin-Fourier transforms, and residue theory. From the validation study, it is shown that the obtained complex roots of the characteristic equation, where the imaginary part is the damped frequency and the real part is the damping ratio, are approximated eigenvalues of the system. In the parametric study, several numerical examples are given to investigate the influence of different parameters on complex roots as well as different masses and numbers of nanoparticles on the damped vibration behavior of a nanobeam system. [ABSTRACT FROM AUTHOR]

This study numerically investigates the mechanism of vibration damping in woven composite structures using a decoupled multi-scale simulation scheme that considers the macroscopic woven structure consisting of bundles and resin-rich regions, as well as the microscopic structure in the bundles made of fiber and resin. For efficient macroscopic modeling of complicated woven structures, the embedded element technique is introduced to utilize separate meshes for bundles and resin regions. A special treatment is introduced for volumetric integration in the mesh overlapped between bundle and resin regions, which is required to calculate the strain energy and modal damping ratio of the entire woven structure. Using the developed scheme, the natural frequencies and damping ratios of braided and laminated composite cylinders are investigated. By comparing the vibration properties of two braided composites with different braided angles and two unidirectional laminates with different fiber volume fractions, the effects of the fiber volume fraction, braided angle, and out-of-plane waviness on vibration properties are discussed. Based on the mode shape and resultant energy dissipation within each bundle and resin-rich region, the braided composite with a large braided angle exhibited the best damping properties, mainly owing to the in-plane shear deformation in the crimped braided bundles. [ABSTRACT FROM AUTHOR]

Rubber is an effective and low-cost material for mechanical vibration suppression because in the glass-transition zone it exhibits high damping abilities. However, analytical predictions of the viscoelasticity of rubber are inaccurate because viscoelasticity depends on the frequency, amplitude and pre-deformation; this inaccuracy impedes the mechanical design of rubber parts. Previously, viscoelasticity measurements under uniaxial deformation have been performed. However, the dominant parameters cannot be clarified in these tests because the strain distribution is not uniform, and the shear strain and hydrostatic pressure are cross-coupled. In this research, a new test method was studied that enabled the direct measurement of the high-frequency viscoelasticity of rubber by independently applying simple shear pre-strain and hydrostatic pressure. The viscoelasticity of nitrile rubber was measured using this method at frequencies from 200 Hz to 2000 Hz under shear pre-strain and pre-compression. The results showed that hydrostatic pressure had a much larger influence than shear pre-strain. The hydrostatic pressure should be considered as a more essential parameter than the stretch or strain in this material. [ABSTRACT FROM AUTHOR]

In the context of passive damping, various mechanical systems from the space industry use elastomer components (shock absorbers, silent blocks, flexible joints,…). Among other specificities, elastomers have frequency dependent characteristics. The computational cost of the associated numerical models, using viscoelastic constitutive behavior, may become too expensive during a design process. To solve this problem, the aim of this work is to propose an efficient reduced viscoelastic model of rubber devices. The first step is to choose an accurate material model that represents the viscoelasticity. The second step is to reduce the rubber device finite element model to a super-element that keeps its frequency dependent properties. This reduced model is first built by taking into account the fact that the device's interfaces are much more rigid than the rubber core. Therefore, kinematic constraints enforce the rigid body motion of these interfaces, reducing them to twelve degrees of freedom only (three rotations and three translations per face). The super-element is then built by condensing the core of the finite element model on the interfaces via a Component Mode Synthesis (CMS) method, adapted here to viscoelastic damping. As an application, the dynamic behavior of a structure supported by four rubber devices under harmonic loads is analyzed to show the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper considers dampers comprising collections of viscoelastic particles that are subjected to vibrations whose amplitude is such that slip between particles is negligible. Energy dissipation occurs primarily by viscoelastic processes within each particle and is maximized when standing waves are set up in the granular medium. In this work, the medium is represented as an equivalent viscoelastic solid and predictions of performance employ models constructed using standard finite element software. Two numerical approaches are considered: one uses the Direct Frequency Response and the other uses standard modal analysis in conjunction with analytical expressions for energy dissipation based on the wave equation. The performance of these prediction techniques is compared with measured behavior from experiments on a box-shaped structure and a hollow composite tube assembly. The computational efficiency of the modal technique allowed a brief investigation of the effects of uncertainties in the actual nature of the granular arrangement. Results show that both prediction methods give a reasonable level of accuracy. Differences between predicted and measured behavior are shown to be of the same order as the uncertainty in the prediction itself. For the systems considered, it is shown that the methods are appropriate for acceleration amplitudes up to almost that of gravity. [ABSTRACT FROM AUTHOR]

The optimal design of viscoelastic laminated composite panels with active piezoelectric patches is addressed in this paper. Constrained optimization is conducted to determine optimal distributions of piezoelectric patches on the top and bottom surfaces of laminated plates with viscoelastic layers. The design variables are the number and position of these patches, and the objectives are the minimization of the number of patches, the maximization of the fundamental modal loss factor and the maximization of the fundamental natural frequency. The problem is solved using the Direct MultiSearch (DMS) solver for derivative-free MultiObjective Optimization (MOO). The objective functions are evaluated by a finite element model that was developed for laminated sandwich plates incorporating piezoelectric or viscoelastic layers. Trade-off Pareto optimal fronts and the respective optimal active patch configurations are obtained and the results are analyzed and discussed. [ABSTRACT FROM AUTHOR]

Development and design of novel materials based on their micro-structural arrangements are being intensely investigated due to their wide range of real and potential applications. One of the key objectives of such design is to achieve multiple properties, which are often competing in nature (such as high stiffness-high damping, high strength-high toughness etc.), within a single composite material. In the present work we propose a novel interlocking micro-architecture design to achieve high symmetry in a plane within a composite. The present study shows that constraining a very low volume fraction of high damping polymer within this micro-architecture, together with a stiff polymer, results in a simultaneously high stiffness and high damping polymer composite. The proposed micro-architecture design possesses high symmetry that is not commonly found in fiber-reinforced polymer composites. The interlocking feature avoids use of extra adhesives for holding two adjacent building blocks. Finite element simulations are performed by considering the micro-architecture made of two widely used polymeric materials such as polymethyl methacrylate (PMMA as the stiffer building block) and polyurethane (PU as the soft viscous material). Our numerical predictions show remarkable stiffness and damping properties for the design over a wide range of frequencies. Simulations are also performed considering contact between two polymer interfaces to establish the fact that the geometric interlocking works well without any use of adhesive for holding the blocks together. Further simulations are performed under high frequency impulse pressure loading to study dynamic wave propagation through the micro-architecture that shows the near-isotropic response of the proposed micro-architecture. [ABSTRACT FROM AUTHOR]

Propagation of a torsional wave in a doubly-layered half-space structure of an initially stressed heterogeneous viscoelastic layer sandwiched between a layer and a half-space of heterogeneous dry sandy media is studied. A closed form complex expression for the velocity profile is obtained under effective boundary conditions. The real part of the complex expression provides a dispersion equation, and the imaginary part yields a damping equation. The derived dispersion and damped equations are in well agreement with the classical Love wave condition. In addition, to study the effect of the dissipation factor, the attenuation coefficient, the sandy parameters, the initial stress, the heterogeneity parameters, and the thickness ratio parameter, some noteworthy contemplations are made by numerical calculations and graphical visuals. The results of this paper may present a deeper insight into the behaviour of propagation phenomena in heterogeneous viscoelastic and heterogeneous dry sandy materials that can provide a theoretical guide for the design and optimization in the field of earthquake engineering. The study also reveals that the presence of a damping part due to viscoelasticity affects the torsional wave propagation significantly. [ABSTRACT FROM AUTHOR]

This paper presents dynamic behavior of an isotropic magnetorheological elastomer (MRE) under harmonic tensile-compressive loadings. The dynamic viscoelastic behavior of the MRE is experimentally investigated at various external magnetic fields as well as different loadings of frequency and strain. A generalized Maxwell viscoelastic model is developed to portray the relationships between the stress and strain of the MRE based on input frequency, strain, and magnetic flux density. The coefficients of the proposed model under various input conditions, such as magnetic flux density, strain amplitude, and input frequency, are calculated by implementing the least-squares method. Unlike the previous models of MRE, which mostly focused on shear mode, the present model enables to capture dynamic behavior of MRE in tensile-compressive loadings. Furthermore, tensile-compressive operation offers the most compact design in many axial loading applications such as rotor systems, MRE bearing isolators in bridges, suspension systems in cars, building isolators, and vertical vibration settings, which cannot be controlled with MRE in shear mode due to its low capacity of stiffness. The results show that the proposed model can effectively predict dynamic behavior of MREs under tensile-compressive loadings. This model is useful to simulate the performances of MRE base devices under harmonic tensile-compressive loadings. [ABSTRACT FROM PUBLISHER]

Explicit expressions for the complex longitudinal shear moduli of viscoelastic composites with arbitrary symmetric structure are obtained. Specific formulas of dissipative properties are obtained for tetragonal composites with elliptic and rectangular fibre cross-sections, as well as for hexagonal (not necessarily regular) composites with elliptic fibre cross-section. The correspondence principle and the duality rule are used. The results of calculations for particular cases agree well with the known published data. [ABSTRACT FROM AUTHOR]

We investigate a hyperbolic PDE, modeling wave propagation in viscoelastic media, under the influence of a linear memory term of Boltzmann type, and a nonlinear damping modeling friction, as well as an energy-amplifying supercritical nonlinear source: { u t t − k ( 0 ) Δ u − ∫ 0 ∞ k ′ ( s ) Δ u ( t − s ) d s + | u t | m − 1 u t = | u | p − 1 u , in Ω × ( 0 , T ) , u ( x , t ) = u 0 ( x , t ) , in Ω × ( − ∞ , 0 ] , where Ω is a bounded domain in R 3 with a Dirichlét boundary condition. The relaxation kernel k is monotone decreasing and k ( ∞ ) = 1 . We study blow-up of solutions when the source is stronger than dissipations, i.e., p > max ⁡ { m , k ( 0 ) } , under two different scenarios: first, the total energy is negative, and the second, the total energy is positive with sufficiently large quadratic energy. This manuscript is a follow-up work of the paper [30] in which Hadamard well-posedness of this equation has been established in the finite energy space. The model under consideration features a supercritical source and a linear memory that accounts for the full past history as time goes to −∞, which is distinct from other relevant models studied in the literature which usually involve subcritical sources and a finite-time memory. [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]

Lamb wave inspection is a promising structural health monitoring method for carbon fiber reinforced plastic laminates. The optimal design of the excitation waveform based on Lamb wave pulse compression is an effective way to improve the inspection resolution in elastic plates. However, due to the viscoelastic property of the composite materials, the material damping effect will influence the amplitude response of the output signals; thus, the current design strategy is no longer applicable. The purpose of this paper is to develop an excitation waveform design strategy based on pulse compression to meet the demands of high-resolution Lamb wave inspection in composite materials. Different parameters that affect the design of excitation such as material damping effect, amplitude response, relative frequency bandwidth, and the selection of excitation waveform are considered synthetically. In addition, an excitation waveform design strategy based on the corrected amplitude response is also established to eliminate the effect of material damping and thus achieve better detection resolution. Finally, an experiment was carried out on a quasi-isotropic composite plate. The experimental results validate the robustness of the amplitude response correction method and the effectiveness of the excitation waveform design strategy. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present a finite element model based on first order shear theory (zig-zag approach) to compute the damping characteristics of sandwich structures with multi-layered frequency-dependent viscoelastic cores. The model is validated versus a layerwise finite element model and used to study damping and rigidity of a laminated glass configuration with a multi-layered visco-elastic core composed of acoustic PVB and PVB. It is shown that the rigidity index of the structure (defined as the adimensionalized inverse of the maximal transverse displacement under a static load) evolves linearly with the viscoelastic layers’ thicknesses and quadratically versus elastic layer’s thickness. The first mode damping and resonant frequency show a non monotonous behaviour. In particular, the existence of an optimal faces thickness for damping is shown while a quadratic behaviour of frequency versus acoustic PVB layer thickness is reported. [ABSTRACT FROM AUTHOR]

This paper presents a simplified coupled thermal-mechanical model for the modelling of viscoelastic dampers with temperatureand frequency-dependent properties subjected to long-term and short-term dynamic loading due to wind and earthquakes. In this numerical model, the self-heating effect caused by molecular-level friction in the viscoelastic (VE) material is captured explicitly using a finite volume thermal diffusion model based only on the physical properties of the steel and VE material. The thermal model is coupled to a single degree of freedom (SDOF) mechanical model, which produces an efficient computational scheme for time-history analyses of VE dampers under both long-term and short-term loading scenarios. The predictions from the proposed model are compared with full-scale experimental results of long-duration wind loading ranging from design level events to extremely rare events, and for shorter but more intense seismic loading scenarios. It is shown that results obtained using this proposed simplified model with idealized geometry predicted well the dynamic response of the damper for all ranges of experimental results thus validating a robust physics based tool for predicting the response of VE dampers. [ABSTRACT FROM AUTHOR]

This paper presents a unified formulation for vibration and damping analysis of a sandwich beams made up of laminated composite face sheets and a viscoelastic core with arbitrary lay-ups and general boundary conditions. A modified Fourier–Ritz method is employed to derive this unified formulation based on Reddy’s higher order shear deformation theory. In composite facings, the material couplings including bending–stretching, bending–twist, and stretching–twist as well as the Poisson’s effect are taken into consideration. Regardless of boundary conditions, the displacements of each layer are expanded as the linear combination of a standard Fourier series and closed-form functions introduced to eliminate all the relevant discontinuities, ensure and accelerate the convergence of the series expansions. This method can be universally applicable to laminated sandwich beams with classical boundaries, elastic boundaries and their combinations without any special change in the solution procedure. Both convergence and accuracy are discussed and this modified Fourier–Ritz method yields many new and accurate results at a low computational cost for various boundary conditions including general elastic boundaries. Furthermore, the effects of some key parameters such as ply configuration, layer number, moduli and thickness ratios on the natural frequency and loss factor are illustrated. Especially the effects of restraints from different directions on two ends of the sandwich beam are deeply investigated. [ABSTRACT FROM AUTHOR]

Stringed instruments are made of high quality wood species from physical, mechanical and acoustical point of view, being carefully selected, kiln dried and processed under specific conditions that assure micro-structural integrity. Maple wood (Acer Pseudoplatanus) for musical instruments is used to getting back plates and sides for string instruments (violin family). This species of wood is valued for both acoustic qualities but mostly for aesthetic, using a natural defect of maple wood characterized by wavy grain. The paper presents the research on visco-elasticity behavior of maple wood with different types of grain deviation in wood from very curly maple to common maple. The storage modulus, loss modulus, damping capacity in varying temperature conditions and for different loading frequencies were determined using dynamical mechanical analysis (DMA). It was found that specimens characterized by very wavy grain shows a high damping capacity of frequency range between 33.33 to 50Hz, unlike specimens of common maple which do not have the capacity of frequency selectivity. [ABSTRACT FROM AUTHOR]

Damping is often an invisible requirement for a good mechanical design. To render the long-term service of viscoelastic dampers, it is essential for design engineers to estimate the degradation of the damping characteristics with age. Nitrile butadiene rubber (NBR) is a widely used damping and sealing material. Viscoelastic sandwich beam configurations have been used to mount electronic components for various automobile and aerospace applications. The present work emphasizes the estimation of modal parameter degradation of NBR with age in an oxidative environment. NBR is assumed to be homogeneous and isotropic and is allowed to age naturally with no load under ambient conditions. Fourier-transform infrared spectroscopy (FTIR) was used to detect age-related changes in the functional groups of the NBR material with age. Dynamic mechanical analysis (DMA) tests were performed to relate the complex properties of naturally aged materials to those of virgin materials in the frequency and temperature domains. Mechanical tests were performed to determine the hardness, elongation break, and failure stress of the virgin NBR and naturally aged NBR. The damping ability of the NBR was investigated using an unconstrained sandwich cantilever beam with aluminum as the base material. For sinusoidal sweep excitation, the influence of viscoelasticity on structural damping was investigated. Based on the experimental results, the damping ability of the NBR has been observed to degrade with age. As the age increased, the damping ability of the NBR decreased by 8% at the first resonance frequency and by 34% at the third resonance frequency. • Deterioration of Mechanical properties of NBR with time and temperature. • Damping ability deterioration of NBR at 40 °C. • Relaxation strength and Specific damping capacity deterioration with temperature and time. • First three fundamental frequencies of Sandwich beam with time and temperature are studied. [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]

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

An analysis of the energy dissipation sources acting in a vibrating aluminum plate is presented in this paper. In the first step, the contact-free modal analysis of a suspended plate is conducted using a laser vibrometer and an acoustic excitation to obtain reference data. The thin nylon suspension set-up guarantees a low boundary damping, which is assumed to be negligible. In the second step, a number of damping sources are modeled. Acoustic damping due to the noise radiation of the nonbaffled plate is computed using the boundary integral method and a light fluid approximation to express the vibroacoustic coupling in analytical terms. The damping due to the sheared air flow along the free-plate borders is determined on the basis of a simple two-dimensional boundary layer model. Thermoelastic damping is assessed using a Fourier series expression for the temperature field along with a perturbation technique to take thermoelastic coupling into account. Since no robust model is available so far to quantify viscoelastic material damping in aluminum, it is determined in a last step by subtracting measured values of damping from those previously computed. Aluminum viscoelastic damping turns out to be very small and almost independent of frequency. [ABSTRACT FROM PUBLISHER]

A model of a medium consisting of parallel layers of elastic rectangular blocks separated by deformable viscoelastic interlayers is considered. The model is proposed for describing the lowfrequency part of the spectrum in waves propagating in media with such a structure. For a twodimensional assembly consisting of 36 blocks, the results of numerical calculations are compared with experimental data. [ABSTRACT FROM AUTHOR]

Constrained layer dampers (CLD) are in widespread use for passive vibration damping, in applications including aerospace structures which are often lightweight. The location and dimensions of CLD devices on structures has been the target of several optimisation studies using a variety of techniques such as genetic algorithms, cellular automata, and gradient techniques. The recently developed double shear lap-joint (DSLJ) damper is an alternative method for vibration damping, and can be placed internally within structures. The performance of the DSLJ damper is compared in a parametric study with that of CLD dampers on beam and plate structures under both cantilever and simply supported boundary conditions, using finite element analysis. The objective was to determine which damper and in which configuration produced the highest modal loss factor and amplitude reduction for least added mass, as would be important for lightweight applications. The DSLJ tend to be more mass efficient in terms of loss factor and amplitude reduction for cantilevered beam and plate structure, and are competitive with CLD dampers in simply supported beam and plate structures. The DSLJ works well because it has the potential to magnify global flexural deformation into shear deformation in the viscoelastic more effectively than traditional CLD dampers. [ABSTRACT FROM AUTHOR]

This paper presents a disk-spacer damper (DSD), a new damper structure, for reducing disk flutter. Three types of DSD structures, which consist of an aluminum disk spacer having grooves embedded with viscoelastic (VE) films, have been developed in this paper. First, we investigated the material properties of the VE film, such as shear modulus and discrete relaxation spectra, and then carried out numerical analysis of the damping effect using the material properties. Further, we measured the damping effect of each DSD structure and confirmed that the proposed DSD reduces the disk flutter amplitude between the (0,1) mode and the (0,4) mode by 20%–30%. [ABSTRACT FROM AUTHOR]

Abstract: The introduction of material into the void of honeycomb-like structures, such as foam, viscoelastic or particulate filling, has been credited with improving the damping properties of the honeycombs. Optimisation of such damping inserts has been investigated, and indicates that partial occupation of the void could be more efficient, on a density basis, than full filling. The main goal of this study is to explore fully damping in honeycomb cells with inserts from the point of view of minimal increase in density and location of inserts. In this paper, damping of vibrations in the plane is investigated using analytical, finite element and topological optimisation methods to find the best locations of a damping insert within the cell. [Copyright &y& Elsevier]

Abstract: This paper presents a parametric model to study the transient bending wave propagation in a viscoelastic sandwich plate due to impact loading. The effect of partial constrained layer damping (PCLD) geometry on wave propagation is investigated by comparing with propagation in single layer elastic plate. Several boundary conditions are also considered, and their effect on wave propagation is highlighted. The equation of motion is obtained from Lagrange’s equations. For the single layer plate, the governing equation is solved in time domain using Newman and Wilson method. For the plate with PCLD, the frequency dependant viscoelastic behavior of the core is represented by Prony series; the equation of motion is converted into frequency domain using Fourier transform the displacement is obtained in the frequency domain and is converted into time domain with the Inverse Fast Fourier Transform. The model was validated in our previous paper (Khalfi and Ross (2013)) with experimental results, additional validation is carried in this paper with literature, and good agreement is recorded. The results show that the plate covered with PCLD remains a dispersive medium. The shape of the wave is mainly related to the sandwich stiffness while the viscoelastic layer contributes in reducing the amplitude and speed of propagation. The particularity of this transient model lies in its ability to follow the shape of the bending wave at all times to observe formation, propagation and disappearance. With this model, the influence of any structural input parameters on the bending wave can be studied. The findings presented will also serve as a research base for more advanced horizons. [Copyright &y& Elsevier]

Passive vibration control using blocks of viscoelastic materials with macro- and microscopic inclusions has been widely investigated. Significant changes in the vibration response have been observed with such inclusions. We have found that their response changes much more significantly if thin microstructures and channels are carved within these materials and are filled with a high-viscosity fluid. In this paper, we report the passive response of a replicated array of oil-filled microchannels, structured within a block made up of polydimethylsiloxane. Constrained and unconstrained vibration-damping experiments are performed on this block, wherein its vibration suppression ability is detected by applying an excitation signal transversely at the geometric center of the lower face of the block. We observe an increase in the fundamental frequency due to change in stiffness of the block and an increase in damping ratio and loss factor owing to the development of a slip boundary condition between the oil and the microchannel walls causing frictional dissipation of the coupled energy. All vibration experiments have been performed using a single-point laser to ascertain the experimental behavior of the system. We have also modeled the vibration suppression characteristics of such systems both analytically and by using simulation tools \hfill[2011-0273] [ABSTRACT FROM AUTHOR]

Abstract: In this paper we investigate the design of composite materials with simultaneously high stiffness and high damping. We consider layered composite materials with parallel plane layers made of a stiff constituent and a lossy polymer. We analyze the response of these composites to a dynamic load with an arbitrary direction. Using the viscoelastic correspondence principle and linear frequency domain viscoelastic models, we derive an expression for the effective complex modulus of layered composites of infinite size at infinitesimal strains. The dependence of the effective dynamic modulus and loss factor on the geometrical parameters and on the tensile and bulk loss factors of the lossy constituent is analyzed. Moreover we determine the magnitude of the strains in the lossy constituent and demonstrate that the combination of high stiffness and high damping of these composites is due to the high normal and/or shear strains in the lossy material. We use nonlinear constrained optimization to design layered composites with simultaneously high stiffness and high damping while constraining the strains in the polymer. To determine the range of validity of the linear viscoelastic model, simulations using finite deformations models are compared to the theoretical results. Finally, we compute the effective properties of composites of finite size using finite element methods and determine the minimum size required to approach the formulae derived for composites of infinite size. [Copyright &y& Elsevier]

Instrumented indentation is used to measure the complex modulus of highly plasticized polyvinyl chloride (HP-PVC) and four kinds of polyethylene over the frequency range of 1-50Hz. Over this range, the loss factor for the HP-PVC increases from 0.3 to 1, making this an ideal material for damping out noise and vibration. The storage moduli for the four polyethylene samples are ordered according to density, with the lowest-density material have the lowest storage modulus. Results for both storage modulus and loss factor compare well with published results obtained by dynamic mechanical analysis for nominally similar materials. [ABSTRACT FROM AUTHOR]

Abstract: In this paper a global optimisation technique for the design of damping properties of hybrid elastomer/composite laminates is presented. The goal of the procedure is to maximise the first N modal loss factors of the laminate subject to constraints on the in-plane and out-of-plane stiffness along with a constraint on the weight of the plate. The problem is considered in the most general case: no simplifying hypotheses are made on the behaviour of the hybrid laminate, thus allowing us to consider as design variables the number of layers (both of the elastic and viscoelastic layers), their thickness and orientations as well as the position of the viscoelastic plies within the stacking sequence. The proposed approach relies on one hand, upon the dynamic response of the structure in terms of natural undamped frequencies and modal loss factors which are evaluated using the well-known Iterative Modal Strain Energy (IMSE) method, and on the other hand on the use of genetic algorithms as optimisation tool to perform the solution’s search. As an example, the method is applied to a rectangular plate and the results demonstrate the effectiveness of the proposed strategy. [Copyright &y& Elsevier]

This paper presents a theoretical investigation on the energy dissipation in a nearly saturated poroviscoelastic soil column under quasi-static compressional excitations. Different components of the energy dissipation are evaluated and compared. The magnitude of fluid- induced energy dissipation is primarily a function of a normalized excitation frequency . For small values of , a drained soil column is fully relaxed and essentially behaves as a dry column with negligible pore pressure. For such a soil column, fluid-induced energy dissipation is negligible, and the total damping ratio of the column is essentially the same as that of the solid skeleton. For very high values of , a drained soil column is fully loaded and the excitation-generated pore pressure decreases as the fluid becomes more compressible. For such a soil column, the fluid pressure gradient only exists in a thin boundary layer near the drainage boundary, where drainage occurs and fluid induces energy dissipation, whereas the rest of the column is essentially undrained. Significant fluid-induced energy dissipation occurs for moderate values of because of a combination of moderate fluid pressure, pressure gradient, and fluid relative motion throughout the soil column. The effects of the boundary drainage condition, saturation, porosity, and skeleton damping ratio on fluid-induced energy dissipation are discussed. [ABSTRACT FROM AUTHOR]

Abstract: Spalling is an important failure mode which triggers delamination, thus affects through-thickness integrity of a laminate and hinders the later integral plate action. The aim of the present study is to model the propagation of one-dimensional waves caused by a short-duration dynamic load through a visco-elastic medium. Two types of viscous effects are considered and described by means of partial differential equations. Four pulse load shapes are considered and four cases analysed. A higher order Lagrangian finite element is used to model the wave propagation and the weak-form Galerkin method is adopted to solve the differential equations. Numerical solutions are compared to analytical ones (where they exist) and excellent temporal and spatial correlation is achieved. It is found that damping leads to a decrease in peak stresses and strains by up to 11% for 5% of critical damping, even during the direct loading phase. It is shown that the inclusion of strain-rate did not have an effect on strains but led to an increase in stresses by almost 100%. The inclusion of damping and strain-rate effects increased stress values by up to 70% compared to the non-viscous cases, rendering strain-rate effects more pronounced than damping effects. [Copyright &y& Elsevier]

Human hand movements have been studied for many decades, yet the role of hand biomechanics in achieving dexterity has not been fully understood. In this paper, we investigate the contributions of the intrinsic passive viscoelastic component in the hand during the coordinated wrist and hand movements. We compare the contributions of stiffness, damping, and dynamics torques under two types of joint phase movements at two speeds. The analysis of the data collected from subject studies demonstrated that the passive visco-elastic component is dominant over dynamic coupling terms. Although the exact contributions of the three torques vary under different speeds and phasic movements, the stiffness torque was the highest (at least 47%) followed by the damping torque, while the dynamics torque was the lowest (less than 11%) in all movement scenarios. Comparisons with studies involving coordinated arm movements illustrate that dominant torques in arm and hand movements are different suggesting that neural control strategies might be distinct as well. [ABSTRACT FROM PUBLISHER]

In this article, we consider a thermoelastic system of type III with a viscoelastic damping and internal delay. We use the multiplier method to prove, under suitable assumptions, general energy decay results from which the exponential and polynomial types of decay are only special cases. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a method of calculating long-term settlement of a loaded pad on soft clay at Klang, Selangor, Malaysia where the soil model is treated as an anelastic material of viscoelastic property. Initially, an elastic shear modulus (G) value from shear wave velocity profiles of the seismic tests from spectral analysis of surface wave (SASW) and continuous surface wave (CSW) tests was obtained. A value of damping (D) at an equivalent elastic strain is then calculated from the hysteresis of the plate load tests corrected to equivalent strain using the Damping–Strain formula. The calculated elastic settlement and its equivalent damping are then used to calculate the long-term settlement by applying the generalised viscoelastic formula. Comparisons to traditional methods of settlement predictions were made and the viscoelastic formula has shown better agreement to the observed settlement. Further modification of the settlement formula is introduced to improve the settlement accuracy to 10%. [Copyright &y& Elsevier]

Living soft tissues have two characteristics for an external force. One is the coupling effect (see Fig. 1) where the tissue deforms not only at the point of application of force but also at its surrounding area without any external force. The other is the direction-dependent response (see Fig. 2) where the response during the loading phase (when the force is applied with increasing displacement) is quicker than that during the unloading phase (when the force is shutdown). In order to represent these characteristics, this paper first proposes a single layered 3-D tissue model constructed by a network composed of two stiffness and two damping parameters, respectively. For such a single-layered model, we solve the inverse problem where four unknown viscoelastic parameters are obtained by assuming that both the applied force and surface deformation of the tissue are given with respect to time. Through both simulation and experimental results, we show that this model can describe good inherent characteristics of soft tissues, namely a direction-dependent response and a coupling effect. [ABSTRACT FROM PUBLISHER]

Abstract: A new sandwich finite element has been previously applied successfully to the vibration analysis of damped metal–polymer–metal beams . In this paper, this element is extended to the vibration of unsymmetrical sandwich plates with a viscoelastic core. The rotational influence of the transversal shearing in the core on the skins behaviour, ensures a displacement consistency over the interfaces between the viscoelastic core and the elastic skins resulting in accurate representations of the physics. To enable the analysis of plates with arbitrary orientation in three-dimensional space, a formulation with nine degrees of freedom per node is employed. Moreover, the element is shown to interface easily with classical plate’s elements. Comparisons with both experimental tests and classical solid FE modeling are shown to prove the accuracy and computational efficiency of the presented element for the modeling of the vibro-acoustic response of the studied metal–polymer–metal panels. [ABSTRACT FROM AUTHOR]

Abstract: A Newmark-diffusive scheme is presented for the time-domain solution of dynamic systems containing fractional derivatives. This scheme combines a classical Newmark time-integration method used to solve second-order mechanical systems (obtained for example after finite element discretization), with a diffusive representation based on the transformation of the fractional operator into a diagonal system of linear differential equations, which can be seen as internal memory variables. The focus is given on the algorithm implementation into a finite element framework, the strategies for choosing diffusive parameters, and applications to beam structures with a fractional Zener model. [Copyright &y& Elsevier]

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]

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]

Abstract: In this paper an analytical method is proposed for damping analysis of sandwich beams with piezoelectric and viscoelastic layers. Based on the classical zig-zag model and some assumptions about the electric field, this method leads to an analytical expression of the modal loss factor and frequency. Considering two feedback control laws, the obtained hybrid damping of the sandwich beam is characterized. Numerical finite element applications are considered, in order to examine the efficiency and limitations of the presented method. [Copyright &y& Elsevier]

The paper deals with the coupled problem of flexural vibrations and dissipative heating of a viscoelastic ring plate with piezoceramic actuators under monoharmonic electromechanical loading. The temperature dependence of the complex characteristics of passive and piezoactive materials is taken into account. The coupled nonlinear problem of thermoviscoelasticity is solved by an iterative method. At each iteration, orthogonal discretization is used to integrate the equations of elasticity and an explicit finite-difference scheme is used to solve the heat-conduction equation with a nonlinear heat source. The effect of the dissipative heating temperature, boundary conditions, and the thickness and area of the actuator on the active damping of the forced vibrations of the plate under uniform transverse harmonic pressure is examined [ABSTRACT FROM AUTHOR]