Viscoelastic Sandwich Research Articles

Variability analysis of frequency dependent visco-elastic three-layered beams

The modal stability procedure is combined with Monte-Carlo simulations to estimate the variability of natural frequencies and damping ratios of frequency dependent visco-elastic sandwich structures. In the pre-processing phase, the Diamant approach is used, at nominal, to compute complex eigenvalues and eigenmodes. Then, in the on-line phase i.e within the Monte-Carlo simulation loop, a non-linear equation is solved with Newton–Raphson algorithm to obtain perturbed complex eigenvalues. The low computational times of the method enable the use of large scale Monte-Carlo simulations yielding accurate estimates of means and coefficients of variation of frequencies and damping ratios. The method is illustrated on a three-layered sandwich rectangular beam with visco-elastic core. A frequency dependent visco-elastic material 3M ISD112 is used and two different set of boundary conditions are considered. The stochastic variables are the Young modulus of the elastic faces and the delayed elasticity shear modulus. In particular, it is shown that the mechanism of uncertainty propagation affects mostly damping ratios that experience higher coefficients of variation than natural frequencies.

Dynamic properties comparisons between experimental measurements and nondeterministic numerical models of viscoelastic sandwich beams

In order to design viscoelastic sandwich structures used as passive damping treatment, many aspects should be considered. In all methods available in the literature to model Viscoelastic Materials (VEM) a crucial step is the determination of the complex modulus, usually obtained by curve fitting experimental results. Considering that dispersions are inherent to experimental tests and also those small variations in the fitted parameters lead to considerable changes on the dynamic behavior of VEMs hence a nondeterministic model seems to be more suitable than the usual deterministic ones. In that way, starting from dynamic properties of a VEM, a nondeterministic numerical model, which takes into account incertitudes in the VEM curve fitting procedure, is proposed. This model was used to evaluate the behavior of sandwich structures, showing the advantages and disadvantages of the presented methodology, comparing damping ratios and natural frequencies results of experimental tests with the ones extracted from the proposed nondeterministic numerical GHM based model, in order to establish a method to support viscoelastic sandwich beams design.

State recognition of the viscoelastic sandwich structure based on the adaptive redundant second generation wavelet packet transform, permutation entropy and the wavelet support vector machine

The viscoelastic sandwich structure is widely used in mechanical equipment, yet the structure always suffers from damage during long-term service. Therefore, state recognition of the viscoelastic sandwich structure is very necessary for monitoring structural health states and keeping the equipment running with high reliability. Through the analysis of vibration response signals, this paper presents a novel method for this task based on the adaptive redundant second generation wavelet packet transform (ARSGWPT), permutation entropy (PE) and the wavelet support vector machine (WSVM). In order to tackle the non-linearity existing in the structure vibration response, the PE is introduced to reveal the state changes of the structure. In the case of complex non-stationary vibration response signals, in order to obtain more effective information regarding the structural health states, the ARSGWPT, which can adaptively match the characteristics of a given signal, is proposed to process the vibration response signals, and then multiple PE features are extracted from the resultant wavelet packet coefficients. The WSVM, which can benefit from the conventional SVM as well as wavelet theory, is applied to classify the various structural states automatically. In this study, to achieve accurate and automated state recognition, the ARSGWPT, PE and WSVM are combined for signal processing, feature extraction and state classification, respectively. To demonstrate the effectiveness of the proposed method, a typical viscoelastic sandwich structure is designed, and the different degrees of preload on the structure are used to characterize the various looseness states. The test results show that the proposed method can reliably recognize the different looseness states of the viscoelastic sandwich structure, and the WSVM can achieve a better classification performance than the conventional SVM. Moreover, the superiority of the proposed ARSGWPT in processing the complex vibration response signals and the powerful ability of the PE in revealing the structural state changes are also demonstrated by the test results.

Nonlinear dynamic behavior of viscoelastic sandwich composite plates under non-uniform blast load: Theory and experiment

In this paper, the dynamic behavior of a viscoelastic sandwich composite plate subjected to the non-uniform blast load is investigated. The theoretical and experimental study is carried out. The plate examined has carbon/epoxy face sheets and an aramid honeycomb core. In the theoretical study, the sandwich plate is modeled using first order shear deformation theory. Because of the large deformations which occurred after the blast load in some tests, geometrical nonlinearities are considered in the derivations. The shear and large deflection effects are considered. The equations of motion are derived by the use of virtual work principle for the sandwich plate. The clamped boundary conditions are considered for all edges of the plate. The viscoelastic properties of carbon/epoxy coupons and sandwich coupons are determined using Dynamic Mechanical Analyzer. The viscoelastic behavior is modeled by using the Kelvin-Voigt linear viscoelastic theory. The equations of motion are obtained in the time domain using Galerkin's method. The nonlinear coupled equation system is solved by Mathematica Software. A special experimental setup is used to obtain the blast pressure for the blast test. The experimental, theoretical and finite element analysis results are compared and the vibration characteristics, peak points, vibration frequencies are found to be in an agreement.

A novel manifold–manifold distance index applied to looseness state assessment of viscoelastic sandwich structures

Viscoelastic sandwich structures (VSS) are widely used in mechanical equipment; their state assessment is necessary to detect structural states and to keep equipment running with high reliability. This paper proposes a novel manifold–manifold distance-based assessment (M2DBA) method for assessing the looseness state in VSSs. In the M2DBA method, a manifold–manifold distance is viewed as a health index. To design the index, response signals from the structure are firstly acquired by condition monitoring technology and a Hankel matrix is constructed by using the response signals to describe state patterns of the VSS. Thereafter, a subspace analysis method, that is, principal component analysis (PCA), is performed to extract the condition subspace hidden in the Hankel matrix. From the subspace, pattern changes in dynamic structural properties are characterized. Further, a Grassmann manifold (GM) is formed by organizing a set of subspaces. The manifold is mapped to a reproducing kernel Hilbert space (RKHS), where support vector data description (SVDD) is used to model the manifold as a hypersphere. Finally, a health index is defined as the cosine of the angle between the hypersphere centers corresponding to the structural baseline state and the looseness state. The defined health index contains similarity information existing in the two structural states, so structural looseness states can be effectively identified. Moreover, the health index is derived by analysis of the global properties of subspace sets, which is different from traditional subspace analysis methods. The effectiveness of the health index for state assessment is validated by test data collected from a VSS subjected to different degrees of looseness. The results show that the health index is a very effective metric for detecting the occurrence and extension of structural looseness. Comparison results indicate that the defined index outperforms some existing state-of-the-art ones.

A reduction model for eigensolutions of damped viscoelastic sandwich structures

The aim of this paper is to develop a reduction method to determine the modal characteristics of viscoelastic sandwich structures. The method is based on the high order Newton algorithm and reduction techniques. Numerical tests have been performed in the case of sandwich beams and cylindrical shells. The comparison of the results obtained by the reduction method with those given by direct simulation shows both a good agreement and a significant reduction in computational cost.

The effects of nonlinearities on the vibration of viscoelastic sandwich plates

The nonlinear free and forced bending vibration of sandwich plates with incompressible viscoelastic core is investigated under the effects of different source of nonlinearities. For the core constrained between stiffer layers, the transverse shear strains, as well as the rotations are assumed to be moderate. The linear and quadratic displacement fields are also adopted for the in-plane and out-of-plane displacements of the core, respectively. The assumption of moderate transverse strains requires a nonlinear constitutive equation which is obtained from a single-integral nonlinear viscoelastic model using the assumed order of magnitudes for linear strains and rotations. The 5th-order method of multiple scales is directly applied to solve the equations of motion. The different-order linear partial differential equations that were obtained during the perturbation solution, are solved by the method of eigenfunction expansion and the nonhomogeneous boundary conditions are dealt with by transforming to homogeneous boundaries, or using the extended Green's formula. The effects of different system parameters on the nonlinear estimation of frequencies, damping ratios, and peak response are studied. Also, the importance of different nonlinear terms arisen from different ordering assumptions is assessed and the ranges of system parameters with higher values of error are identified.

Reduced-order model for non-linear dynamic analysis of viscoelastic sandwich structures in time domain

The present paper deals with the analysis of the dynamic behavior of viscoelastic sandwich structures with localized nonlinearities. The Golla-Hughes Mac Tavish (GHM) viscoelastic model is used and the finite elements procedure is established to derive both linear and non-linear equations of motion. This model increase the order of the differential equations of motion through the addition of dissipative coordinates, which complicate further the numerical resolution with the addition of local nonlinearities in the junctions of the assembled structures. Hence, a reduced-order model is proposed to enhance the control of the dynamic behavior of such structures incorporating viscoelastic materials especially for structures with large finite element model.

Static Behaviour of Visco-elastic Sandwich Plate with Nano-composite Facings under Mechanical Load

Static behaviour of visco-elastic sandwich plate with functionally graded carbon nano tube reinforced polymer nano composite facings has been analyzed using finite element method. Parameter studies have been carried out to analyze influence of volume fraction of carbon nanotube (CNT), nature of functional grading of CNT, core material and core thickness to facing layer thickness ratio on static bending deflection, axial stress and transverse shear stresses of the plate under mechanical load. It is found that functional grading of CNTs in FG-X pattern enhances the static characteristics compare to uniform distribution of CNTs. It is found that maximum static bending deflection of the visco-elastic plate decreases with increase in volume fraction of CNTs. Influence of visco-elastic core thickness and visco-elastic core material on static characteristics is significant.

A concept to reduce vibrations in steel catenary risers by the use of viscoelastic materials

One of the most important issues in steel riser systems is the VIV phenomenon (Vortex Induced Vibration). VIV may induce high levels of structural vibrations and stresses what eventually lead to considerable fatigue damage and reduction in structural lifetime. The use of suppression devices is a feasible solution to tackle this problem. Nevertheless, their disadvantage is the increase in drag coefficient; moreover, it is very expensive. This work proposes and investigates a concept aimed at suppressing vibrations in steel catenary risers by the use of viscoelastic sandwich layers and it is based on three steps. The first one considers the calibration of a viscoelastic constitutive model based on complex shear modulus measurements in a controlled experimental environment. The second one is a model validation scheme applied on the calibrated model provided by the first step and it is based on experimental data obtained out of a 1.6m long tubular sandwich structure. The third step assesses the effectiveness of viscoelastic sandwich layers using a small scale model of a steel catenary riser installed in P18 platform which is in operation in Campos Basin, Brazil. The results are quite compelling due to the great increase of damping that was observed.

Transverse vibration of viscoelastic sandwich beam with time-dependent axial tension and axially varying moving velocity

Nonlinearly parametric resonances of axially accelerating moving viscoelastic sandwich beams with time-dependent tension are investigated in this paper. Based on the Kelvin differential constitutive equation, the controlling equation of the transverse vibration of a beam with large deflection is established. The system has been subjected to a time varying velocity and a harmonic axial tension. Here the governing equation of motion contains linear parametric terms and two frequencies, one is the frequency of axially moving velocity and the other one is the frequency of varying tension. The method of multiple scales is applied directly to the governing equation to obtain the complex eigenfunctions and natural frequencies of the system. The elimination of secular terms leads to the steady-state response and amplitude of vibrations. The influence of various parameters such as initial tension on natural frequencies and the amplitude of axial fluctuation, the phase angle between the two frequencies on response curves has been investigated for two different resonance conditions. With the help of numerical results, it has been shown that by using suitable initial tension, the amplitude of axial fluctuation, the phase angle, the vibration of the sandwich beam can be significantly controlled.

A discrete convolutional Hilbert transform with the consistent imaginary initial conditions for the time-domain analysis of five-layered viscoelastic sandwich beam

A discrete convolutional Hilbert transform (DCHT) with the consistent imaginary initial conditions, together with the development of 2-node 8-DOF damped beam element, are presented for the reliable DOF-efficient time-domain analysis of five-layered viscoelastic sandwich beam. Motivated by the fact that the longitudinal displacements of three metallic layers can be replaced with the transverse shear strains of two viscoelastic core layers, a DOF-efficient damped beam element with the nodal DOFs composed of the deflection and rotation of beam and shear strains of two viscoelastic core layers is derived according to the virtual work principle and the compatibility relation. The standard Hilbert transform using Fourier and inverse Fourier transform of impulse signals produces the totally different results from the analytically derived ones near the end of time period, and the non-conjugate complex eigen values in a state-space formulation cause the unbounded growth in the time response of the damped structural dynamic system when a standard time integration scheme is used. To resolve these numerical problems, the imaginary external force is obtained by dividing the real external force into a finite number of rectangular impulses and by superposing Hilbert transforms of each rectangular impulse. And the time response of the damped sandwich beam subject to arbitrary external force is obtained by the convolution of time response to unit impulse. Meanwhile, the consistent imaginary initial conditions which can provide the bounded damped time response are numerically derived by splitting each decoupled complex second-order differential equation in the mode superposition approach into real and imaginary ones and by solving general solutions of each two split equations in the space-state formulation. The proposed method is validated through the numerical experiments composed of analytic and five-layered damped sandwich beam examples.

Influence of partial constrained layer damping on the bending wave propagation in an impacted viscoelastic sandwich

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.

Nonlinear vibration of viscoelastic sandwich plates under narrow-band random excitations

The effect of the narrow-band random excitation on the non-linear response of sandwich plates with an incompressible viscoelastic core is investigated. To model the core, both the transverse shear strains and rotations are assumed to be moderate and the displacement field in the thickness direction is assumed to be linear for the in-plane components and quadratic for the out-of-plane components. In connection to the moderate shear strains considered for the core, a non-linear single-integral viscoelastic model is also used for constitutive modeling of the core. The fifth-order perturbation method is used together with the Galerkin method to transform the nine partial differential equations to a single ordinary integro-differential equation. Converting the lower-order viscoelastic integral term to the differential form, the fifth-order method of multiple scale is applied together with the method of reconstitution to obtain the stochastic phase-amplitude equations. The Fokker–Planck–Kolmogorov equation corresponding to these equations is then solved by the finite difference method, to determine the probability density of the response. The variation of root mean square and marginal probability density of the response amplitude with excitation deterministic frequency and magnitudes are investigated and the bimodal distribution is recognized in narrow ranges of excitation frequency and magnitude.

Buckling Delamination of a Rectangular Viscoelastic Sandwich Plate Containing Interface Inner Cracks

AbstractIn this paper, buckling delamination around interface inner cracks contained within the simply supported elastic and viscoelastic rectangular sandwich plate under biaxial loading is studied. It is assumed that the materials of the face layers are viscoelastic and the material of the core layer is pure elastic. Moreover, it is assumed that the material of the core layer is stiffer than the materials of the face layers. Within these assumptions it is supposed that between the face and core layers there are rectangular inner cracks, the locations of which are symmetric with respect to the plate geometry. The edge surfaces of the cracks have insignificant initial imperfections before the loading. The evolution of these initial imperfections with the flow of time is investigated within the scope of the three-dimensional (3D) geometrically nonlinear field equations of the theory of viscoelasticity. For determination of the values of the critical parameters (buckling force, time, and buckling mode), the ...

Coupled Thermoelastic Vibration of the Axially Moving Sandwich Beam

The transverse vibration characteristic of the viscoelastic sandwich beam with axial speed is studied under the coupled temperature field and displacement field. Based on the theory of Euler - Bernouli beam and the constitutive relation of Kelvin viscoelastic material model, the transverse vibration equation of the axially moving beam is established ; considering the interaction of the material deformation and the heat conduction, the coupled governing equation of the beam is obtained. and the coupled thermoelastic dynamics system are obtained by Galerkin method. The related thermal parameters on the vibration frequency are analyzed by using numerical method.

Finite element model for damping optimization of viscoelastic sandwich structures

In this work a simple and efficient finite element model is used for the damping optimization of multilayer sandwich plates, with a viscoelastic core sandwiched between elastic layers, including piezoelectric layers. The elastic layers are modeled using the classical plate theory and the core is modeled using Reddy’s third-order shear deformation theory. The finite element formulation is obtained by assembly of N “elements” through the thickness, using specific assumptions on the displacement continuity at the interfaces between layers. The free vibration response of damped multilayer sandwich structures is characterized by solving an eigenvalue problem to obtain the fundamental natural frequency and corresponding modal loss factor. The optimization is conducted in order to maximize the fundamental modal loss factor, using gradient based algorithms, and afterwards, considering steady state harmonic motion the analysis is conducted in time domain to obtain the structure response. The model is applied in the solution of some illustrative examples and the results are presented and discussed.

Elastic Foundation Analysis of Uniformly Loaded Functionally Graded Viscoelastic Sandwich Plates

AbstractThis paper deals with the static response of simply supported functionally graded material (FGM) viscoelastic sandwich plates subjected to transverse uniform loads. The FG sandwich plates are considered to be resting on Pasternak's elastic foundations. The sandwich plate is assumed to consist of a fully elastic core sandwiched by elastic-viscoelastic FGM layers. Material properties are graded according to a power-law variation from the interfaces to the faces of the plate. The equilibrium equations of the FG sandwich plate are given based on a trigonometric shear deformation plate theory. Using Illyushin's method, the governing equations of the viscoelastic sandwich plate can be solved. Parametric study on the bending analysis of FG sandwich plates is being investigated. These parameters include (i) power-law index, (ii) plate aspect ratio, (iii) side-to-thickness ratio, (iv) loading type, (v) foundation stiffnesses, and (vi) time parameter.

A finite element model using a unified formulation for the analysis of viscoelastic sandwich laminates

In this paper we present a layerwise finite element model for the analysis of sandwich laminated plates with a viscoelastic core and laminated anisotropic face layers. The stiffness and mass matrices of the element are obtained by Carrera’s Unified Formulation (CUF). The dynamic problem is solved in the frequency domain with viscoelastic frequency-dependent material properties for the core. The dynamic behaviour of the model is compared with solutions found in the literature, including experimental data.

Viscoelastic analysis of an exponentially graded sandwich plate

Bending response of an exponentially graded fiber-reinforced viscoelastic (EGFV) sandwich plate is investigated using various plate theories. The plate consists of viscoelastic material faces and an elastic material core. The effective moduli and Illyushin’s approximation methods are used to solve the equations governing the bending of simply-support EGFV sandwich plates. Numerical results for deflections and stresses are presented and some of them are compared. The effects due to aspect ratio, side-to-thickness ratio and constitutive parameter as well as time parameter are all investigated. Concluding remarks are made.