Viscoelastic Sandwich Research Articles

Dynamic response of viscoelastic multiple-core sandwich structures

This work focuses on the free and forced vibrations of sandwich beams and plates hosting an arbitrary number of damping cores. A fractional derivatives Zener-type model is adopted for representing the frequency-dependent viscoelastic behaviour, along with conventional series developments. The structural models are formulated within an established variable kinematics approach, which enables to investigate the role of specific assumptions and to identify the most accurate model at a least number of degrees of freedom. Approximate solutions are found by a computationally efficient Ritz method that allows to take into account any type of boundary conditions. Modal loss factors and damped eigenfrequencies are obtained from a complex eigenvalue problem, for which a modal strain energy approach or a complex eigensolution can be employed. Frequency responses can be computed by a direct approach or by elementary modal projection algorithms. Results are reported for conventional and innovative sandwich configurations. Different modelling and solution strategies are compared and the role of transverse normal deformation of the mechanically weak viscoelastic plies is particularly emphasised.

Hygrothermal effect on vibration of magnetostrictive viscoelastic sandwich plates supported by Pasternak's foundations

In hygrothermal environment, vibration study of a simply supported smart sandwich plate embedded in an elastic substrate medium is presented in the present article. The sandwich plate contains layers of fiber-reinforced and magnetostrictive materials and core of viscoelastic material. The kinematic equations system is derived via employing Hamilton's principle with considering the transverse shear strains with and without the normal strains effect. Various numerical examples are carried out to study the effects of temperature rise, degree of moisture concentration, elastic foundations parameters, thickness ratio, aspect ratio, thickness ratio of magnetostrictive layer to viscoelastic layer, modes, lamination schemes, magnitude of the feedback coefficient, position of the magnetostrictive layers and viscoelastic structural damping coefficient on controlled motion and vibration characteristics of plate. Some observation about influences of the temperature and humidity concentrations on vibration characteristics of studied plate are presented in detail. The outcomes indicate that the hygrothermal environments have negative effects on vibration suppression of advanced composite structures especially the uniform hygrothermal distribution. The frequencies increase with increasing the viscoelastic structural damping coefficient and the foundation constants.

Vibro-acoustic characteristics of viscoelastic sandwich panel: effect of inherent damping

This paper presents the effect of the inherent material damping of aluminium facings and fibre reinforced polymer (FRP) core composite sandwich panel on vibro-acoustics and sound transmission loss characteristics. The modal strain energy method is used to calculate the modal damping ratio at each mode. To determine the forced vibration response, the harmonic analysis is carried out. From the kinematic continuity of velocity of the structure and the acoustic particle velocity at the surface, the sound power level is calculated. From the results, it is revealed that 19.89 dB of overall sound power level is reduced by including the modal damping ratio in the finite element modeling. Further, it is noticed that by replacing the aluminium plate to aluminium face sheet with an FRP core sandwich panel, the overall sound power level of 11.76 dB and 10.78 dB is reduced based on the same volume and weight analysis respectively.

TheFinite Element Modeling and Experimental Study of Sandwich Plates with Frequency-Dependent Viscoelastic Material Model.

Athree-layer composite plate element is developed for finite element modeling and vibration analysis of sandwich plate with frequency-dependent viscoelastic material core. The plate element is quadrilateral element bounded by four-node with 7-degree-of-freedom per node. The frequency-dependent characteristics of viscoelastic material parameters are described using the Biot model. The method of identifying the parameters of the Biot model is given. By introducing auxiliary coordinates, the Biot model is combined with the finite element equation of the viscoelastic sandwich plate. Through a series of mathematical transformations, the equation is transformed into a standard second-order steady linear system equation form to simplify the solution process. Finally, the vibration characteristics of the viscoelastic sandwich plate are analyzed and experimentally studied. The results show that the method in this paper is correct and reliable, and it has certain reference and application value for solving similar engineering vibration problems.

Multiobjective optimization solutions for noise reduction in composite sandwich panels using active control

In this paper, optimal solutions for noise reduction in laminated viscoelastic soft core sandwich plates are obtained, using active control with surface bonded piezoelectric sensors and actuators. An in–house finite element implementation of the active laminated sandwich plate is used to obtain the frequency response of the panels. Since the structural/acoustic problem is lightly coupled, the sound transmission characteristics of the panels are evaluated by computing their radiated sound power, using the Rayleigh integral method. A negative velocity feedback control law has been used to implement the active damping. The optimal location of the surface co-located pairs of piezoelectric patches is then obtained, using the Direct MultiSearch (DMS) optimization algorithm to minimize simultaneously the added weight, the number of controllers and noise radiation. The minimization of noise radiation is accomplished by minimizing the total length of the radiated sound power frequency response curve. Trade-off Pareto fronts and the respective optimal active patch configurations are obtained and discussed.

Transient instability analysis of viscoelastic sandwich CNTs-reinforced microplates exposed to 2D magnetic field and hygrothermal conditions

Transient size-dependent mechanical and thermal buckling analyses of sandwich microplates with viscoelastic core and single-walled carbon nanotubes (CNTs)-reinforced face sheets are introduced in this paper. The CNTs are uniformly distributed or functionally graded (FG) through the thickness of the face layers. The viscoelastic sandwich microplate is resting on three-parameter viscoelastic foundations that modeled according to the viscoelastic Kelvin-Voigt model with a shear layer. Effects of a 2D magnetic field as well as hygrothermal conditions on the present analyses are studied. The modified couple stress model containing one material length scale parameter is employed to capture the small scale effect. A body force (Lorentz force) is deduced from Maxwell’s magnetic equations, that is applied to each particle of the structure. The higher-order shear deformation plate theory with four unknowns is utilized to describe the displacement field. The stability equations are obtained using the principle of virtual displacement. By applying Navier method, the stability equations are solved to obtain the mechanical and thermal buckling of viscoelastic sandwich microplates. Various numerical examples are presented including the effects of the length scale parameter, moisture concentration, magnetic field parameter and other parameters on the buckling of the viscoelastic FGCNTs-reinforced sandwich microplates.

Vibration characteristics of viscoelastic sandwich tube conveying fluid

In the present work, the damping characteristics of clamped–clamped viscoelastic sandwich tube conveying fluid are investigated in relation to the length-to-radius and radius-to-thickness ratios. It is observed that the modal loss factor is very less for lower circumferential modes compared to higher modes while the modal loss factors of higher modes increases with the aforesaid ratios. A significant effect of flow velocity in reducing the natural frequency and enhancing the loss factor appears only in sandwich shells, whereas this effect is negligible for sandwich pipes and have very low fundamental modal loss factor. The symmetric sandwich tube conveying fluid has a better damping capability compared to an asymmetric one.

Damping of circular composite viscoelastic plate vibration under neutron irradiation

During the irradiation of structural elements with neutrons, ions, electrons, the mechanical properties of materials change. The neutron irradiation is of particular interest. Therefore, the relevance of the study is beyond doubt. The main purpose of this paper is to investigate the vibration damping of a circular composite viscoelastic plate under neutron irradiation. According to existing concepts, two mechanisms of accelerated radiation creep are possible. An initial-boundary value problem of free vibrations damping in a circular linearly viscoelastic sandwich plate under neutron irradiation is considered. It is determined that when the frequency of the perturbing force coincides with higher frequencies of natural oscillations, the periodicity is blurred, although the amplitude of oscillations increases and, in this case, a "false resonance" is observed. An analytical solution is obtained using the averaging method in dynamic viscoelasticity problems. The logarithmic decrement of oscillations is investigated numerically. Its dependence on the intensity of the neutron flux is revealed.

Modal analysis of rotating pre-twisted viscoelastic sandwich beams

This paper presents an analysis of the vibrational behavior of a rotating viscoelastic sandwich pre-twisted beams with a setting angle and with various viscoelastic stiffness laws. The governing equations of motion are derived using the Lagrange formulation and the assumed modes method. The obtained nonlinear eigenvalue problems are solved by using an iterative nonlinear eigensolver leading to complex eigensolutions composed of damped frequencies and loss factors with high accuracy. Further, the effects of the rotating speed, pre-twist angle, thickness ratio of core layer on the dynamic characteristics are investigated with taking into account the dependence of Young modulus with respect to frequency. Different numerical tests on rotating pre-twisted beams are performed for both isotropic and sandwich materials with a constant then a variable core modulus and the obtained results coincide very well with those provided in literature.

Analysis of Viscoelastic Functionally Graded Sandwich Plates with CNT Reinforced Composite Face Sheets on Viscoelastic Foundation

In this article, bending, buckling, and free vibration of viscoelastic sandwich plate with carbon nanotubes reinforced composite facesheets and an isotropic homogeneous core on viscoelastic foundation are presented using a new first order shear deformation theory. According to this theory, the number of unknown’s parameters and governing equations are reduced and also the using of shear correction factor is not necessary because the transverse shear stresses are directly computed from the transverse shear forces by using equilibrium equations. The governing equations obtained using Hamilton’s principle is solved for a rectangular viscoelastic sandwich plate. The effects of the main parameters on the vibration characteristics of the viscoelastic sandwich plates are also elucidated. The results show that the frequency significantly decreases with using foundation and increasing the viscoelastic structural damping coefficient as well as the damping coefficient of materials and foundation.

Uncertainty propagation and numerical evaluation of viscoelastic sandwich plates having nonlinear behavior

The dynamic analysis of nonlinear viscoelastic systems in the frequency domain is not an easy task. In most cases, it is due to the frequency- and temperature-dependent properties of the viscoelastic part. Additionally, due to the inherent uncertainties affecting the viscoelastic efficiency in practical situations, their handling in the nonlinear modeling methodology becomes essential nowadays. However, it is still an issue. Thus, this paper presents a numerical modeling methodology intended to perform dynamic analyses in the frequency domain of thin sandwich plates under large displacements. The uncertainties characterizing the nonlinear dynamics of the viscoelastic system are introduced on the random linear and nonlinear finite element matrices by performing the Karhunen–Loève expansion technique. The Latin hypercube sampling method is used herein as the stochastic solver, and the nonlinear frequency responses are computed using the harmonic balance method combined with the Galerkin bases. To overcome the difficulty in solving the resulting complex nonlinear eigenproblem with a frequency-dependent viscoelastic stiffness, making the stochastic nonlinear analyses in the frequency domain very costly, sometimes unfeasible, an efficient and accurate iterative reduction method is proposed to approximate the complex eigenmodes. The envelopes of nonlinear frequency responses demonstrate clearly the relevance of considering the uncertainties in design variables of viscoelastic systems having nonlinear behavior to deal with more realistic situations.

A Finite Element Model for the Vibration Analysis of Sandwich Beam with Frequency-Dependent Viscoelastic Material Core.

In this work, a finite element model was developed for vibration analysis of sandwich beam with a viscoelastic material core sandwiched between two elastic layers. The frequency-dependent viscoelastic dynamics of the sandwich beam were investigated by using finite element analysis and experimental validation. The stiffness and damping of the viscoelastic material core is frequency-dependent, which results in complex vibration modes of the sandwich beam system. A third order seven parameter Biot model was used to describe the frequency-dependent viscoelastic behavior, which was then incorporated with the finite elements of the sandwich beam. Considering the parameters identification, a strategy to determine the parameters of the Biot model has been outlined, and the curve fitting results closely follow the experiment. With identified model parameters, numerical simulations were carried out to predict the vibration and damping behavior in the first three vibration modes, and the results showed that the finite model presented here had good accuracy and efficiency in the specific frequency range of interest. The experimental testing on the viscoelastic sandwich beam validated the numerical predication. The experimental results also showed that the finite element modeling method of sandwich beams that was proposed was correct, simple and effective.

Influence of a 2D magnetic field on hygrothermal bending of sandwich CNTs-reinforced microplates with viscoelastic core embedded in a viscoelastic medium

The present work is concerned with the bending analysis of viscoelastic sandwich microplates with carbon nanotubes (CNTs)-reinforced face sheets under the effects of a 2D magnetic field as well as hygrothermal conditions. The core layer is assumed to be a fully homogeneous viscoelastic material, whereas the face sheets are made of a polymer matrix stiffened by uniformly distributed or functionally graded (FG) CNTs. The applied magnetic field results in a body force (Lorentz force) that is applied to each particle of the plate. In order to take into account the size effect, the modified couple stress theory is employed containing only one length scale parameter. The viscoelastic sandwich microplate is assumed to be resting on two layers of the foundations. The first is modeled as the viscoelastic Kelvin–Voigt model. However, the second represents the elastic Pasternak shear layer. Based on the sinusoidal four-variable plate theory, four governing equations are obtained involving Lorentz force and foundation interaction. An analytical solution for the obtained equations is presented to get the displacements and stresses of the reinforced sandwich plates. The present solution is examined by introducing comparison examples. Influences of the geometric parameters, material length scale parameter, magnetic field parameter, damping parameters, temperature rise, moisture concentration, and foundation coefficients on the bending of the FG-CNTs-reinforced viscoelastic sandwich microplates are discussed.

Study of damped vibrations of a vibroacoustic interior problem with viscoelastic sandwich structure using a High Order Newton solver

The aim of this study is to compute damped eigenfrequencies and modes of a vibroacoustic interior problem with fluid-structure coupling. Damping is introduced using a sandwich structure with viscoelastic core. In this paper, the coupled problem is solved by a High Order Newton (HON) solver, based on homotopy and perturbation techniques. Thus, the initial non-linear problem is turned into a set of linear algebraic systems, easier to solve. Comparison of the results obtained by the HON solver with those obtained by the Newton classical method highlights the efficiency of the proposed method. Finally, the mechanical behavior of the coupled damped problem is studied.

Looseness condition feature extraction of viscoelastic sandwich structure using dual-tree complex wavelet packet-based deep autoencoder network

It is significant to perform looseness condition detection of viscoelastic sandwich structures to avoid serious accidents. Due to the multilayer characteristic of the viscoelastic sandwich structure, the vibration response signal of such structures is nonlinear and nonstationary. Furthermore, the looseness condition feature signal contained in the vibration response signal is very puny. Condition feature extraction has become a challenging task in the looseness condition detection of viscoelastic sandwich structures. Therefore, a novel method called dual-tree complex wavelet packet-based deep autoencoder network is proposed for this task. First, the vibration response signal of the viscoelastic sandwich structure is decomposed by dual-tree complex wavelet packet transform and the sub-band signals which contain rich energy are extracted. Then, the energies of the extracted sub-band signals are calculated to form a feature set. Finally, a deep autoencoder network is established to fuse the feature set, and the fused feature is viewed as the detection index to detect the looseness condition of the viscoelastic sandwich structure. The proposed method is applied to the connecting bolt looseness condition detection of the viscoelastic sandwich structure to validate its effectiveness. Compared with the detection method based on dual-tree complex wavelet packet transform and energy and the detection method based on dual-tree complex wavelet packet transform and permutation entropy, the results indicate that the effectiveness of the proposed method in this article is more superior to that of the other two methods.

Uncertainty propagation and experimental verification of nonlinear viscoelastic sandwich beams

Abstract The nonlinear dynamic analysis of viscoelastic systems is not an easy task. In some cases, it is due to the difficulty in dealing with the temperature- and frequency-dependent properties of the viscoelastic substructure. Also, since the real-life viscoelastic treatments are characterized by inherent uncertainties affecting their efficiency, their handling in the nonlinear modeling is essential from an engineering point of view. In this contribution, a stochastic modeling based on the Karhunen-Loeve expansion is proposed for a three-layer sandwich beam having nonlinear behavior using the concept of complex modulus and shift factor. The nonlinear frequency responses were obtained by using an approximated harmonic balance method with the Galerkin bases. Due to the difficulty in solving the resulting complex nonlinear eigenproblem with a frequency-dependent stiffness, making the stochastic nonlinear analyses very costly, it is proposed an iterative reduction method to approximate the complex eigenmodes. The influence of the forcing amplitude and temperature on the computed nonlinear frequency responses has been confirmed by performing laboratory experiments with a three-layer sandwich beam specimen placed inside an environmental chamber. Also, a curve-fitting has been performed to calibrate the deterministic nonlinear model using optimization tools. The envelopes of nonlinear responses demonstrate the relevance of considering the uncertainties in design variables.

Uncertainty propagation in modal analysis of viscoelastic sandwich structures using a stochastic collocation method

This paper presents an uncertainty propagation analysis of viscoelastic sandwich laminated structures using a stochastic collocation method based on Smolyak’s sparse grids approach. Shear deformation in the viscoelastic layers is accurately captured by means of layer-wise plate finite elements. Modal properties are determined by solving nonlinear eigenvalue problems due to the frequency-dependent nature of the considered viscoelastic materials. Variations in material properties and layer thicknesses are both treated in a probabilistic way. The variabilities of natural frequencies and modal loss factors of two different viscoelastic laminated plate structures (plane and cylindrical) are studied. Results show that the present method converges quickly with small sample sizes when compared to the classical Monte-Carlo method. The influence of the variability of several parameters on viscoelastic structure modal properties is commented.

Dynamic deflection analysis induced by blast load in viscoelastic sandwich plates with nanocomposite facesheets

The current work suggests a mathematical model for the dynamic response of sandwich concrete foundation with nano-fiber reinforced polymer (NFRP) layers at the top and bottom face sheets subjected to a blast load. The facesheets are reinforced by carbon nano-fibers where the equivalent material properties of the nanocomposite layers are obtained using Mori-Tanaka model considering agglomeration effects. The Kelvin-Voigt model is employed to consider the viscoelastic properties of the structure. The sandwich structure is rested on a soil foundation which is modeled by spring element. Based on refined zigzag theory, energy method and Hamilton’s principle, the motion equations are derived. The differential quadrature method in conjunction with Newmark method is utilized for obtaining the dynamic deflection of the structure for different boundary conditions. The effects of various parameters such as blast load, soil foundation, structural damping, volume fraction of carbon nano-fibers, NFRP layer, geometrical parameters of the structure are considered on the dynamic deflection of the structure. The results show that the NFRP layer can improve the resistance of the concrete foundation with respect to blast load.

Dynamic and instability analyses of FG graphene-reinforced sandwich deep curved nanobeams with viscoelastic core under magnetic field effect

Based on the nonlocal strain gradient theory, the effect of an axial magnetic field on the free vibration and mechanical buckling responses of an FG graphene-reinforced sandwich deep curved nanobeam with viscoelastic core embedded in a viscoelastic medium is elucidated in this paper. The curved beam is also assumed to be exposed to axial external compressions. The volume fraction of the constituents of the composite face layers are presumed to be functionally graded through the thickness according to a layer-wise law. The material properties are calculated in the framework of Halpin-Tsai micromechanical scheme. Lorentz magnetic force is deduced employing electro-dynamic Maxwell's relations for a conducting body. According to a refined shear and normal deformations curved beam theory, the motion equations are introduced in the polar coordinates. Analytical solutions are obtained for the natural frequencies and critical buckling load of the viscoelastic sandwich curved nanobeams. By comparing the present results with the available data in the literature, the developed formulations are validated. Furthermore, other several numerical examples are performed to show the effects of different parameters including viscoelastic core thickness, magnetic field, structural and foundation damping factor, opening angle and graphene concentration on the frequency and buckling load of the viscoelastic sandwich curved beams.

Free vibration and parametric instability of viscoelastic sandwich plates with functionally graded material constraining layer

Free vibration and parametric instability analyses of a three-layered sandwich plate with viscoelastic constrained layer and functionally graded material constraining layer are carried out in this work. A finite element model is developed for the vibration and parametric instability analyses of the sandwich plate. The lateral and transverse displacements of the viscoelastic core layer are considered as linear functions of top and bottom layer displacements. The first-order shear deformation theory is used to incorporate the effect of transverse sheer of the face layers, and in addition to the effect of shear deformation of the core, the effects of transverse and longitudinal deformations are also considered in this analysis. So that the present finite element model can be applied to the sandwich plates with thin as well as thick layers of core. The variations of fundamental frequency, mode loss factors and instability regions with different aspect ratios, thickness ratios, and boundary conditions are examined.