Viscoelastic Sandwich Plates Research Articles

Global sensitivity analysis of damped sandwich plates using sparse polynomial chaos expansions

The present article aims at performing a global sensitivity analysis of modal properties of a frequency dependent viscoelastic sandwich plate. The latter are evaluated using a finite element model relying on Kirchhoff theory for the elastic faces and the Mindlin-Reissner approach for the viscoelastic layer. The plate’s characteristics are considered as random variables following log normal laws. Sparse polynomial chaos expansions are employed to evaluate Sobol’s indices. For high damping, the resonant frequencies and loss factors turn to be sensitive to the elastic face properties, while in the weak damping case they are mostly affected by the viscoelastic model parameters.

Nonlinear dynamic response and damping performance of the viscoelastic composite core-based sandwich plates subjected to blast load

Nonlinear dynamic response and damping performance of the viscoelastic composite core-based sandwich plates subjected to blast load

A new guided mode so-called minimum group velocity in viscoelastic sandwich plates: A parametric numerical study

Zero-Group-Velocity (ZGV) guided mode has recently received particular attention because of its highly sensitive to structural changes, such as defects. Parallel to ZGV, in the present work, we introduce a new guided mode so-called Minimum-Group-Velocity (MGV) that is a remarkable phenomenon in defect detection applications. Strictly speaking, when any two phase-velocity dispersion curves of Lamb modes approach each other without overlapping, we observe this new mode in group-velocity dispersion curves. It is worth noting that this MGV mode has never been addressed in literature. We compute the Lamb-like modes in asymmetric viscoelastic sandwich plates using the Stiffness Matrix Method (SMM). We show that the change in properties of this sandwich can dramatically affect frequency ranges associated with ZGV and MGV modes. However, a linear correlation between phase velocities and this change on viscoelastic properties is discussed, where we observed an interconnection phenomenon in the dispersion curves. This interconnection happens between specific points on the dispersion curves, each corresponding to a ZGV- or MGV-mode. On the other hand, we verify that the detection of changes in level of viscoelastic properties or variations in the thickness of the buffer viscoelastic layer is possible within a limited segment of the damped mode curve.

Numerical analysis of brake squeal noise – Application to the disk brake systems

Exploring Noise Reduction in Automotive Disc Brake Systems: Investigating the Impact of Viscoelastic Core Sandwich Plates. This study delves into the phenomenon of brake squeal noise generated by automotive disc brake systems. It focuses on analyzing the response of sandwich plates with viscoelastic cores, which are employed within brake systems to mitigate squeal noise arising from friction between brake pads and the brake disk. Through a series of finite element analyses conducted under varying operational conditions, including friction coefficient and angular velocity, the research aims to ascertain the complex eigenvalue of the disc brake system in order to identify unstable modes. The findings underscore that the incorporation of viscoelastic layers within preloaded, slender sandwich plates introduces nonlinear dynamic characteristics that contribute to the reduction of squeal noise within braking systems.

FINITE ELEMENT ANALYSIS FOR DYNAMIC RESPONSE OF VISCOELASTIC SANDWICHED STRUCTURES INTEGRATED WITH ALUMINUM SHEETS

Passive vibration attenuation of modern mechanical structures is one of the most essential technologies applied to the arsenal of modern mechanical structures. In this work, dynamics analysis is performed on viscoelastic (VE) sandwich beam and plate by using finite element method. The proposed structure is composed of a VE core and aluminum face sheets as substrate layers on both sides of the structure. Small-strain VE material is modeled based on complex constant moduli model and numerical method is used to develop the finite element (FE) shear model based on first-order shear deformation theory (FSDT) and Hamilton principle. In modal analysis, model-effective mass analysis is performed to investigate its dominant mode shape and sweet spot at resonance using C3D20 and CPS8 elements. The former is indicated as a 3-D element with 20 nodes while the latter is indicated as a 2-D plane strain element with eight nodes. In harmonic analysis, resonance frequency is obtained based on mode superposition method to evaluate the steady-state response of VE sandwich beam via maximum deformation. Thereafter, the results are compared against analytical solutions from the literature. Moreover, a parametric study shows that the natural frequency of the beam did not change with the increase in core thickness. However, normalized loss factor of VE sandwich beam is directly proportional to VE damping factor and the thickness of VE core layer. Based on frequency response function, the results of resonance frequencies for VE beam are in the range of modal natural frequency.

Numerical modeling for viscoelastic sandwich smart structures bonded with piezoelectric materials

Regarding to viscoelastic laminated piezo smart plates and shells, electro-mechanically coupled finite element (FE) formations are derived based on zig-zag hypothesis for vibration and damping analyses. Three lamination configurations are considered in the model, where both elastic layers and viscoelastic layers are assumed to be Reissner–Mindlin plate. The quadratic element is adopted for FE modeling, each node has seven mechanical degrees of freedom (DOFs), which considers the complex shear modulus of viscoelastic materials. The analytical model is first validated by FE simulation of viscoelastic sandwich plates. Later, the effects of various parameters on the damping performance of piezo-viscoelastic laminated cylindrical structures are carried out, e.g. boundary conditions, reinforcement orientation angle, thickness of the viscoelastic core and structural curvature. The present FE modeling and analyses provide a powerful tool to accurately investigate the behaviors of viscoelastic laminated structures.

Development of an analytical framework for viscoelastic corrugated-core sandwich plates and validation against FEM

In this study, an analytical procedure for the bending problem of a viscoelastic sandwich plate with a corrugated core is presented. Reissner–Mindlin plate theory and N-termed Prony series are employed to define the elastic and time-dependent contributions of the governing equations, respectively. Three different corrugation patterns, i.e., rectangular, trapezoidal, and triangular, are examined. Moreover, the structure is analyzed under both simply support and clamp boundary conditions. The calibrated material parameters of polymethyl methacrylate (PMMA) for the Generalized Maxwell rheological model are employed to show the viscoelastic response of the structure. A 3D finite element simulation of the problem is also conducted to confirm the accuracy of the analytical formulation. The two well-known creep and stress relaxation phenomena of the viscoelastic materials are examined for the mentioned corrugation cores and both boundary conditions analytically and numerically. The time-dependent dimensionless deflection and resultant von Mises stress distributions are provided. Besides, the variation of the results with various rise-times and applied load are studied in detail. The von Mises stress contours of the upper surface of the structure at the end of the creep test are also presented. The finite element method outcomes verify the analytical results with excellent compatibility. The proposed analytical procedure can be used as an efficient tool to study the effects of various parameters such as material, geometrical constants, and corrugation pattern on bending of viscoelastic sandwich plates with corrugated core problems for design and optimization, which involves a high number of simulations.

Controlled motion of viscoelastic fiber-reinforced magnetostrictive sandwich plates resting on visco-Pasternak foundation

This article presents a controlled motion investigation of viscoelastic/fiber-reinforced/magnetostrictive/sandwich plates supported via visco-Pasternak foundations. The core of the plate is modeled as a Kelvin-Voigt viscoelastic model. The governing dynamic system is derived using Hamilton’s principle according to simple sinusoidal shear deformation plate theory. A simple feedback control system is utilized to control the structural vibration. Navier’s type solution of the system is obtained to study the influence of significant parameters, especially, the effect of the general thickness ratios, aspect ratio, the thickness ratio of the magnetostrictive layer to viscoelastic layer, sequence staking, foundations, viscoelastic structural damping coefficient, the magnitude of the feedback coefficient, and location of magnetostrictive layers on the vibrational behavior of studied sandwich plate. A comparison with previous studies is performed for validation of the corresponding numerical results and present formulation. Numerical outcomes indicate that increasing the thickness ratio of the viscoelastic layer to the magnetostrictive layer leads to improvement of the system vibration control, as well as the damping coefficient, grows and the damped natural frequency decreases with the increase of viscoelastic structural damping coefficient. The study maybe helps the designers and engineers in development of structural control systems in several applied fields.

Free vibration of doubly-curved generally laminated composite panels with viscoelastic matrix

As a first endeavor, this study scrutinizes the effects of general lamination schemes on the natural frequencies and loss factors of simply supported doubly-curved laminated composite panels. Transversely isotropic fibers obey linear elastic rule while isotropic polymeric matrix follows both standard solid and Kelvin-Voigt viscoelastic models. Frequency-dependent properties are obtained by multi-cell micromechanical approach and Alfrey correspondence principle. The governing equations of motions with frequency-dependent shear-stretching, bending-stretching and bending-twisting couplings are derived using Hamilton principle and third-order shear deformation theory. The coupled PDEs of motions are figured out via Galerkin method and eigenvalue solver. To verify, vibrational characteristics are compared with available results of elastic laminated panels and viscoelastic sandwich plates. Then, the effects of constitutive relations, fiber volume fraction, different fibers, geometrical parameters, symmetric, anti-symmetric and asymmetric laminations schemes are investigated on vibrational characteristics of spherical, cylindrical and hyperboloid panels. Also, crossing phenomenon and curve veering of frequencies and loss factors are observed.

Optimal distribution of active piezoelectric elements for noise attenuation in sandwich panels

ABSTRACT In this paper, a multiobjective optimization approach for obtaining the optimal distribution of surface-bonded piezoelectric sensors and actuators for noise attenuation in sandwich panels is presented. The noise attenuation is achieved by using negative velocity feedback control with co-located sensors and actuators. The control gains are also optimized in order to obtain the most efficient noise attenuation in a given frequency band. An in-house implementation of a viscoelastic soft core sandwich plate finite element, including surface-bonded piezoelectric sensors and actuators with active control capabilities, is used for obtaining the frequency response of the panels. The sound transmission capability of the panels is evaluated using the radiated sound power, along with the Rayleigh integral approach, which is suitable for lightly coupled structural/acoustic problems. The Direct MultiSearch (DMS) optimization algorithm is used to minimize the added weight due to the piezoelectric material, minimizing also the number of required controllers and maximizing the noise attenuation. The total length of the radiated sound power curve is shown to be an effective measure of noise attenuation in a given frequency band. Trade-off Pareto fronts and the obtained optimal configurations are presented and discussed.

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.

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.

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.

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.

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.

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.

A layerwise finite element formulation for vibration and damping analysis of sandwich plate with moderately thick viscoelastic core

Most previous studies of viscoelastic sandwich plates were based on the assumption that damping was only resulting from shear deformation in the viscoelastic core. However, extensive and compressive deformations in the viscoelastic core should also be considered especially for sandwich plates with moderately thick viscoelastic core. This paper presents a finite element formulation for vibration and damping analysis of sandwich plates with moderately thick viscoelastic core based on a mixed layerwise theory. The face layers satisfy the Kirchhoff theory while the viscoelastic core meets a general high-order deformation theory. The viscoelastic core is modeled as a quasi-three-dimensional solid where other types of deformation such as longitudinal extension and transverse compression are also considered. To better describe the distribution of the displacement fields, auxiliary points located across the depth of the sandwich plate are introduced. And based on the auxiliary points, the longitudinal and transverse displacements of the viscoelastic core are interpolated independently by Lagrange interpolation functions. Quadrilateral finite elements are developed and dynamic equations are derived by Hamilton’s principle in the variation form. Allowing for the frequency-dependent characteristics of the viscoelastic material, an iterative procedure is introduced to solve the nonlinear eigenvalue problem. The comparison with results in the open literature validates the remarkable accuracy of the present model for sandwich plates with moderately thick viscoelastic core, and demonstrates the importance of the higher-order variation of the transverse displacement along the thickness of the viscoelastic core for the improvement of the analysis accuracy. Moreover, the influence of the thickness and stiffness ratios of the viscoelastic core to the face layers on the damping characteristics of the viscoelastic sandwich plate is discussed.

Vibration response of viscoelastic sandwich plate with magnetorheological fluid core and functionally graded-piezoelectric nanocomposite face sheets

In this research, vibration analysis of a viscoelastic sandwich plate rested on a visco-Pasternak foundation is investigated. Sandwich plate consists of a magnetorheological (MR) fluid core and viscoelastic nanocomposite face sheets which include piezoelectric matrix and functionally graded carbon nanotubes (FG-CNTs) fiber. Core and face sheets are affected by applying magnetic and electric fields, respectively. The elastic medium is simulated by a visco-Pasternak model which is considered in terms of the effects of springiness, shear and damping of foundation. At first, the constitutive equations of sandwich plate are expressed by employing the geometric continuity conditions. Then, the equations of motion are derived by applying the energy method and Hamilton’s principle and an appropriate analytical approach is proposed to solve them. This approach can be considered as the different boundary conditions. Finally, the influences of various parameters such as the type of MR material, core to face sheets thickness ratio, volume fractions and symmetric distributions of CNTs in face sheets, magnetic and electric fields, viscoelastic constant of face sheets and elastic medium on the dimensionless natural frequencies of sandwich plate are studied. The results show that increasing core-to-face sheet thickness ratio leads to a decrease in the natural frequencies because the MR fluid core is softer than nanocomposite face sheets. Thus, the MR fluid core acts like a damper. Also, the loss factor of the MR fluid core decreases with increasing magnetic field intensity, and consequently, the natural frequency grows. In addition, increasing the volume fraction of CNTs causes the stiffness of the structure to increase. The results of this research can be utilized to realize applicable semi-active devices with controllable stiffness.