Analysis of a quasistatic contact problem with adhesion and nonlocal friction for viscoelastic materials

A mathematical model is established to describe a contact problem between a deformable body and a foundation. The contact is bilateral and modelled with a nonlocal friction law, in which adhesion is taken into account. Evolution of the bonding field is described by a first-order differential equation. The materials behavior is modelled with a nonlinear viscoelastic constitutive law. A variational formulation of the mechanical problem is derived, and the existence and uniqueness of the weak solution can be proven if the coefficient of friction is sufficiently small. The proof is based on arguments of time-dependent variational inequalities, differential equations, and the Banach fixed-point theorem.

An Optimum Analysis Method of Sandwich Structures Made from Elastic-viscoelastic Materials

Due to a viscoelastic damping middle layer,sandwich structures have the capacity of energy consumption.In this paper,we describe the frequency-dependent property of viscoelastic materials using complex modulus model,and iterative modal strain energy method and iterative complex eigenvalue method are presented to obtain frequency and loss factor of sandwich structures.The two methods are effective and exact for the large-scale complex composite sandwich structures.Then an optimum analysis method is suggested to apply to sandwich structures.Finally,as an example,an optimum analysis of a clamped-clamped sandwich beams is conducted,theoretical closed-form solution and numerical predictions are studied comparatively,and the results agree well.

Application of Viscoelastic Materials in Ship Collision

With the expansion of global trade routes,ship collision has become a major problem.This article proposes an approach by laying viscoelastic material on the inner side of the ship to increase the crashworthiness.By using the nonlinear finite element model software,this study simulates ship collisions as well as models and analyzes ships along with viscoelastic materials.The results from the simulation suggest that viscoelastic materials can effectively protect ships during collisions.

Generalized Rayleigh Wave Dispersion in a Covered Half-space Made of Viscoelastic Materials

Dispersion of the generalized Rayleigh waves propagating in a covered halfspace made of viscoelastic materials is investigated by utilizing the exact equations of the theory of linear viscoelasticity.The dispersion equation is obtained for an arbitrary type of hereditary operator of the materials of the constituents and a solution algorithm is developed for obtaining numerical results on the dispersion of the waves under consideration.Dispersion curves are presented for certain attenuation cases and the influence of the viscosity of the materials is studied through three rheological parameters of the viscoelastic materials which characterize the characteristic creep time,long-term values and the mechanical behaviour of the viscoelastic material around the initial state of the deformation.Numerical results are presented and discussed for the case where the viscoelasticity of the materials is described through fractional-exponential operators by Rabotnov.As the result of this discussion,in particular,how the rheological parameters influence the dispersion of the generalized Rayleigh waves propagating in the covered half-space under consideration is established.

Dispersion of Axisymmetric Longitudinal Waves in A Bi-Material Compound Solid Cylinder Made of Viscoelastic Materials

The paper studies the dispersion of axisymmetric longitudinal waves in the bi-material compound circular cylinder made of linear viscoelastic materials.The investigations are carried out within the scope of the piecewise homogeneous body model by utilizing the exact equations of linear viscoelasto-dynamics.The corresponding dispersion equation is derived for an arbitrary type of hereditary operator and the algorithm is developed for its numerical solution.Concrete numerical results are obtained for the case where the relations of the constituents of the cylinder are described through fractional exponential operators.The influence of the viscosity of the materials of the compound cylinder on the wave dispersion is studied through the rheological parameters which indicate the characteristic creep time and long-term values of the elastic constants of these materials.Dispersion curves are presented for certain selected dispersive and non-dispersive attenuation cases under various values of the problem parameters and the influence of the aforementioned rheological parameters on these curves is discussed.As a result of the numerical investigations,in particular,it is established that in the case where the rheological parameters of the components of the compound cylinder are the same,the viscosity of the layers’materials causes the axisymmetric wave propagation velocity to decrease.

Modelling and predicting the dynamic response of an axially graded viscoelastic core sandwich beam

The present study explored the influence of axial gradation of viscoelastic materials on the dynamic response of the sandwich beam for structural applications.The finite element(FE)formulations are used to model and investigate dynamic response of the sandwich beam.The classical beam theory is used to develop the FE formulations and Lagrange's approach is considered to obtain the equations of motion(EOM).FE code is developed and validated with the existing literature and also conducted the convergence study for the developed FE method.Further,the influence of different viscoelastic materials and boundary conditions on the dynamic response of the sandwich beam is investigated.Four different axial gradation configurations of viscoelastic materials are considered for the present work to explore the influence on natural frequency,loss factor and frequency response of the sandwich beam.The modeled axial gradation of viscoelastic material has displayed a considerable impact on the peak vibrational amplitude response of the sandwich beam for all the boundary conditions and these configurations improved the damping capabilities at different configurations for the structural applications.

GENERALIZED VARIATIONAL PRINCIPLES FOR VISCOELASTIC THIN AND THICK PLATES WITH DAMAGE

From the constitutive model with generalized force fields for a viscoelastic body with damage, the differential equations of motion for thin and thick plates with damage are derived under arbitrary boundary conditions. The convolution-type functionals for the bending of viscoelastic thin and thick plates with damage are presented, and the corresponding generalized variational principles are given. From these generalized principles, all the basic equations of the displacement and damage variables and initial and boundary conditions can be deduced. As an example, we compare the difference between the dynamical properties of plates with and without damage and consider the effect of damage on the dynamical properties of plates.

A theoretical model for impact protection of flexible polymer material

The relationship between the protective performance of flexible polymer material and material parameters(elasticmodulus,viscosity coefficient)is explored,an impact collision motion equation between two bodies is establishedfrom the viscoelastic material constitutive,and the relationship between the kinematic response and the materialparameters is obtained.Based on the Kelvin constitutive model,a theoretical model for impact between the pro-tective body and the protected body is established,then the dynamic response is obtained.The feasibility of themodel was verified by drop hammer experiment,and the material parameters(elastic modulus,viscosity coeffi-cient)were obtained by formula.The model is discretized and the relationship between local impact response andmaterial parameters is analyzed.The discussion results on the relationship between the impact response and theprotective material performance indicate that adjusting the elastic modulus,viscosity coefficient,and thicknessof the protective material can effectively improve protective effect.

Application of Viscoelastic Material in Structures Control

The factors influencing mechanical performances of viscoelastic material are studied.The proper finite element model for dynamical calculating the passive control of wind-earthquake resistance is constructed.A combined element stiffness matrix of damper-brace system is deduced.At last,the theoretical deduction is verified by comparing the theoretical results with experimental ones.

Accurate and straightforward symplectic approach for fracture analysis of fractional viscoelastic media

An accurate and straightforward symplectic method is presented for the fracture analysis of fractional two-dimensional(2D)viscoelastic media.The fractional Kelvin-Zener constitutive model is used to describe the time-dependent behavior of viscoelastic materials.Within the framework of symplectic elasticity,the governing equations in the Hamiltonian form for the frequency domain(s-domain)can be directly and rigorously calculated.In the s-domain,the analytical solutions of the displacement and stress fields are constructed by superposing the symplectic eigensolutions without any trial function,and the explicit expressions of the intensity factors and J-integral are derived simultaneously.Comparison studies are provided to validate the accuracy and effectiveness of the present solutions.A detailed analysis is made to reveal the effects of viscoelastic parameters and applied loads on the intensity factors and J-integral.

Nonlinear Dynamic Analysis of A Viscoelastic Pipe Conveying Fluid

Incremental harmonic balance method (IHBM) is applied to geometrically nonlinear vibration analysis of a simply supported pipe conveying fluid. the material of which is viscoelastic of the Kelvin- Voigt type. Some unstable phenomena - the appearance of the peak or jumps in the pipe's amplitude frequency curves, which are considered to be of importance to this kind of structure, are presented in the numerical results, and the influence of several parameters of the system on the dynamic characteristic of the pipe are also studied. It is believed that this is the first attempt to search for the periodic solution of the pipe and its intrinsic property with such a method.

Thermomagnetic viscoelastic responses in a functionally graded hollow structure

This paper presents an analytical solution for the interaction of electric potentials, electric displacements, elastic deformations, and thermoelasticity, and describes electromagnetoelastic responses and perturbation of the magnetic field vector in hollow structures （cylinder or sphere）, subjected to mechanical load and electric potential. The material properties, thermal expansion coefficient and magnetic permeability of the structure are assumed to be graded in the radial direction by a power law distribution. In the present model we consider the solution for the case of a hollow structure made of viscoelastic isotropic material, reinforced by elastic isotropic fibers, this material is considered as structurally anisotropic material. The exact solutions for stresses and perturbations of the magnetic field vector in FGM hollow structures are determined using the infinitesimal theory of magnetothermoelasticity, and then the hollow structure model with viscoelastic material is solved using the correspondence principle and Illyushin＇s approximation method. Finally, numerical results are carried out and discussed.

THE MODAL FEATURES OF THE VIBRATION SYSTEMS OF THE WEAKLY- VISCOELASTIC MATERIAL STRUCTURES

This paper discusses the modal features of weakly-viscoelastic material structures both for single-modulus and multi-modulus materials. It is the eigenvalues of these structures that are the roots of a series of rational fraction polynomial equations. A theorem about the roots of these equations is proved in the paper. Based on it, some important conclusions about the modal features of the weakly viscoelastic material structures are given according to their dynamic behaviors.

Dynamic responses of an energy harvesting system based on piezoelectric and electromagnetic mechanisms under colored noise

Because of the increasing demand for electrical energy,vibration energy harvesters(VEHs)that convert vibratory energy into electrical energy are a promising technology.In order to improve the efficiency of harvesting energy from environmental vibration,here we investigate a hybrid VEH.Unlike previous studies,this article analyzes the stochastic responses of the hybrid piezoelectric and electromagnetic energy harvesting system with viscoelastic material under narrow-band(colored)noise.Firstly,a mass-spring-damping system model coupled with piezoelectric and electromagnetic circuits under fundamental acceleration excitation is established,and analytical solutions to the dimensionless equations are derived.Then,the formula of the amplitude-frequency responses in the deterministic case and the first-order and secondorder steady-state moments of the amplitude in the stochastic case are obtained by using the multi-scales method.The amplitude-frequency analytical solutions are in good agreement with the numerical solutions obtained by the Monte Carlo method.Furthermore,the stochastic bifurcation diagram is plotted for the first-order steady-state moment of the amplitude with respect to the detuning frequency and viscoelastic parameter.Eventually,the influence of system parameters on mean-square electric voltage,mean-square electric current and mean output power is discussed.Results show that the electromechanical coupling coefficients,random excitation and viscoelastic parameter have a positive effect on the output power of the system.

Performance evaluation of a novel rotational damper for structural reinforcement steel frames subjected to lateral excitations

In this study,a novel rotational damper called a Rotational Friction Viscoelastic Damper(RFVD) is introduced.Some viscoelastic pads are added to the Rotational Friction Damper(RFD) in addition to the friction discs used in this conventional device.Consequently,the amount of energy dissipated by the damper increases in low excitation frequencies.In fact,the input energy to the structure is simultaneously dissipated in the form of friction and heat by frictional discs and viscoelastic pads.In order to compare the performance of this novel damper with the earlier types,a set of experiments were carried out.According to the test results,the RFVD showed a better performance in dissipating input energy to the structure when compared to the RFD.The seismic behavior of steel frames equipped with these dampers was also numerically evaluated based on a nonlinear time history analysis.The numerical results verifi ed the performance of the dampers in increasing the energy dissipation and decreasing the energy input to the structural elements.In order to achieve the maximum dissipated energy,the dampers need to be installed in certain places called critical points in the structure.An appropriate approach is presented to properly fi nd these points.Finally,the performance of the RFVDs installed at these critical points was investigated in comparison to some other confi gurations and the validity of the suggested method in increasing the energy dissipation was confi rmed.

Free vibration of circular cylindrical shell with constrained layer damping

Free vibration characteristics of circular cylindrical shell with passive constrained layer damping （PCLD）are presented. Wave propagation approach rather than finite element method, transfer matrix method, and Rayleigh-Ritz method is used to solve the problem of vibration of PCLD circular cylindrical shell under a simply supported boundary condition at two ends. The governing equations of motion for the orthotropic cylindrical shell with PCLD are derived on the base of Sanders＇ thin shell theory. Nu- merical results show that the present method is more effective in comparison with other methods. The effects of the thickness of viscoelastic core and constrained layer, the elastic modulus ratio of orthotropic constrained layer, the complex shear modulus of viscoelastic core on frequency parameter, and the loss factor are discussed.

Nonlinear dynamic characteristics of piles embedded in rock

The nonlinear dynamic characteristics of a pile embedded in a rock were investigated. Suppose that both the materials of the pile and the soil around the pile obey nonlinear elastic and linear viscoelastic constitutive relations. The nonlinear partial differential equation governing the dynamic characteristics of the pile was first derived. The Galerkin method was used to simplify the equation and to obtain a nonlinear ordinary differential equation. The methods in nonlinear dynamics were employed to solve the simplified dynamical system, and the time-path curves, phase-trajectory diagrams, power spectrum, Poincare sections and bifurcation and chaos diagrams of the motion of the pile were obtained. The effects of parameters on the dynamic characteristics of the system were also considered in detail.

ANALYSIS OF AN ELASTO-PIEZOELECTRIC SYSTEM OF HEMIVARIATIONAL INEQUALITIES WITH THERMAL EFFECTS

In this paper we prove the existence and uniqueness of a weak solution for a dynamic electo-viscoetastic problem that describes a contact between a body and a foundation. We assume the body is made from thermoviscoelastic material and consider nonmonotone boundary conditions for the contact. We use recent results from the theory of hemivariational inequalities and the fixed point theory.

Numerical Analysis of a Sliding Frictional Contact Problem with Normal Compliance and Unilateral Contact

This paper represents a continuation of [1] and [2]. Here, we consider the numerical analysis of a non-trivial frictional contact problem in a form of a system of evolution nonlinear partial differential equations. The model describes the equilibrium of a viscoelastic body in sliding contact with a moving foundation. The contact is modeled with a multivalued normal compliance condition with memory term restricted by a unilateral constraint and is associated with a sliding version of Coulomb’s law of dry friction. After a description of the model and some assumptions, we derive a variational formulation of the problem, which consists of a system coupling a variational inequality for the displacement field and a nonlinear equation for the stress field. Then, we introduce a fully discrete scheme for the numerical approximation of the sliding contact problem. Under certain solution regularity assumptions, we derive an optimal order error estimate and we provide numerical validation of this result by considering some numerical simulations in the study of a two-dimensional problem.

Forced vibration of smart laminated viscoelastic plates by RPT finite element approach

In this study,a finite element formulation based on the four-variable refined plate theory(RPT)is presented for forced vibration analysis of laminated viscoelastic composite plates integrated with a piezoelectric layer.To the best of the authors’knowledge,this is the first time that the proposed approach is extended for study of the dynamic behavior of the smart viscoelastic plate.The utilized RPT which works for both thick and thin plates predicts a parabolic variation for transverse shear stresses across the plate thickness.Considering a linear viscoelastic model for the substrate material,the relaxation module is predicted by the Prony series.Using Hamilton’s principle,the weak form equation is constructed and a four-node rectangular plate element is utilized for discretizing the domain.The Newmark scheme is employed for advancing the solution in time.A MATLAB code is developed based on the formulations and several benchmark problems are solved.Comparing the findings with existing results in previous studies confirms the accuracy and efficiency of the proposed method.The dynamic response of the smart viscoelastic plates under various electromechanical loads is investigated and the results show that the.vibration can be passively controlled by adding and actuating the piezoelectric layer.The damping effects of viscoelastic parameters on the results are investigated,too.