Dynamical behavior of nonlinear viscoelastic beams

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Prediction of nonlinear viscoelastic behavior of polymeric composites using an artificial neural network

Creep tests at constant stress are performed for the carbon-fiber reinforced epoxy composite at various temperatures and initial stresses. A nonlinear viscoelastic constitutive model is developed, and its material parameters are determined by fitting it to creep test data. Model results are found to agree very well with the experimental data at low temperature and low stress conditions. However, the agreement deteriorates at high temperatures, particularly in the vicinity of the glass transition temperature.An alternative model based on an artificial neural network (ANN) is developed to predict the stress relaxation of the polymer matrix composite. The ANN model is trained and validated with 9000 experimental data sets obtained from stress relaxation tests performed at various constant strain (initial stress) and constant temperature conditions. Training of the ANN employs a scaled conjugate gradient method. The optimal brain surgeon algorithm is employed to optimize the topology. The optimal ANN configuration has 88 processing elements (3 in the input layer, 45 in the first hidden layer, 39 in the second hidden layer, and 1 in the output layer) and 410 links. The predictions of the ANN model are found to be more accurate over a wider range of stress and temperature conditions than those of the explicit nonlinear viscoelastic model, in particular near the glass transition temperature.     

Bifurcation analysis of a nonlinear viscoelastic panel

The dynamic behavior of a nonlinear viscoelastic panel subjected to a simple harmonic excitation is studied. Using the Galerkin principle, the double mode model is presented in this paper. The bifurcation behavior of the panel is examined in detail in the case of internal response. The method of averaging is used to derive a set of autonomous equations. The averaged differential equations are then examined to determine their bifurcation behavior. Finally, the results of theoretical analysis are numericaly verified.     

Effective behavior of linear viscoelastic composites: A time-integration approach

A new method for determining the overall behavior of composite materials comprised of linear viscoelastic constituents is presented. Unlike classical methods which are based on the Laplace transform, the present method operates directly in the time-domain. Upon use of an implicit time-discretization scheme, the evolution equations describing the constitutive behavior of the phases can be reduced to the minimization of an incremental energy function. This minimization problem is rigorously equivalent to a linear thermoelastic problem with a transformation strain which is a nonuniform field (not even uniform within the phases). The variational technique of Ponte Castañeda is used to approximate the nonuniform eigenstrains by piecewise uniform eigenstrains. The latter problem is amenable to simpler calculations and analytical results for appropriate microstructures can be obtained. The accuracy of the proposed scheme is assessed by comparison of the method with exact results obtained either by full finite element simulations in time-domain or by available analytical results obtained by the Laplace transform.     

A hybrid approach for nonlinear computational aeroacoustics predictions

In many aeroacoustics applications involving nonlinear waves and obstructions in the far-field, approaches based on the classical acoustic analogy theory or the linearised Euler equations are unable to fully characterise the acoustic field. Therefore, computational aeroacoustics hybrid methods that incorporate nonlinear wave propagation have to be constructed. In this study, a hybrid approach coupling Navier–Stokes equations in the acoustic source region with nonlinear Euler equations in the acoustic propagation region is introduced and tested. The full Navier–Stokes equations are solved in the source region to identify the acoustic sources. The flow variables of interest are then transferred from the source region to the acoustic propagation region, where the full nonlinear Euler equations with source terms are solved. The transition between the two regions is made through a buffer zone where the flow variables are penalised via a source term added to the Euler equations. Tests were conducted on simple acoustic and vorticity disturbances, two-dimensional jets (Mach 0.9 and 2), and a three-dimensional jet (Mach 1.5), impinging on a wall. The method is proven to be effective and accurate in predicting sound pressure levels associated with the propagation of linear and nonlinear waves in the near- and far-field regions.     

A molecular network model to describe the nonlinear viscoelastic behavior of polymers

A transient molecular network model is built to describe the nonlinear viscoelasticity of polymers by considering the effect of entanglement loss and regeneration on the relaxation of molecular strands. It is an extension of previous network theories. The experimental data on three thermoplastic polymers (ABS, PVC and PA6) obtained under various loading conditions are used to test the model. Agreement between the theoretical and experimental curves shows that the suggested model can describe successfully the relaxation behavior of the thermoplastic polymers under different loading rates by using relatively few relaxation modes. Thus the micromechanism responsible for strain-rate dependence of relaxation process and the origin of nonlinear viscoelasticity may be disclosed. The project supported by the National Natural Science Foundation of China and Doctorial Fund     

Predictions of linear viscoelastic properties for polydisperse entangled polymers

Different blending laws have been proposed in the literature to describe the polydispersity effect on the rheological behavior of polymer melts. In this paper predictions of linear viscoelastic properties of entangled polydisperse polymers have been derived from the double reptation mixing rule. The results in terms of the relaxation modulus, the zero shear-rate viscosity, η₀, and the steady-state compliance, J _e ⁰, have been obtained using three different relaxation functions for the monodisperse fractions, namely the Tuminello step function, the single exponential function and the BSW function. Both discrete and continuous molecular weight distributions (MWDs) have been investigated. The Generalized Exponential Function (GEX) has been considered in the continuous case. The results showed that, in systems with a large number of components, the predictions of linear viscoelastic properties mainly depend on the double reptation mixing rule assumption, while the choice of the relaxation function is not crucial. In particular, the mathematical simplicity of the Tuminello step relaxation function has allowed analytical computation of the linear viscoelastic properties in closed form. Indeed, the analytical results indicated a dependence of η₀ on the MWD that could be expressed in terms of (M _z/M _w)^0.8, in agreement with experimental results reported in the literature. In the case of J _e ⁰, the analytical model defines a dependence on (M _z/M _w)^5.5, i.e. as expected a strong dependence on the MWD is predicted for the steady-state compliance. Finally, dynamic moduli have been computed from the relaxation modulus and their predictions have been favorably compared with experimental results from the literature. Received: 19 July 1999/Accepted: 24 November 1999     

A numerical study on drop formation of viscoelastic liquids using a nonlinear constitutive equation

In this paper, a numerical solution for viscoelastic drop formation from a nozzle into an ambient gas is presented. A volume of fluid (VOF) method is used to predict the formation and break-up process of viscoelastic drop. Here, Giesekus model is used as the constitutive equation. The major features of the phenomenon, such as instantaneous drop length, limiting length of a drop at breakup, minimum drop radius and the volume of the primary drop is determined for a range of the parameter space spanned by the appropriate dimensionless groups. The results reveal that enhancing the mobility factor, Wiessenberg number, and viscosity ratio causes a noticeable decrease in limiting drop length and a small decrease on the primary drop volume. Also, the increasing of gravitational bond number and capillary number causes the limiting drop length increases while the primary drop volume is reduced.     

On a nonlinear viscoelastic model of Hunt-Crossley impact

We consider a nonlinear viscoelastic model of the impact of a body on a stationary Hunt-Crossley obstacle. We obtain the first integral of the equation of motion and determine the coefficient of restitution, the kinetic energy lost at the impact, and their dependence on the impact velocity. We find the solution of the equation of motion of the body in terms of integrals by using the Lambert W-function and present the results of mathematical modeling.     

Propagation of nonlinear waves along a viscoelastic bar

Various types of nonlinear waves propagating along a viscoelastic bar are considered. The rheological equation of state has strong physical and geometric nonlinearities, and nonisothermal effects are included. Both weak (isentropic) and shock waves of loading and unloading are investigated. It is shown that, for certain rubber-like materials, stable shock waves of extension can exist along with the shock waves of compression at very large strains. We then consider the strike of a viscoelastic bar of finite length against a rigid obstacle. Numerical solutions to this problem illustrate the influence of stress relaxation on nonlinear wave processes. A model for sticking and bouncing off is formulated and the mass-averaged velocity of the bar at the moment when it bounces off the obstacle is calculated.     

Modeling and control of a nonlinear half-vehicle suspension system: a hybrid fuzzy logic approach

Modeling and control of vehicle suspension system are high noteworthy from safety to comfort. In this paper, an analytical nonlinear half-vehicle model which is included quadratic tire stiffness, cubic suspension stiffness, and coulomb friction is derived based on fundamental physics. A hybrid fuzzy logic approach which combines fuzzy logic and PID controllers is designed for reducing the vibration levels of passenger seat and vehicle body. Performances of designed controllers have been evaluated by numerical simulations. Comparisons with classical PID control, Fuzzy Logic Control (FLC) and Hybrid Fuzzy-PID control (HFPID) have also been provided. Results of numerical simulations are evaluated in terms of time histories of displacement and acceleration responses and ride index comparison. A good performance for the Hybrid Fuzzy-PID controller with coupled rules (HFPIDCR) is achieved in simulation studies despite the nonlinearities.     

Shock pulse attenuation in a nonlinear viscoelastic solid

Thin, one-dimensional shock pulses were generated in a nonlinear viscoelastic material (polymethyl methacrylate) by a new experimental technique. The observed pulse attenuation was compared with an approximate theory based on the viscoelastic shock amplitude equation. The central assumption of this approximate theory is that the unloading wave propagates as a simple wave. Given an initial pulse shape it is shown that the attenuation and the pulse shape at any later time are accurately approximated. The calculated attenuation in polymethyl methacrylate agreed well with the experimental results.     

Bifurcation of response of a nonlinear viscoelastic spherical membrane

The quasistatic inflation of a nonlinear viscoelastic spherical membrane by monotonically increasing pressure is considered. The deformation is assumed to be spherically symmetric. For the constitutive equation assumed, circumstances are shown to exist when the radius history must either have a jump discontinuity or bifurcate. A necessary condition for bifurcation and its dependence on material properties and radius history is analysed. Examples of bifurcation for various pressure histories are presented. Post-bifurcation branches are constructed and the possibility of secondary bifurcation is discussed.     

The effect of shear deformation on the post-buckling behavior of imperfect nonlinear viscoelastic columns

Summary The post-buckling behavior of imperfect columns made of nonlinear viscoelastic materials is investigated, taking into account the effect of shear deformation. The material is modeled according to the Leaderman representation of nonlinear viscoelasticity. Solutions are developed, within the elastica and the shear deformation theories, in order to calculate the growth in time of the total deflection. The numerical results establish the importance of the shear and the nonlinear viscoelasticity effects, and of the h/ℓ ratio in the column post-buckling behavior. Accepted for publication 11 November 1996     

Analysing dynamic deep stall recovery using a nonlinear frequency approach

Nonlinear Dynamics - Based on bifurcation theory, nonlinear frequency response analysis is a recent development in the field of flight dynamics studies. Here, we consider how this method can be...     

General decay of energy to a nonlinear viscoelastic two-dimensional beam

A viscoelastic beam in a two-dimensional space is considered with nonlinear tension. A boundary feedback is applied at the right boundary of the beam to suppress the undesirable vibration. The well-posedness of the problem is established. With the multiplier method, a uniform decay result is proven.