Global existence and uniform stability of solutions for a quasilinear viscoelastic problem

In this paper the nonlinear viscoelastic wave equation in canonical form with Dirichlet boundary condition is considered. By introducing a new functional and using the potential well method, we show that the damping induced by the viscoelastic term is enough to ensure global existence and uniform decay of solutions provided that the initial data are in some stable set. Copyright © 2006 John Wiley & Sons, Ltd.     

Effect of moisture on the viscoelastic properties of an epoxy-clay nanocomposite

The results of a complex study on the viscoelastic behavior of an epoxy-clay nanocomposite after a long-term exposure to moisture are presented. The main laws of variation in the glass-transition temperature of the nanocomposite in relation to the different content of filler and absorbed moisture were determined by using a thermomechanical analysis. The loading levels in creep experiments were chosen according to the results of quasi-static tensile tests. The sets of creep and creep recovery curves obtained were approximated by the Boltzmann–Volterra linear integral equation with account of the principle of moisture-time analogy. The variation in the spectrum of retardation time of the epoxy resin with introduction of the nanofiller was estimated. It is shown that the moisture-time reduction function correlates with changes in the forced rubber-like elasticity and the volume of nanocomposite specimens upon their moistening.     

A note on the polynomial decay of a weakly dissipative viscoelastic system

In this note we study an abstract class of weakly dissipative second-order systems with finite memory. We establish the polynomial decay of Rivera, Naso and Vegni for the solution of the system under a very weak condition on the relaxation function.     

Polynomial stability without polynomial decay of the relaxation function

We consider a linear viscoelastic problem and prove polynomial asymptotic stability of the steady state. This work improves previous works where it is proved that polynomial decay of solutions to the equilibrium state occurs provided that the relaxation function itself is polynomially decaying to zero. In this paper we will not assume any decay rate of the relaxation function. In case the kernel has some flat zones then we prove polynomial decay of solutions provided that these flat zones are not too big. If the kernel is strictly decreasing then there is no need for this assumption. Copyright © 2008 John Wiley & Sons, Ltd.     

Control and exponential stabilization for the equation of an axially moving viscoelastic strip

The aim through this work is to suppress the transverse vibrations of an axially moving viscoelastic strip. A controller mechanism (dynamic actuator) is attached at the right boundary to control the undesirable vibrations. The moving strip is modeled as a moving beam pulled at a constant speed through 2 eyelets. The left eyelet is fixed in the sense that there is no transverse displacement (see Figure 1 ). The mathematical model of this system consists of an integro‐partial differential equation describing the dynamic of the strip and an integro‐differential equation describing the dynamic of the actuator. The multiplier method is used to design a boundary control law ensuring an exponential stabilization result.     

Control of a viscoelastic translational Euler–Bernoulli beam

In this paper, we study a cantilevered Euler–Bernoulli beam fixed to a base in a translational motion at one end and to a tip mass at its free end. The beam is subject to undesirable vibrations, and it is made of a viscoelastic material that permits a certain weak damping. By applying a control force at the base, we shall attenuate these vibrations in a fast manner. In fact, we establish the exponential stability of the system. Our method is based on the multiplier technique. Copyright © 2016 John Wiley & Sons, Ltd.     

Similarity to an isometry of a composition operator

We study the composition operators which are similar to an isometry on the classical Hardy space .

     

Effect of small additives of oligomer on the viscoelastic properties of carbon fiber plastics

The viscoelastic properties of carbon fiber composites whose phenol-formaldehyde matrix is modified by thermodynamically incompatible isocyanate derivatives have been investigated. Data are given on fiber wetting (Table 11), internal stress (Table 2), viscoelastic properties (Fig. 1), and tensile strength (Fig. 2). The modified composites are strengthened by the addition of 0.5–4% oligomer additive. This process involves the formation of a two-phase structure, in which the additive phase microparticles act as a polymer filler. Due to selective interactions, the intermediate layer formed at the fiber-binder interface leads to changes in the viscoelastic properties and tensile strength of the matrix and improved maintenance characteristics for the material as a whole.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 4, pp. 440–445, July–August, 1993.     

Limiting properties of the occurrence/exposure rate and simple risk rate

In this paper, we study the asymptotic distributions of the functions of the occurrence/exposure rates of several groups of patients as well as Berry-Esseen bound on the distribution function of the occurrence/exposure rate. Asymptotic distributions of functions of the simple risk rates are also derived. The results are useful in not only medical research but also in the area of reliability.The work of the first two authors was supported by Contract F49620-C5-C-0008 of the Air Force Office of Scientific Research. The United States Government is authorized to reproduce and distribute reprints for governmental purposes.     

Probabilistic properties of the dual structure of the multidimensional knapsack problem and fast statistically efficient algorithms

Properties of several dual characteristics of the multidimensional knapsack problem (such as the probability of existence of-optimal and optimal-feasible Lagrange function generalized saddle points, magnitude of relative duality gap, etc.) are investigated for different probabilistic models. Sufficient conditions of good asymptotic behavior of the dual characteristics are given. A fast statistically efficient approximate algorithm with linear running time complexity for problems with random coefficients is presented.This paper was written when the author was affiliated with Chelyabinsk State Technical University and the Moscow Physical and Technical Institute, Russia.     

Approximation of Subharmonic Functions in the Half-Plane by the Logarithm of the Modulus of an Analytic Function

We approximate subharmonic functions defined in the open half-plane in the uniform metric outside the exceptional set by the logarithm of the modulus of an analytic (in the half-plane) function for the cases of a finite order and of an infinite lower order. We also obtain an estimate for the size of the exceptional set. It is shown that, in the case of a finite order, the obtained accuracy of the approximation cannot be essentially improved.     

Effect of age on the mechanical properties and biochemical composition of human cardiac arteries

Conclusions 1. The human left coronary arterial wall in subjects from age 15 to 28 has better deformative properties than the right artery.2. With increasing age, a worsening of mechanical properties of the walls is observed specifically for the left coronary artery in comparison with the right coronary artery.3. Quantitative biochemical analysis of the major components of the connective tissue of the human coronary arteries (fibrillar and nonfibrillar proteins and glycoproteins) also disclosed differences among the age groups and the position of the artery (left or right).4. As a result of a dispersion analysis carried out by computer, it was found that both age and position of the artery have a significant effect on the elastin content in the arterial wall and only the age of the subject has a significant effect on the contents of collagen, tyrosine, and hexuronic acids.5. Neither age nor type of artery have a significant effect on the contents of arginine, hexosamines, and hexoses in the arterial wall.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Riga Scientific-Research Institute of Traumatology and Orthopedics. Translated from Mekhanika Polimerov, No. 3, pp. 502–506, May–June, 1978.     

Stress Intensity Factors near the Cracks on the Edges of Openings in Composite Plates

Based on the photoelasticity method, the behavior of stress intensity factors (SIFs) near cracks propagating from the edges of openings in plates made of elastic and linearly viscoelastic fibrous composite materials is studied. It is found that the relative value of the SIF, K ₁/K ₁ ⁰ (K ₁ ⁰=₀c), near the crack tips on the edges of openings in composite plates is a function of the ratio c/R, whose numerical values depend on the mechanical properties of materials of the plates. Using the quasi-elastic method for solving the viscoelastic problems, the effect of viscoelastic properties of the plate material on the value of K ₁/K ₁ ⁰ is estimated. It is shown that the values of the function K ₁(t)/>/K ₁ ⁰ near the cracks on the opening edges in plates made of linearly viscoelastic fibrous composites grow under creep.     

Exponential decay of solution to the viscoelastic porous‐thermoelastic system of type III with boundary time‐varying delay

In this paper, we are concerned with a one‐dimensional porous‐thermoelastic system of type III with a viscoelastic damping and boundary time‐varying delay. Under suitable assumptions on relaxation function and time delay, we establish the exponential decay result of the system in which the damping is strong enough to stabilize the thermoelastic system in the presence of time delay. Copyright © 2015 John Wiley & Sons, Ltd.