We present a quantitative method for determining the viscoelastic properties of materials with nanometer spatial resolution. The approach is based on the atomic force acoustic microscopy technique that involves the resonant frequencies of the atomic force microscopy cantilever when its tip is in contact with a sample surface. We derive expressions for the viscoelastic properties of the sample i...

Damping in air gaps is studied at RF frequencies and modelled with a viscoelastic wave propagation model, since the traditional squeezed-film damping model is not valid in the MHz regime. The FEM study shows that above a certain frequency the wave propagation in the air gap can be modelled assuming closed damper borders. This closed-border problem is solved analytically from the linearized Navi...

We present some models of viscoelastic systems with long-memory behaviour; we then provide both thorough mathematical analysis and numerical simulations of these models by means of so-called diiusive representations. The models under consideration are the basic harmonic oscillator with fractional damping, the generalized Lokshin model of waves, and also the boundary feedback control of the Eule...

A combination of stiffness and loss (the product Etan ) is desirable in damping layer and structural damping applications. Composite materials of structure which gives rise to Reuss or Hashin–Shtrikman lower bound behavior can give rise to such properties. Hierarchical particulate morphologies attain the Hashin– Shtrikman curve. We show that hierarchical composites give rise to complex Poisson’...

The effect of a complex coefficient of thermal expansion upon the thermoelastic relaxation mechanism is analyzed. A phase angle in the thermal expansion has the effect of generating a very broad band of mechanical damping, in addition to the peak usually observed. Phase angles in the thermal expansion have been observed in several polymers, and they may be generated in composite materials in wh...

In this paper we obtain an exponential rate of decay for the solution of the viscoelastic nonlinear wave equation utt −∆u+ f(x, t, u) + ∫ t 0 g(t− τ)∆u(τ) dτ + a(x)ut = 0 in Ω× (0,∞). Here the damping term a(x)ut may be null for some part of the domain Ω. By assuming that the kernel g in the memory term decays exponentially, the damping effect allows us to avoid compactness arguments and and to...

With the objective of achieving composite material systems that feature high stiffness and high mechanical damping, consideration is given here to unit cell analysis of particulate composites with high volume fraction of inclusions. Effective elastic properties of the composite are computed with computational homogenization based on unit cell analysis. The correspondence principle together with...

Linear viscoelastic structures are characterized by dissipative forces that depend on the history of the velocity response via hereditary damping functions. The free motion equation leads to a nonlinear eigenvalue problem characterized by a frequency–dependent damping matrix. In the present paper, a novel and efficient numerical method for the computation of the eigenvalues of linear and propor...

In this study, we assessed kinematics and viscoelastic features of knee joint in adults with Down syndrome (DS) by means of the Wartenberg pendulum test. This test allows the measuring of the kinematics of the knee joint during passive pendular motion of leg under the influence of gravity. In addition, by a combination of kinematic and anthropometric data, pendulum test provides estimates of jo...

*Correspondence: [email protected] School of Mathematical Sciences, Ocean University of China, Qingdao, P.R. China Abstract This work is concerned with the Dirichlet initial boundary problem for a semilinear viscoelastic wave system with nonlinear weak damping and source terms. For nonincreasing positive functions g and h, we show the finite time blow-up of some solutions whose initial data hav...