Numerical simulations of the frequency modulation atomic force microscope, including the whole dynamical regulation by the electronics, show that the cantilever dynamics is conditionally stable and that there is a direct link between the frequency shift and the conservative tip-sample interaction. However, a soft coupling between the electronics and the nonlinearity of the interaction may signi...

In this paper, we present efficient, unconditionally stable and accurate numerical methods for approximations of the Klein–Gordon–Schrödinger (KGS) equations with/without damping terms. The key features of our methods are based on: (i) the application of a time-splitting spectral discretization for a Schrödinger-type equation in KGS, (ii) the utilization of Fourier pseudospectral discretization...

We describe a conservative numerical scheme with the property of uniform exponential decay for the critical case of the Generalized Korteweg-de Vrie equation (p = 4), with damping.

Damping material is usually applied on the steel panel of a vehicle to reduce vibration level. On the other hand, the weight reduction is also required to improve fuel consumption. Therefore, modal loss factors induced by damping material on the steel panel of a vehicle body structure need to be maximized with a given volume. In this paper we propose a practical design method to maximize modal ...

This paper introduces the semi-analytical and nite element models implemented to study a Falling Weight De ectometer test conducted on a exible pavement. These dynamic models take into account the e ects of both Rayleigh damping in soil and viscous damping in bituminous materials, with respect to temperature, on structural de ection. Moreover, numerical results have been compared with in situ m...

In this study the dynamic behaviour of perforated microplates oscillating under the effect of squeeze film damping is analyzed. A numerical approach is adopted to predict the effects of damping and stiffness transferred from the surrounding ambient air to oscillating structures; the effect of hole’s cross section and plate’s extension is observed. Results obtained by F.E.M. models are compared ...

Numerical methods for solving weakly damped Hamiltonian systems are constructed using the popular Störmer-Verlet and implicit midpoint methods. Each method is shown to preserve dissipation of symplecticity and dissipation of angular momentum of an N -body system with pairwise distance dependent interactions. Necessary and sufficient conditions for second order accuracy are derived. Analysis for...

In this article thermoelastic damping in nano-beam resonators is investigated based on nonlocal theory of elasticity and the Euler-Bernoulli beam assumptions. The governing equation of deflection of the beam is obtained from shear and moment resultants and stress–strain relationship of the nonlocal elasticity model and also the governing equations of thermoelastic damping are established by usi...

In this study the dynamic behaviour of perforated microplates oscillating under the effect of squeeze film damping is analyzed. A numerical approach is adopted to predict the effects of damping and stiffness transferred from the surrounding ambient air to oscillating structures; the effect of hole’s cross section and plate’s extension is observed. Results obtained by F.E.M. models are compared ...

A simple linear smoothing operator of general order p is constructed for discretized functions. It is particularly suited for problems in numerical integration where it is necessary or desirable to suppress two-grid-interval waves. The operator is ideal in the sense that for the class of damping operators of order p, which remove two-gridinterval waves without changing the phase of any wave com...