Related papers: On Periodical Damping Ratio of a Controlled Dynami…
Summary: A system of autonomous ordinary differential equations depending on a small parameter is considered such that the unperturbed system has an invariant manifold of periodic solutions that is not normally hyperbolic but is normally…
The periodically driven harmonic oscillator with damping is one of the most elementary and trusted models in physics and normally applied in its steady state, disregarding specific initial conditions and associated transients. For example,…
This work analyses the dynamical properties of periodically-driven band models. Focusing on the case of Bose-Einstein condensates, and using a meanfield approach to treat inter-particle collisions, we identify the origin of dynamical…
In this study, we investigated the dynamics of a droplet impacting and oscillating a polycarbonate cantilever beam of nine varying lengths. We analyzed the cantilever's damping and vibration frequency in relation to a resonance length,…
Teaching by direct models in science has been weakening the learning process of the students, because the real problems in engineering are not solved by direct models instead commonly they are solved by inverse models. On the other hand,…
We develop a computational method for evaluating the damping of vibrational modes in mono-atomic metallic chains suspended between bulk crystals under external strain. The damping is due to the coupling between the chain and contact modes…
We show that the dipole, a system usually proposed to model relaxation phenomena, exhibits a maximum in the signal-to-noise ratio at a non-zero noise level, thus indicating the appearance of stochastic resonance. The phenomenon occurs in…
The characterization and monitoring of buildings is an issue that has attracted the interest of many sectors over the last two decades. With the increasing use of permanent, continuous and real-time networks, ambient vibrations can provide…
Dynamic Mode Decomposition (DMD) is a model-order reduction approach, whereby spatial modes of fixed temporal frequencies are extracted from numerical or experimental data sets. The DMD low-rank or reduced operator is typically obtained by…
This paper aims to improve existing results about using averaging method for analysis of dynamic systems on time scales. We obtain a more accurate estimate for proximity between solutions of original and averaged systems regarding…
The phenomenon of stochastic resonance (SR) is known to occur mostly in bistable systems. However, the question of occurrence of SR in periodic potential systems is not conclusively resolved. Our present numerical work shows that the…
We study the robustness of system estimation to parametric perturbations in system dynamics and initial conditions. We define the problem of sensitivity-based parametric uncertainty quantification in dynamical system estimation. The main…
We propose a mechanism which produces periodic variations of the degree of predictability in dynamical systems. It is shown that even in the absence of noise when the control parameter changes periodically in time, below and above the…
Small amplitude oscillations are a commonly observed feature in prominences/filaments. These oscillations appear to be of local nature, are associated to the fine structure of prominence plasmas, and simultaneous flows and counterflows are…
The long-term mean-field dynamics of coupled underdamped Duffing oscillators driven by an external periodic signal with Gaussian noise is investigated. A Boltzmann-type H-theorem is proved for the associated nonlinear Fokker-Planck equation…
The steady state motion of a folded pendulum has been studied using frequencies of drive that are mainly below the natural (resonance) frequency of the instrument. Although the free-decay of this mechanical oscillator appears textbook…
We present a class of systems for which the signal-to-noise ratio always increases when increasing the noise and diverges at infinite noise level. This new phenomenon is a direct consequence of the existence of a scaling law for the…
Using the damped pendulum system we introduce the averaging method to study the periodic solutions of a dynamical system with small perturbation. We provide sufficient conditions for the existence of periodic solutions with small amplitude…
A novel probabilistic approach for the design of mechanical structures with friction interfaces is proposed. The objective function is defined as the probability that a specified performance measure of the forced vibration response is…
The Brownian dynamics of an optically trapped water droplet are investigated across the transition from over to under-damped oscillations. The spectrum of position fluctuations evolves from a Lorentzian shape typical of over-damped systems…