Related papers: Vibrational resonance: a study with high-order wor…
We show that, for appropriate combinations of the values of the delay and the forcing frequency, it is possible to obtain easily high-order averaged versions of periodically forced systems of delay differential equations with constant…
Over the past two decades, vibrational resonance has garnered significant interest and evolved into a prominent research field. Classical vibrational resonance examines the response of a nonlinear system excited by two signals: a weak,…
The averaging method is a classical powerful tool in perturbation theory of dynamical systems. There are two major obstacles to applying the averaging method, resonances and separatrices. In this paper we obtain realistic asymptotic…
The dynamical analysis of vibrational systems of masses interconnected by restitution elements each with a single degree of freedom, and different configurations between masses and spring constants, is presented. Finite circular and linear…
We introduce a higher order phase averaging method for nonlinear oscillatory systems. Phase averaging is a technique to filter fast motions from the dynamics whilst still accounting for their effect on the slow dynamics. Phase averaging is…
We develop a rigorously controlled multi-time scale averaging technique; the averaging is done on a finite time interval, properly chosen, and then, via iterations and normal form transformations, the time intervals are scaled to arbitrary…
The long time effect of nonlinear perturbation to oscillatory linear systems can be characterized by the averaging method, and we consider first-order averaging for its simplest applicability to high-dimensional problems. Instead of the…
Vibrational resonance focuses on the resonance behavior of a nonlinear system when it is subjected to both a weak low-frequency characteristic signal and a high-frequency auxiliary signal. A traditional Duffing system has a fixed natural…
Vibration and dissipation in vibro-acoustic systems can be assessed using frequency response analysis. Evaluating a frequency sweep on a full-order model can be very costly, so model order reduction methods are employed to compute…
There are many problems that lead to analysis of dynamical systems in which one can distinguish motions of two types: slow one and fast one. An averaging over fast motion is used for approximate description of the slow motion. First…
In this paper we propose a multiscale method for the acoustic wave equation in highly oscillatory media. We use a higher-order extension of the localized orthogonal decomposition method combined with a higher-order time stepping scheme and…
We consider {\it small solutions} of a vibrating system with smooth non-linearities for which we provide an approximate solution by using a double scale analysis; a rigorous proof of convergence of a double scale expansion is included; for…
The stability of dynamical systems with oscillatory behaviors and well-defined average vector fields has traditionally been studied using averaging theory. These tools have also been applied to hybrid dynamical systems, which combine…
The mathematical model of a real flexible elastic system with distributed and discrete parameters is considered. It is a partial differential equation with non-classical boundary conditions. Complexity of the boundary conditions results in…
This work was developed aiming to employ Statistical techniques to the field of Music Emotion Recognition, a well-recognized area within the Signal Processing world, but hardly explored from the statistical point of view. Here, we opened…
The phenomenon of sequential vibrational resonance existed in a multistable system that is excited by both high- and low-frequency signals is reported. By the method of direct separation of motions, the theoretical investigation on…
The paper presents a new study method of mechanic vibrations with the help of the data acquisition systems. The study of vibrations with the help of data acquisition systems allows the solving of some engineering problems connected to the…
This article focuses on the prediction of the vibration frequency response of handheld probes. A novel approach that involves machine learning and readily available data from probes was explored. Vibration probes are efficient and…
We propose a method for variable selection and basis learning for high-dimensional classification with ordinal responses. The proposed method extends sparse multiclass linear discriminant analysis, with the aim of identifying not only the…
Many multi-planet systems have been discovered in recent years. Some of them are in mean-motion resonances (MMR). Planet formation theory was successful in explaining the formation of 2:1, 3:1 and other low resonances as a result of…