Related papers: Phase resonance nonlinear modes of mechanical syst…
Inspired by concepts developed for fermionic systems in the framework of condensed matter physics, topology and topological states are recently being explored also in bosonic systems. The possibility of engineering systems with…
In this study we consider the Hamiltonian approach for the construction of a map for a system with nonlinear resonant interaction, including phase trapping and phase bunching effects. We derive basic equations for a single resonant…
This is a part of an overview of my early studies on nonlinear spin-phonon dynamics in solid state optical-wavelength phonon lasers (phasers) started in 1984. The main goal of this work is a short description and a qualitative analysis of…
Broad-area semiconductor lasers are employed in many high-power applications, however, their spatio-temporal dynamics is complex and intrinsically unstable due to the interaction of several transverse lasing modes. A dynamical and…
This paper considers nonlinear dynamics of plasma oscillations modeled by a forced modified Van der Pol-Duffing oscillator. These plasma oscillations are described by a nonlinear differential equation of the form $ \ddot{x}+ \epsilon (1…
Floquet topological phases emerge when systems are periodically driven out-of-equilibrium. They gained attention due to their external control, which allows to simulate a wide variety of static systems by just tuning the external field in…
While resonant modes do not exist within band gaps in infinite periodic materials, they may appear as in-gap localized edge modes once the material is truncated to form a finite periodic structure. Here, we provide an analysis framework…
This paper considers the dynamic response of a single degree of freedom system with nonlinear stiffness and nonlinear damping that is subjected to both resonant direct excitation and resonant parametric excitation, with a general phase…
We present direct observation of the ring-down dynamics in the rotating frame of a resonantly driven single-mode nonlinear nanomechanical resonator. An additional close to resonance harmonic force excites nonlinear oscillations about the…
New, fundamental resonant properties of laser resonators are theoretically predicted and experimentally demonstrated. These resonances occur either in the time dependence of the beam width and that of beam radius of curvature of the…
The invariance principle, through which the steady-state behavior of nonlinear systems was introduced by Isidori and Byrnes, is leveraged in this article to bring forth a unifying characterization of the frequency response of nonlinear…
A study of the non linear modes of a two degree of freedom mechanical system with bilateral elastic stop is considered. The issue related to the non-smoothness of the impact force is handled through a regularization technique. In order to…
The increasing penetration of renewable energy sources, characterised by low inertia and intermittent disturbances, presents substantial challenges to power system stability. As critical indicators of system stability, frequency dynamics…
The statistical behavior of a nonlinear system described by a mapping with phase rotation is studied. We use the Kolmogorov-Chapman equations for the multi-time probability distribution functions for investigation of dynamics under the…
The concept of nonlinear modes is applied in order to analyze the behavior of a model of woodwind reed instruments. Using a modal expansion of the impedance of the instrument, and by projecting the equation for the acoustic pressure on the…
Mechanical resonators are widely used as precision clocks and sensitive detectors that rely on the stability of their eigenfrequencies. The phase noise is determined by different factors ranging from thermal noise and frequency noise of the…
We consider two cantilevered beams undergoing frictional impacts at the free end. The beams are designed to be of similar geometry so that they have distinct but close natural frequencies. Under harmonic base excitation near the primary…
We present a method to stabilize the frequency of self-sustained vibrations in micro- and nanomechanical resonators. The method refers to a two-mode system with the vibrations at significantly different frequencies. The signal from one mode…
The resonance frequency of ultra-thin layered two-dimensional (2D) materials changes nonlinearly with the tension induced by the pressure from the surrounding gas. Although the dynamics of pressurized 2D material membranes have been…
We introduce a new method for reducing phase noise in oscillators, thereby improving their frequency precision. The noise reduction device consists of a pair of coupled nonlinear resonating elements that are driven parametrically by the…