Related papers: On Periodical Damping Ratio of a Controlled Dynami…
Nonlinear dynamics plays a significant role in interdisciplinary fields spanning biology, engineering, mathematics, and physics. Under small-amplitude approximations, certain nonlinear systems can be effectively described by the linear…
The phase reduction technique is essential for studying rhythmic phenomena across various scientific fields. It allows the complex dynamics of high-dimensional oscillatory systems to be expressed by a single phase variable. This paper…
Vibrational structures are susceptible to catastrophic failures or structural damages when external forces induce resonances or repeated unwanted oscillations. One common mitigation strategy is to use dampers to suppress these disturbances.…
Inertia amplification is a mechanism coupling degrees of freedom within a vibrating structure. Its goal is to achieve an apparent high dynamic mass and, accordingly, a low resonance frequency. Such structures have been described for use in…
The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level the system undergoes ordering transitions and demonstrates…
If a contact of two purely elastic bodies with no sliding (infinite coefficient of friction) is subjected to superimposed oscillations in the normal and tangential directions, then a specific damping appears, that is not dependent on…
We consider an optimization problem related to semi-active damping of vibrating systems. The main problem is to determine the best damping matrix able to minimize influence of the input on the output of the system. We use a minimization…
A discrete time control algorithm using the damped least squares is introduced for acceleration and energy exchange controls in nonlinear vibrating systems. It is shown that the damping constant of least squares and sampling time step of…
Damping is defined through various terms such as energy loss per cycle (for cyclic tests), logarithmic decrement (for vibration tests), complex modulus, rise-time or spectrum ratio (for wave propagation analysis), etc. For numerical…
Multi-system interaction is an important and difficult problem in physics. Motivated by the experimental result of an electronic circuit element "Fractor", we introduce the concept of dynamic-order fractional dynamic system, in which the…
We study phonon-mediated damping of mechanical vibrations in a finite quantum-mechanical atomic-chain model. Our study is motivated by the quest to understand the quality factors (Q) of nanomechanical resonators and nanoelectromechanical…
Dynamic mode decomposition (DMD) is a popular technique for modal decomposition, flow analysis, and reduced-order modeling. In situations where a system is time varying, one would like to update the system's description online as time…
The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…
We consider a standard optomechanical system where a mechanical oscillator is coupled to a cavity mode through the radiation pressure interaction. The oscillator is coherently driven at its resonance frequency, whereas the cavity mode is…
A mathematical model describing the initial stage of the capture of oscillatory systems into autoresonance under the action of slowly varying pumping is considered. Solutions with an infinitely growing amplitude are associated with the…
A mathematical model describing the initial stage of the capture into the parametric autoresonance in nonlinear oscillating systems with a dissipation is considered. Solutions with unboundedly growing energy in time at infinity are…
The nanobeam resonator is the key mechanical component in the nano-electromechanical system. In addition to its high frequency originating from its low dimension, the performance is significantly influenced by the circumstances, especially…
The direct parametrisation method for invariant manifold is a model-order reduction technique that can be applied to nonlinear systems described by PDEs and discretised e.g. with a finite element procedure in order to derive efficient…
It is well-established that a proportional current control gain emulates a resistor in the converter output impedance. Even though this resistance can provide additional damping to grid resonances, its effect for traditional linear current…
There is currently a strong interest in mirrorless lasing systems, in which the electromagnetic feedback is provided either by disorder (multiple scattering in the gain medium) or by order (multiple Bragg reflection). These mechanisms…