Related papers: Dynamics of a linear oscillator connected to a sma…
We perform a detailed study of the dynamics of a nonlinear, one-dimensional oscillator driven by a periodic force under hysteretic damping, whose linear version was originally proposed and analyzed by Bishop in [1]. We first add a small…
We present an experimentally realizable, simple mechanical system with linear interactions whose geometric nature leads to nontrivial, nonlinear dynamical equations. The equations of motion are derived and their ground state structures are…
We consider a Brownian oscillator whose coupling to the environment may lead to the formation of a localized normal mode. For lower values of the oscillator's natural frequency, $\omega\le\omega_c$, the localized mode is absent and the…
Hybrid vibro-impact (HVI) oscillations is a strongly nonlinear dynamical regime that involves both linear oscillations and collisions under periodic, impulsive, or stochastic excitation. This regime arises in various engineering systems,…
Industrial coating processes create thin liquid films with tight thickness tolerances, and thus models that predict the response to inevitable disturbances are essential. The mathematical modeling complexities are reduced through…
We study the transition probability and coherence of a two-site system, interacting with an oscillator. Both properties depend on the initial preparation. The oscillator is prepared in a thermal state and, even though it cannot be…
The linear natural and forced oscillations of a hemispherical bubble on a solid substrate are under theoretical consideration. The contact line dynamics is taken into account with the Hocking condition, which eventually leads to interaction…
Two-level system strongly coupled to a single resonator mode (harmonic oscillator) is a paradigmatic model in many subfields of physics. We study theoretically the Landau-Zener transition in this model. Analytical solution for the…
This paper considers the oscillations modeled by a forced Van der Pol generalized oscillator. These oscillations are described by a nonlinear differential equation of the form $…
We analytically investigate the nonlinear response of a damped doubly clamped nanomechanical beam under static longitudinal compression which is excited to transverse vibrations. Starting from a continuous elasticity model for the beam, we…
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…
Aspects of transition mechanisms on a $14^{\circ}$ sharp-nosed ogive-cylinder at Mach~$6$ are elucidated by considering linear and nonlinear disturbance evolution of freestream stochastic and wave packet forcing at different locations…
A mechanical system consisting of an elastic beam under harmonic excitation and an attached sliding body is investigated. Recent experimental observations suggest that the system passively (self-)adapts the axial location of the slider to…
Considerable attention has been given to the use of a nonlinear energy sink (NES) as a nonlinear absorber. The NES is an efficient passive control device, which has been the focus of extensive research. This paper uses the…
A one-dimensional model on a line of the length L is investigated, which involves particle diffusion as well as single particle annihilation. There are also creation and annihilation at the boundaries. The static and dynamical behaviors of…
Flutter stability is a dominant design constraint of modern gas and steam turbines. To further increase the feasible design space, flutter-tolerant designs are currently explored, which may undergo Limit Cycle Oscillations (LCOs) of…
A bistable nonlinear energy sink conceived to mitigate the vibrations of host structural systems is considered in this paper. The hosting structure consists of two coupled symmetric linear oscillators (LOs) and the nonlinear energy sink…
We consider the nonlinear nonlocal beam evolution equation introduced by Woinowsky- Krieger. We study the existence and behavior of periodic solutions: these are called nonlinear modes. Some solutions only have two active modes and we…
We study the evolution of a wave packet in a nonlinear Schr\"odinger lattice equation subject to a dc bias. In the absence of nonlinearity all normal modes are spatially localized giving rise to a Stark ladder with an equidistant eigenvalue…
An enhancement of localized nonlinear modes in coupled systems gives rise to a novel type of escape process. We study a spatially one dimensional set-up consisting of a linearly coupled oscillator chain of $N$ mass-points situated in a…