Related papers: Resonant forcing of nonlinear systems of different…
Combined action of noise and deterministic force in dynamical systems can induce resonant effects. Here, we demonstrate a minimal, deterministic-force-free, setup allowing for occurrence of resonant, noise induced effects. We show that in…
Linear and nonlinear resonant states can be restrictive: they exist at particular discrete states in frequency and/or elasticity, under particular (e.g., simple-harmonic) waveforms. In forced oscillators, this restrictiveness is an obstacle…
An iterative optimization approach that simultaneously minimizes the energy and optimizes the Lagrange multipliers enforcing desired constraints is presented. The method is tested on previously established benchmark systems and it is proved…
In this paper, we use the fractional calculus to discuss the fractional mechanics, where the time derivative is replaced with the fractional derivative of order $\nu$. We deal with the motion of a body in a resisting medium where the…
In this paper we provide a variational derivation of the Euler-Poincar\'e equations for systems subjected to external forces using an adaptation of the techniques introduced by Galley and others. Moreover, we study in detail the underlying…
We consider a class of singular ordinary differential equations describing analytic systems of arbitrary finite dimension, subject to a quasi-periodic forcing term and in the presence of dissipation. We study the existence of response…
Long-term simulations of energetic electron fluxes in many space plasma systems require accounting for two groups of processes with well separated time-scales: microphysics of electron resonant scattering by electromagnetic waves and…
We consider the case of finite-size spherical particles which are settling under gravity in a homogeneous turbulent background flow. Turbulence is forced with the aid of the random forcing method of Eswaran and Pope [Comput. Fluids,…
We use symmetry considerations to investigate how damped modes affect pattern selection in multi-frequency forced Faraday waves. We classify and tabulate the most important damped modes and determine how the corresponding resonant triad…
Problems involving rolling without slipping or no sideways skidding, to name a few, introduce velocity-dependent constraints that can be efficiently treated by the method of Lagrange multipliers in the Lagrangian formulation of the…
We discuss two generalizations of the inverse problem of the calculus of variations, one in which a given mechanical system can be brought into the form of Lagrangian equations with non-conservative forces of a generalized Rayleigh…
Stochastic resonance (SR) is a prominent phenomenon in many natural and engineered noisy system, whereby the response to a periodic forcing is greatly amplified when the intensity of the noise is tuned to within a specific range of values.…
We consider a class of ordinary differential equations describing one-dimensional systems with a quasi-periodic forcing term and in the presence of large damping. We discuss the conditions to be assumed on the mechanical force and the…
We derive the equations of nonlinear magnetoelastostatics using several variational formulations involving the mechanical deformation and an independent field representing the magnetic component. An equivalence is also discussed, modulo…
We develop a general form of the Ritz method for trial functions that do not satisfy the essential boundary conditions. The idea is to treat the latter as variational constraints and remove them using the Lagrange multipliers. In…
Forced oscillation of a system composed of two pendulums coupled by a spring in the presence of damping is investigated. In the steady state and within the small angle approximation we solve the system equations of motion and obtain the…
We are able to derive the equations of motion for forced mechanical systems in a purely variational setting, both in the context of Lagrangian or Hamiltonian mechanics, by duplicating the variables of the system as introduced by Galley…
We extend linear input/output (resolvent) analysis to take into account nonlinear triadic interactions by considering a finite number of harmonics in the frequency domain using the harmonic balance method. Forcing mechanisms that maximize…
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 obtain closed-form solutions of several inhomogeneous Lienard equations by the factorization method. The two factorization conditions involved in the method are turned into a system of first-order differential equations containing the…