Related papers: Resonant forcing of nonlinear systems of different…
Many modern engineering structures exhibit nonlinear vibration. Characterizing such vibrations efficiently is critical to optimizing designs for reliability and performance. For linear systems, steady-state vibration occurs only at the…
Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of…
A mechanical covariant equation is introduced which retains all the effectingness of the Lagrange equation while being able to describe in a unified way other phenomena including friction, non-holonomic constraints and energy radiation…
Resonance plays critical roles in the formation of many physical phenomena, and many techniques have been developed for the exploration of resonance. In a recent letter [Phys. Rev. Lett. 117, 062502 (2016)], we proposed a new method for…
We report on the onset of anti-resonant behaviour of mass transport systems driven by time-dependent forces. Anti-resonances arise from the coupling of a sufficiently high number of space-time modes of the force. The presence of forces…
We prove existence of quasi-periodic solutions with two frequencies of completely resonant, periodically forced nonlinear wave equations with periodic spatial boundary conditions. We consider both the cases the forcing frequency is: (Case…
We revisit the problem of a triad of resonantly interacting nonlinear waves driven by an external force applied to the unstable mode of the triad. The equations are Hamiltonian, and can be reduced to a dynamical system for 5 real variables…
In the simulation of biological molecules, it is customary to impose constraints on the fastest degrees of freedom to increase the time step. The evaluation of the involved constraint forces must be performed in an efficient manner, for…
Employing a phase space which includes the (Riemann-Liouville) fractional derivative of curves evolving on real space, we develop a restricted variational principle for Lagrangian systems yielding the so-called restricted fractional…
The paper deals with the interaction between buckling and resonance instabilities of mechanical systems. Taking into account the effect of geometric nonlinearity in the equations of motion through the geometric stiffness matrix, the problem…
We study a system of partial differential equations with integer and fractional derivatives arising in the study of forced oscillatory motion of a viscoelastic rod. We propose a new approach considering a quotient of relations appearing in…
Transport coefficients, such as the mobility, thermal conductivity and shear viscosity, are quantities of prime interest in statistical physics. At the macroscopic level, transport coefficients relate an external forcing of magnitude…
We consider several models (including both multidimensional ordinary differential equations (ODEs) and partial differential equations (PDEs), possibly ill-posed), subject to very strong damping and quasi-periodic external forcing. We study…
Physically-inspired latent force models offer an interpretable alternative to purely data driven tools for inference in dynamical systems. They carry the structure of differential equations and the flexibility of Gaussian processes,…
We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wavefunctions of one-dimensional Klein-Gordon and Dirac equation with linear…
In this note we unify the results of A.C. Lazer and P.O. Frederickson [3], A.C. Lazer [6], A.C. Lazer and D.E. Leach [7], J.M. Alonso and R. Ortega [1], and P. Korman and Y. Li [4] on periodic oscillations and unbounded solutions of…
We prove existence and regularity of periodic in time solutions of completely resonant nonlinear forced wave equations with Dirichlet boundary conditions for a large class of non-monotone forcing terms. Our approach is based on a…
Self-sustained vibrations in systems ranging from lasers to clocks to biological systems are often associated with the coefficient of linear friction, which relates the friction force to the velocity, becoming negative [1,2]. The runaway of…
Potential resonances are usually investigated either directly in the complex energy plane or indirectly in the complex angular momentum plane. Another formulation complementing these two is presented in this work. It is an indirect method…
This work introduces a systematic method for identifying analytical and semi-analytical solutions of force-free magnetic fields with plane-parallel and axial symmetry. The method of separation of variables is used, allowing the…