We revisit an early example of a nonlinear oscillator that exhibits chaotic motions when subjected to periodic excitation: the magneto-elastically buckled beam. In the paper of Moons and Holmes (1980) [1] magnetic field calculations were outlined but not carried through; instead the nonlinear forces responsible for creation of a two-well potential and buckling were fitted to a polynomial functi...

Within the framework of the thermal wave model, an investigation is made of the longitudinal dynamics of high-energy charged-particle beams. The model includes the nonlinear self-consistent interaction between the beam and its surroundings in terms of a coupling impedance, and when resistive as well as reactive parts are included, the evolution equation becomes a generalized nonlinear Schröding...

The nonlinear system becomes an area with numerous investigations over the past decades. The conventional modal analysis could not be  applied on nonlinear continuous system which makes it impossible to construct the reduced order models and obtain system response based on limited number of measurement points. Nonlinear normal modes provide a useful tool for extending modal analysis to nonlinea...

This paper presents a nonlinear formulation to model flexible-link robots based on finite element approach. To derive nonlinear dynamic equations of the flexible-link robot, links are modeled by some finite elements, and Lagrange’s principle is used for dynamic modeling. A local coordinate system is attached to each link and the local displacement of an arbitrary point is formulated based on no...

Microelectromechanical Systems (MEMS) is difficult to take transient analysis due to the tight coupling between the multiple energy domains, typically nonlinear. An effective increment-dimensional precise integration method (PIM) combined with the model order reduction (MOR) technique based on Krylov subspace is present to solve large-scale nonlinear finite element dynamics systems. The numeric...

Within the framework of the thermal wave model, an investigation is made of the longitudinal dynamics of high energy charged particle beams. The model includes the self-consistent interaction between the beam and its surroundings in terms of a nonlinear coupling impedance, and when resistive as well as reactive parts are included, the evolution equation becomes a generalised nonlinear Schröding...

This paper is concerned with the dynamics for nonlinear one-dimensional beam equations. We consider a nonlinear beam equation with viscosity or with a lower order damping term instead of the viscosity, and we establish the existence of global attractors for both systems. Keyword: beam equations; global attractor; in nite-dimensional dynamics MSC 2000: 35G25; 35B41

In this paper, inelastic pile-soil-structure interaction under static loading is presented by using finite element and boundary element methods. Linear beam column finite elements are used to model the piles and structural elements. Nonlinear soil is modeled by using nonlinear springs along the piles. Modified Özdemir’s nonlinear model is implemented for springs and systems of equations are cou...

We apply two recently formulated mathematical techniques, Slow-Fast Decomposition (SFD) and Spectral Submanifold (SSM) reduction, to a von Kármán beam with geometric nonlinearities and viscoelastic damping. SFD identifies a global slow manifold in the full system which attracts solutions at rates faster than typical rates within the manifold. An SSM, the smoothest nonlinear continuation of a li...