Related papers: Path following and numerical continuation methods …
We present simulations of the dynamic and temperature dependent behavior of Micro-Electro-Mechanical Systems (MEMS) by utilizing recently developed parallel codes which enable a coupling of length scales. The novel techniques used in this…
The motion of beams in particle accelerators is dominated by a plethora of non-linear effects which can enhance chaotic motion and limit their performance. The application of advanced non-linear dynamics methods for detecting and correcting…
This paper investigates a path-following method inspired by the semismooth$^*$ approach for solving algebraic inclusions, with a primary emphasis on the role of uniform subregularity. Uniform subregularity is crucial for ensuring the…
The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…
A lack of software reproducibility has become increasingly apparent in the last several years, calling into question the validity of scientific findings affected by published tools. Reproducibility issues may have numerous sources of error,…
A study of the non linear modes of a two degree of freedom mechanical system with bilateral elastic stop is considered. The issue related to the non-smoothness of the impact force is handled through a regularization technique. In order to…
This study investigates the complex nonlinear coupling of magnetic gears arranged in proximity on a plane. Acknowledging the rich array of geometric and electromagnetic parameters involved, we initiate our exploration with a simplified…
We propose and analyze a mathematical model of the mechanics of gels, consisting of the laws of balance of mass and linear momentum. We consider a gel to be an immiscible and incompressible mixture of a nonlinearly elastic polymer and a…
The content of this contribution is based on the course on numerical analysis techniques for non-linear dynamics. After introducing basic concepts as the visual analysis of trajectories in phase space and the importance of the nature of…
This paper presents a simplified implementation of the arc-length method for computing the equilibrium paths of nonlinear structural mechanics problems using the finite element method. In the proposed technique, the predictor is computed by…
The minimum energy path (MEP) is the most probable transition path that connects two equilibrium states of a potential energy landscape. It has been widely used to study transition mechanisms as well as transition rates in the fields of…
This paper concerns the experimental validation of some mathematical models previously developed by the authors, to predict the static behaviour of microelectrostatic actuators, basically free-clamped microbeams. This layout is currently…
This technical note is concerned with aeroelastic flutter problems: the analysis of aeroelastic systems undergoing airspeed-dependent dynamic instability. Existing continuation methods for parametric stability analysis are based on marching…
Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the…
Nanoelectromechanical systems (NEMS) are devices integrating electrical and mechanical functionality on the nanoscale. Because of individual electron tunneling, such systems can show rich self-induced, highly non-linear dynamics. We show…
The nonlinear dynamics of a microbeam-rigid body gyroscope are investigated by using a continuation method. To study the nonlinear dynamics of the system, the Lagrangian of the system is discretized and the reduced-order model is obtained.…
One of the most severe limitations in particle accelerators and beam transport are non-linear effects. Techniques to study and possibly suppress some of these detrimental effects exist, the most popular are based on particle tracking and…
The goal of this paper is to sketch a broader outline of the mathematical structures present in the Nonlinear Maxwell Theory in continuation of work presented in my previous articles. In particular, I display new types of both dynamic and…
Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…
We consider a nonlinear non-autonomous system with time-varying delays $$ \dot{x_i}(t)=-a_i(t)x_{i}(h_i(t))+\sum_{j=1}^mF_{ij}(t,x_j(g_{ij}(t))) $$ which has a large number of applications in the theory of artificial neural networks. Via…