Abstracts Overview

We study the nonlinear dynamics of 2D material nanoresonators during a second-order phase transition. We probe the dynamics of these resonators at the vicinity of the phase transition temperature. We observe dramatic changes in the nonlinear parameters of the system while sweeping the temperature at...

A simplified mechanical model of shimmying towed wheel subjected to stochastic excitation has been investigated by using the method of bifurcation theory and numerical simulation. A Gaussian white noise is used to model the stochastic disturbance originated in side wind effects. Unstable periodic mo...

In the study, we analyse the experimental implementation of the act-and-wait control concept used for the purpose of digital position control. The initial model and simulation demonstrates the relevance of the control concept, which results are validated by experiments on a linear actuator. To get a...

This paper analyses the nonlinear inertia and its effect in coupling with an X-shaped anti-vibration mechanism in more depth based on the proposed novel inertia design mechanism. The inertia unit is designed with an inspiration from arm swing of human body in walking and integrated within an anti-vi...

We propose a methodology to carry out nonlinear system identification based on bifurcations. The proposed approach relies on fold bifurcation curves identified experimentally through control-based continuation and an optimization framework to minimize the distance between the experimental and numeri...

In this paper, we propose formulations for several elastoplastic models, using nonsmooth differential algebraic systems of equations (DAE) which are suitable for numerical evaluation in an implicit time-stepping scheme. We will extend the Jenkins element, i.e. ˙a spring in series with a friction el...

In this paper, the nonstationary response of nonlinear single-degree-of-freedom systems subject to stochastic excitations is examined. A version of the Path Integral (PI) approach is developed for determining the evolution of the response probability density function (PDF). Specifically, the PI appr...

Steam generators inner tubes wear out over time due to flow induced vibrations and impacts with the support structures. In order to better understand the non-linear response of these structures, a simplified mock-up of a steam generator straight section placed inside a hole with clearance was used t...

We present observer designs for hybrid systems in two scenarios: one where the jump times (i.e., the times when discontinuities in solutions occur) are known, and the other where these are unknown. For the first case, we first consider systems with linear maps by proposing a Kalman-like observer, th...

Dipolar Bose-Einstein condensates emerged as a unique platform permitting the exploration of nonlinear dynamics at the classical-quantum interface, phase-transitions and the realization of supersolidity. In this talk we present theoretical results discussing self-organized pattern-formation in this ...

Artificial muscles are dielectric elastomeric system that mimic the response of natural muscle and are helpful in many bio-mimicking applications. The existing literature are based on the assumption that electrodes are compliant and are focused on materials with greater extensibility than biological...

Imperfections of cutting tool manufacturing and clamping are regular problems in machining, which affect the chip formation kinematics, forced vibrations, quality of the machined surface, and tool wear. Such effects are often neglected in classical studies due to the modeling difficulties, measureme...

The free undamped propagation of nonlinear multi-harmonic waves in mechanical 2D metamaterials with inertial amplification is investigated. A Lagrangian model is formulated to describe the weakly nonlinear dynamics of a periodic array of elastically coupled oscillators, pantographically connected wi...

Acoustic and free-surface gravity waves have been considered as separate phenomena due to the disparate length- and time-scales that characterises them. Recent studies show that acoustic-gravity wave interaction is possible via a nonlinear triad mechanism. Such interaction allows energy exchange whi...

Over the past three decades, there has been a growing interest in dynamical systems characterized by non-differentiability, switches, and discontinuities. This surge has given rise to a novel research domain known as Nonsmooth Dynamics, finding diverse applications such as sliding mode control theor...

Reduced dynamics obtained via the normal form style in the parametrisation method for invariant manifolds are analyzed for nonlinear vibratory systems. Thanks to symbolic and numerical asymptotic expansions, systematic developments allow one to show how the solutions are a generalization to arbitrar...

We describe how some minimal surface bifurcation problems can be treated with the Matlab continuation and bifurcation toolbox pde2path, and present symmetry breaking bifurcation results for Enneper's surface, and Schwarz--P and Schwarz--H families. Some of these results are analytically known and th...

A time-series based approach has been developed to overcome the tedious calculations involved in the center manifold reduction for delay-differential equations. By using a numerical solution at the critical value of the bifurcation parameter, the coefficients of flow on the center manifold are recov...

In this paper, the transverse vibrations of a one-dimensional string attached to a parabolic-shaped obstacle at one end are studied. Gravity and axial vibrations are taken into account. The changing position of the attachment point leads to a moving boundary problem. A boundary fixing transformation...

Cracks and resonance stand out as primary factors contributing to the failure of engineering components subjected to dynamic loading. Numerous studies have affirmed that the existence of cracks can alter modal frequencies, thereby increasing the likelihood of resonance occurring at frequencies other...

Nonlinear vibrations of a homogeneous, isotropic, and shallow spherical caps under a harmonic pressure field are studied. The problem is addressed using a semi-analytical method based on Novozhilov's nonlinear shell theory. The partial differential equations (PDEs) are reduced to a set of ordinary d...

Force reconstruction in Atomic Force Microscopy (AFM) data represents a significant challenge due to the complex dynamic interactions between the AFM tip and the sample, which are both highly nonlinear and non-smooth. Various methods have been proposed to retrieve this information, yet traditional a...

The method for the numerical simulation of complex process of interaction between nonlinear oscillations, creep and wear in fuel rod claddings is presented. Geometrically nonlinear oscillations of the fuel rod are modelled by Galerkin and time integration methods. The cyclic creep governing equation...

A parametric nonlinear model of two-dimensional textile metamaterials is formulated to investigate the free undamped propagation of elastic waves. The mechanical system is characterized by spatially periodic prestressed configuration and governed by differential difference equations with quadratic a...

There is an ongoing effort to develop nonsmooth versions of high-order schemes for the simulation of mechanical systems with frictional contact. In this paper, we introduce a particular version of the principle of virtual action, which allows to derive a nonsmooth extensions to the Lobatto IIIA-IIIB...

This study presents a unique nonlinear frequency response NLFR extraction method introduced for smooth nonlinear vibrating systems. The proposed methodology is built on the geometrical representation of the harmonic balance solution for the undamped cubic Duffing oscillator. It is demonstrated that ...

A novel approach to the practical study of delay equations consists in reformulating them as abstract differential equations, applying a pseudospectral discretization in order to obtain a system of ordinary differential equations (ODEs) and using available numerical methods for ODEs. This technique ...

A data-driven approach has been developed to provide the equations of the Hopf normal form from time-series data. The coefficients of the numerically constructed flow yield the Poincaré-Lyapunov constant, an important quantity determining the criticality of the Hopf bifurcations, as well as the sca...

Network dynamics is nowadays of extreme relevance to model and analyze complex systems. From a dynamical systems perspective, understanding the local behavior near equilibria is of utmost importance. In particular, equilibria with at least one zero eigenvalue play a crucial role in bifurcation analy...