This work presents a shooting algorithm to compute the periodic responses of geometrically nonlinear structures modelled under the special Euclidean (SE) Lie group formulation. The formulation is combined with a pseudo-arclength continuation method, while special adaptations are made to ensure compatibility with the SE framework. Nonlinear normal modes (NNMs) of various two...
Numerous powerful methods exist for developing reduced-order models (ROMs) from finite element (FE) models. Ensuring the accuracy of these ROMs is essential; however, the validation using dynamic responses is expensive. In this work, we propose a method to ensure the accuracy of ROMs without extra dynamic FE simulations. It has been shown that the well-established implicit...
The Lorenz system presents a double-zero bifurcation (a double-zero eigenvalue with geometric multiplicity two). However, its study by means of standard techniques is not possible because it occurs for a non-isolated equilibrium. To circumvent this difficulty, we add in the third equation a new term, $$Dz^2$$ . In this Lorenz-like system, the analysis of the double-zero...
The dynamics of elastic systems coupled with rotating bladed-rotors is rich and complex, and the blade number may have an influence on the in-vacuo system dynamics. This paper aims to model its nonlinear dynamics in-vacuo and study the effects of blade number on its dynamics. To this end, a nonlinear model consisting of a nonlinear inextensible beam, a motor assembly and a...
Numerical continuation tools are nowadays standard methods for the bifurcation analysis of dynamical systems. Unfortunately, the full power of these methods is still unavailable in experiments, in particular, if no underlying mathematical model is at hand. We here aim to narrow this gap by providing control based continuation of periodic states which can be ultimately implemented...
To obtain explicit understanding of the behavior of dynamical systems, geometrical methods and slow–fast analysis have proved to be highly useful. Such methods are standard for smooth dynamical systems and increasingly used for continuous, non-smooth dynamical systems. However, they are much less used for random dynamical systems, in particular for hybrid models with discrete...
Animals are capable of robust and reliable control in unstructured environments, where they effortlessly overcome the uncertainty of interaction and are capable of exploiting singularities. These conditions are a well-known challenge for robots due to the limitations of projected dynamics, which requires accurate modelling and is susceptible to singularities. This work proposes a...
A passive dynamic walker is a mechanical system that walks down a slope without any control, and gives useful insights into the dynamic mechanism of stable walking. This system shows specific attractor characteristics depending on the slope angle due to nonlinear dynamics, such as period-doubling to chaos and its disappearance by a boundary crisis. However, it remains unclear...
Mastering the emergence and suppression of chaos of complex networks is currently a fundamental task for the nonlinear science community with potential relevant applications in diverse fields such as microgrid technologies, neural control engineering, and ecological networks. Here, the emergence and suppression of chaos in a complex network of driven damped pendula, which...
Automatization of hydraulic machinery requires accurate information of the current dynamic state of the machinery but also information of the underlying dynamic model characterized by a set of parameters. Some of the parameters can be considered static and well defined, such as machinery dimensions, whereas a part of the parameter set is time varying and needs to be identified...
In this paper we examine the effect of delamination on wave scattering, with the aim of creating a control measure for layered waveguides of various bonding types. Previous works have considered specific widths of solitary waves for the simulations, without analysing the effect of changing the soliton parameters. We consider two multi-layered structures: one containing...
Foil air bearings (FABs) are the mainstay of oil-free turbomachinery technology which is undergoing rapid expansion. A rotor system using such bearings is a nonlinear multi-domain dynamical system comprising the rotor, the air films and the foil structures. Multi-pad (segmented) FABs offer opportunity for enhanced stability performance but are naturally more computationally...
Nonlinear control-affine systems described by ordinary differential equations with time-varying vector fields are considered in the paper. We propose a unified control design scheme with oscillating inputs for solving the trajectory tracking and stabilization problems under the bracket-generating condition. This methodology is based on the approximation of a gradient-like...
This work focuses on the modeling of contact between sheaves and flexible axially moving beams. A two-dimensional beam finite element is employed, based on the absolute nodal coordinate formulation (ANCF) with an improved selective reduced integration for the virtual work of elastic and viscous damping forces. For the efficient modeling of contact between flexible axially moving...
Escape and level-crossing are fundamental and closely related problems in transient dynamics. Often, when a particle reaches a critical displacement, its escape becomes inevitable. Therefore, escape models based on truncated potentials are often used, resulting in similar problems to level-crossing formulations. Two different types of dynamics can be identified, leading to...
In this paper, the nonlinear dynamics of a piezoelectrically sandwiched initially curved microbeam subjected to fringing-field electrostatic actuation is investigated. The governing motion equation is derived by minimizing the Hamiltonian over the time and discretized to a reduced-order model using the Galerkin technique. The modelling accounts for nonlinearities due to the...
This paper proposes a novel method for predicting the presence of saddle-node bifurcations in dynamical systems. The method exploits the effect that saddle-node bifurcations have on transient dynamics in the surrounding phase space and parameter space, and does not require any information about the steady-state solutions associated with the bifurcation. Specifically, trajectories...
In this paper, singular perturbation theory is exploited to obtain a reduced-order model of a slow–fast piecewise linear 2-DOF oscillator subjected to harmonic excitation. The nonsmooth nonlinearity of piecewise linear nature is studied in the case of bilinear damping as well as with bilinear stiffness characteristics. We propose a continuous matching of the locally invariant...
Chaotic motion in a fluttering wind turbine blade is investigated by the development of an efficient analytical predictive model that is then used to suppress the phenomenon. Flutter is a dynamic instability of an elastic structure in a fluid, such as an airfoil section of a wind turbine blade. It is presently modelled using generalised two degree of freedom coupled modes of a...
Various special effects occur during the operation of vibratory conveyors, e.g., multiple feeding velocities at the same excitation amplitude or so-called microthrows. In this work, a model for the simulation and prediction of the behavior of such a conveying system is presented. The simulation model is based on the bouncing ball model which is known from literature. The...