Qualitative changes in bifurcation structure for soft vs hard impact models of a vibro-impact energy harvester

Funding Information: The authors gratefully acknowledge partial funding for this work from NSF-CMMI (No. 2009270) and EPSRC (No. EP/V034391/1).Peer reviewedPublisher PD

7th International Conference on Nonlinear Vibrations, Localization and Energy Transfer: Extended Abstracts

International audienceThe purpose of our conference is more than ever to promote exchange and discussions between scientists from all around the world about the latest research developments in the area of nonlinear vibrations, with a particular emphasis on the concept of nonlinear normal modes and targeted energytransfer

Rotating potential of a stochastic parametric pendulum

The parametric pendulum is a fruitful dynamical system manifesting some of the most interesting phenomena of nonlinear dynamics, well-known to exhibit rather complex motion including period doubling, fold and pitchfork bifurcations, let alone the global bifurcations leading to chaotic or rotational motion. In this thesis, the potential of establishing rotational motion is studied considering the bobbing motion of ocean waves as the source of excitation of a oating pendulum. The challenge within this investigation lies on the fact that waves are random, as well as their observed low frequency, characteristics which pose a broader signi cance within the study of vibrating systems. Thus, a generic study is conducted with the parametric pendulum being excited by a narrow-band stochastic process and particularly, the random phase modulation is utilized. In order to explore the dynamics of the stochastic system, Markov-chain Monte-Calro simulations are performed to acquire a view on the in uence of randomness onto the parameter regions leading to rotational response. Furthermore, the Probability Density Function of the response is calculated, applying a numerical iterative scheme to solve the total probability law, exploiting the Chapman-Kolmogorov equation inherent to Markov processes. A special case of the studied structure undergoing impacts is considered to account for extreme weather conditions and nally, a novel design is investigated experimentally, aiming to set the ground for future development

15th Conference on Dynamical Systems Theory and Applications DSTA 2019 ABSTRACTS

From Preface: This is the fifteen time when the conference „Dynamical Systems – Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and the Ministry of Science and Higher Education. It is a great pleasure that our invitation has been accepted by so many people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcome nearly 255 persons from 47 countries all over the world. They decided to share the results of their research and many years experiences in the discipline of dynamical systems by submitting many very interesting papers. This booklet contains a collection of 338 abstracts, which have gained the acceptance of referees and have been qualified for publication in the conference edited books.Technical editor and cover design: Kaźmierczak, MarekCover design: Ogińska, Ewelina; Kaźmierczak, Mare

Numerical computation of nonlinear normal modes in mechanical engineering

This paper reviews the recent advances in computational methods for nonlinear normal modes (NNMs). Different algorithms for the computation of undamped and damped NNMs are presented, and their respective advantages and limitations are discussed. The methods are illustrated using various applications ranging from low-dimensional weakly nonlinear systems to strongly nonlinear industrial structures. © 2015 Elsevier Ltd

14th Conference on Dynamical Systems Theory and Applications DSTA 2017 ABSTRACTS

From Preface: This is the fourteen time when the conference “Dynamical Systems – Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and the Ministry of Science and Higher Education. It is a great pleasure that our invitation has been accepted by so many people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcome nearly 250 persons from 38 countries all over the world. They decided to share the results of their research and many years experiences in the discipline of dynamical systems by submitting many very interesting papers. This booklet contains a collection of 375 abstracts, which have gained the acceptance of referees and have been qualified for publication in the conference proceedings [...]

Vortex-induced vibration of a linearly-sprung cylinder with nonlinear energy sinks

We investigate the effect of coupling an essentially nonlinear and dissipative attachment to a linearly-sprung circular cylinder undergoing rectilinear vortex-induced vibration (VIV) normal to the mean flow. The attachment is a nonlinear energy sink (NES). The essentially nonlinear coupling between the rectilinear motion of the cylinder and the motion of the NES allows for efficient, one-way transfer of kinetic energy from the former to the latter, where it is dissipated through a process known as targeted energy transfer. We use a spectral-element approach to compute the flow and the rigid-body quantities, and show that for values of the Reynolds number in the laminar regime (20 ≤ Re ≤ 350) and well into the turbulent regime (Re ≈ 10,000), the addition of an NES to a linearly-sprung cylinder undergoing transverse VIV gives rise to a variety of physical phenomena not seen otherwise. We consider two NES configurations, namely, a rotational NES and a translational NES. The former consists of a mass allowed to rotate about the cylinder axis, with its rotational motion being linearly damped. The latter consists of a mass allowed to translate in the direction of travel of the cylinder, with its rectilinear motion being restrained by a cubic spring and a linear viscous damper. We show that, in a range of Re values (20 ≤ Re ≤ 100) in which the flow is expected to be two-dimensional and laminar, a rotational NES leads to phenomena as diverse as passive VIV suppression, partial stabilization of the vortex street formed downstream of the cylinder, drag reduction, capture of the trajectory on underlying slow-invariant resonance manifolds, and coexistence of multiple long-time solutions. We also investigate the extent to which a rotational NES affects the linear stability of the steady, symmetric, motionless-cylinder solution, as well as the onset of three-dimensionality in the wake. We additionally present preliminary evidence that, in the turbulent regime, the rotational NES displays great potential for being used not only as a VIV suppression device, but also as an efficient hydrokinetic energy harvester. For a translational NES, at a value of the Reynolds number slightly above the fixed-cylinder Hopf bifurcation, we construct a reduced-order model (ROM) of the fluid–structure interaction based on a wake oscillator, asymptotic analysis of which predicts the existence of complete and partial VIV-suppression mechanisms, relaxation cycles, as well as Hopf and Shilnikov bifurcations. These outcomes are confirmed by numerical integration of the ROM and comparison against spectral-element computations of the full-order system

Theoretical Approaches in Non-Linear Dynamical Systems

From Preface: The 15th International Conference „Dynamical Systems - Theory and Applications” (DSTA 2019, 2-5 December, 2019, Lodz, Poland) gathered a numerous group of outstanding scientists and engineers who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without great effort of the staff of the Department of Automation, Biomechanics and Mechatronics of the Lodz University of Technology. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our event was attended by over 180 researchers from 35 countries all over the world, who decided to share the results of their research and experience in different fields related to dynamical systems. This year, the DSTA Conference Proceedings were split into two volumes entitled „Theoretical Approaches in Non-Linear Dynamical Systems” and „Applicable Solutions in Non-Linear Dynamical Systems”. In addition, DSTA 2019 resulted in three volumes of Springer Proceedings in Mathematics and Statistics entitled „Control and Stability of Dynamical Systems”, „Mathematical and Numerical Approaches in Dynamical Systems” and „Dynamical Systems in Mechatronics and Life Sciences”. Also, many outstanding papers will be recommended to special issues of renowned scientific journals.Cover design: Kaźmierczak, MarekTechnical editor: Kaźmierczak, Mare

Dynamical systems : control and stability

Proceedings of the 13th Conference „Dynamical Systems - Theory and Applications" summarize 164 and the Springer Proceedings summarize 60 best papers of university teachers and students, researchers and engineers from whole the world. The papers were chosen by the International Scientific Committee from 315 papers submitted to the conference. The reader thus obtains an overview of the recent developments of dynamical systems and can study the most progressive tendencies in this field of science