Past, present and future of nonlinear system identification in structural dynamics

G Kerschen, K Worden, AF Vakakis… - Mechanical systems and …, 2006 - Elsevier
This survey paper contains a review of the past and recent developments in system
identification of nonlinear dynamical structures. The objective is to present some of the …

Recent advances in liquid sloshing dynamics

RA Ibrahim, VN Pilipchuk, T Ikeda - 2001 - asmedigitalcollection.asme.org
A liquid free surface in partially filled containers can experience a wide spectrum of motions
such as planar, non-planar, rotational, quasi-periodic, chaotic, and disintegration. Civil …

Energy pum** in nonlinear mechanical oscillators: part I—dynamics of the underlying Hamiltonian systems

O Gendelman, LI Manevitch… - J. Appl …, 2001 - asmedigitalcollection.asme.org
The systems considered in this work are composed of weakly coupled, linear and essentially
nonlinear (nonlinearizable) components. In Part I of this work we present numerical …

Complicated dynamics of a linear oscillator with a light, essentially nonlinear attachment

YS Lee, G Kerschen, AF Vakakis… - Physica D: Nonlinear …, 2005 - Elsevier
We study the dynamics of a two-degree-of-freedom (DOF) nonlinear system consisting of a
grounded linear oscillator coupled to a light mass by means of an essentially nonlinear …

Passive non-linear targeted energy transfer and its applications to vibration absorption: a review

YS Lee, AF Vakakis, LA Bergman… - Proceedings of the …, 2008 - journals.sagepub.com
This review paper discusses recent efforts to passively move unwanted energy from a
primary structure to a local essentially non-linear attachment (termed a non-linear energy …

Periodic orbits, damped transitions and targeted energy transfers in oscillators with vibro-impact attachments

YS Lee, F Nucera, AF Vakakis, DM McFarland… - Physica D: Nonlinear …, 2009 - Elsevier
We study complex damped and undamped dynamics and targeted energy transfers (TETs)
in systems of coupled oscillators, consisting of single-degree-of-freedom primary linear …

[BOOK][B] Asymptotical mechanics of thin-walled structures

IV Andrianov, J Awrejcewicz, LI Manevitch - 2013 - books.google.com
In this book a detailed and systematic treatment of asymptotic methods in the theory of plates
and shells is presented. The main features of the book are the basic principles of …

Traveling waves and localized modes in one-dimensional homogeneous granular chains with no precompression

Y Starosvetsky, AF Vakakis - Physical Review E—Statistical, Nonlinear, and …, 2010 - APS
We study a class of strongly nonlinear traveling waves and localized modes in one-
dimensional homogeneous granular chains with no precompression. Until now the only …

[BOOK][B] Nonlinear dynamics: between linear and impact limits

VN Pilipchuk - 2010 - books.google.com
Nonlinear Dynamics represents a wide interdisciplinary area of research dealing with a
variety of “unusual” physical phenomena by means of nonlinear differential equations …

Periodic orbits of a conservative 2-DOF vibro-impact system by piecewise continuation: bifurcations and fractals

H Tao, J Gibert - Nonlinear Dynamics, 2019 - Springer
The exact periodic orbits of a conservative 2-degree-of-freedom vibro-impact system with
stereo-mechanical impact model is studied using a piecewise continuation method. Feasible …