Following a brief review of current progress in the field of nonlinear targeted energy transfer
(TET), we discuss some general ideas and methods in this field and describe certain …

This paper is an extension of the previous review, done by the same authors (Mikhlin, Y.,
and Avramov, KV, 2010,“Nonlinear Normal Modes for Vibrating Mechanical Systems …

In this study, we define a new non-commutative number system called hybrid numbers. This
number system can be accepted as a generalization of the complex\left (i^ 2=-1\right) i 2=-1 …

This book is a unique exposition of rich and inspiring geometries associated with Möbius
transformations of the hypercomplex plane. The presentation is self-contained and based on …

We present an analytical study of the conservative and dissipative dynamics of a two-degree-
of-freedom (DOF) system consisting of a linear oscillator coupled to a bistable light …

Two principal concepts of nonlinear normal vibrations modes (NNMs), namely the Kauderer–
Rosenberg and Shaw–Pierre concepts, are analyzed. Properties of the NNMs and methods …

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 …

The dynamics of two coupled pendulums under a magnetic field are considered. Inertial
components of the pendulums are essentially different, and a ratio of masses is chosen as a …

The nonlinear resonance interaction and energy exchange between bending and
circumferential flexure modes in single-walled carbon nanotubes is studied. First, the results …

The dynamics of the system of two elastically coupled pendulums located in a magnetic field
is considered when the masses of the pendulums differ significantly. In this case, both …