We derive conditions under which a general nonlinear mechanical system can be exactly
reduced to a lower-dimensional model that involves only the softer degrees of freedom. This …

We have combined the theories of geometric singular perturbation and proper orthogonal
decomposition to study systematically the dynamics of coupled systems in mechanics …

We consider a one-dimensional linear spring-mass array coupled to a one-dimensional
array of uncoupled pendula. The principal aim of this study is to investigate the non-linear …

The dynamics of a non-linear electro-magneto-mechanical coupled system is addressed.
The non-linear behavior arises from the involved coupling quadratic non-linearities and it is …

This work analyzes the motions of a stiff linear oscillator coupled to a soft nonlinear oscillator
and subject to a forcing term. This system is a representative of a large class of structural …

This book develops analytical methods for studying the dynamical chaos, synchronization,
and dynamics of structures in various models of coupled rotators. Rotators and their systems …

In this paper, we study the effect of a harmonicforcing function and the strength of a
nonlinearityon a two-degrees-of-freedom system namely, an elasticpendulum, with internal …

The alternative theory of existence of cluster structures in lattices of dynamical systems
(oscillators) is proposed. This theory is based on representation of structures as a result of …

The dynamic response of an electro-magneto-mechanical coupled system excited by a
harmonic voltage is addressed. The system mathematical model involves coupling quadratic …

In our experimental structural dynamics studies, we discover that physical beam structures
with displacement controlled hinged endpoints create a three-dimensional nonlinear …