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 …

The concept of nonlinear normal modes (NNMs) is discussed in the present paper and its
companion, Part II. Because there is virtually no application of the NNMs to large-scale …

Notwithstanding the presence of some books summarizing specific research bodies on
structural systems, reviews on nonlinear dynamics and chaos in mechanical systems and …

In this paper, we investigate the dynamic behavior of clamped–clamped micromachined
arches when actuated by a small DC electrostatic load superimposed to an AC harmonic …

Approximations of the resonant non-linear normal modes of a general class of weakly non-
linear one-dimensional continuous systems with quadratic and cubic geometric non …

Amplitude amplification can improve signal-to-noise ratio, which is of great significance in
engineering systems, especially in small-scale MEMS systems. Hesre, we report an …

This paper is first of the two papers dealing with analytical investigation of resonant multi-
modal dynamics due to 2: 1 internal resonances in the finite-amplitude free vibrations of …

Non-linear interactions in a hinged–hinged uniform moderately curved beam with a torsional
spring at one end are investigated. The two-mode interaction is a one-to-one autoparametric …

We investigate experimentally and analytically the effect of initial shapes, arc and cosine
wave, on the static and dynamic behavior of microelectromechanical systems (MEMS) arch …

Competing mechanisms like quadratic/cubic nonlinearities associated with continuous
structures lead to complicated dynamics, and it is meaningful to identify the dominant …