Recent advances in nonlinear passive vibration isolators

A higher order beam finite element for bending and vibration problems

Bending, buckling and free vibration of laminated composite and sandwich beams: A critical review of literature

It has been known for some time that nonlinearity and discreteness play important roles in many branches of condensed-matter physics as evidenced by the appearance of domain walls, kinks, and solitons. A recent discovery is that localized dynamical energy in a perfect nonlinear lattice can be stabilized by the lattice discreteness. Intrinsic localized modes (ILMs) are the resulting signature. Their energy profiles resemble those of localized modes at defects in a harmonic lattice but, like solitons, they can move. ILMs have been observed in macroscopic arrays as diverse as coupled Josephson junctions, optical waveguides, two-dimensional nonlinear photonic crystals, and micromechanical cantilevers. Such dynamically driven localized modes are providing a new window into the underlying simplicity of nonequilibrium dynamics. This Colloquium surveys the studies of ILMs in micromechanical cantilever arrays. Because of the ease of sample fabrication with silicon technology and the intuitive optical visualization techniques, these experiments are able to demonstrate the general nature and properties of dynamical energy localization while at the same time providing new information on ILM generation, locking, pinning, and interaction with impurities.

Colloquium: Nonlinear energy localization and its manipulation in micromechanical oscillator arrays

https://people.maths.ox.ac.uk/ball/Papers/Ball%20J%20Math%20Anal%20Appl%201973.pdf

Initial-boundary value problems for an extensible beam

It can be shown that the vibration of an extensible bar, carrying no transverse load and having the ends fixed at the supports, causes an axial tensile force with a period equal to the half-period of the vibration of the bar. This force modifies the process of the vibration to a nonlinear one and produces an increase of the frequency of vibration according to the increase of the amplitude.

/pdf/the-effect-of-an-axial-force-on-the-vibration-of-hinged-bars-3m194530n7.pdf

S. Woinowsky-Krieger

Papers

The Effect of an Axial Force on the Vibration of Hinged Bars