chirality

A Cosserat rod based continuum approach is presented to obtain phonon dispersion curves of flexural, torsional, longitudinal, shearing and radial breathing modes in chiral nanorods and nanotubes. Upon substituting the continuum wave form in the linearized dynamic equations of stretched and twisted Cosserat rods, we obtain analytical expression of a coefficient matrix (in terms of the rod's stiffnesses, induced axial force and twisting moment) whose eigenvalues and eigenvectors give us frequencies and mode shapes, respectively, for each of the above phonon modes.

The paper presents a model of a chiral multi-structure incorporating gyro-elastic beams. Floquet–Bloch waves in periodic chiral systems are investigated in detail, with the emphasis on localization and the formation of standing waves. It is found that gyricity leads to low-frequency standing modes and generation of stop-bands. A design of an earthquake protection system is offered here, as an interesting application of vibration isolation. Theoretical results are accompanied by numerical simulations in the time-harmonic regime.

For the first time, a design of a “deflecting elastic prism” is proposed and implemented for waves in a chiral medium. A novel model of an elastic lattice connected to a non-uniform system of gyroscopic spinners is designed to create a unidirectional wave pattern, which can be diverted by modifying the arrangement of the spinners within the medium. This important feature of the gyro-system is exploited to send a wave from a point of the lattice to any other point in the lattice plane, in such a way that the wave amplitude is not significantly reduced along the path.

We demonstrate intersting extension-torsion-inflation coupling in intrinsically twisted chiral tubes. In particular, we show that by tuning its intrinsic twist and the material constants, such tubes can show negative poison effect on being stretched. Similarly, such tubes can overwind initially when stretched - the same unusual behavior has been reported earlier when a DNA molecule is stretched.

The paper presents a systematic study of dispersive waves in an elastic chiral lattice. Chirality is introduced through gyroscopes embedded into the junctions of a doubly periodic lattice. Bloch-Floquet waves are assumed to satisfy the quasi-periodicity conditions on the elementary cell.