The perpendicular gyroscope: modal analysis of plate, beam and gyroscope multistructures.

This paper presents a study of the perpendicular gyroscope, which is formed of two orthogonal beams, a flexural plate and a gyroscope. Two sets of chiral-torsional boundary conditions are derived to analytically model the dynamic effects of the gyroscope while taking into account the broken symmetries of the system. The perpendicular junction causes the coupling of the compressional, flexural and torsional displacements in the system.

Negative refraction and mode trapping of flexural-torsional waves in elastic lattices.

We consider the propagation of flexural and torsional waves in a square lattice of Euler-Bernoulli beams. The refraction and reflection of waves across interfaces between two dissimilar lattices is investigated. By carefully controlling the inertial and elastic properties of the lattice elements, we demonstrate that it is possible to induce negative refraction and other associated phenomena.