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

Abstract

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. This complex behaviour is accounted for with a comprehensive set of kinematic and dynamic junction conditions. Modal analysis demonstrates the fully coupled system and reveals how the spinning gyroscope induces dynamic chiral Chladni patterns in the plate. This article is part of the theme issue ‘Current developments in elastic and acoustic metamaterials science (Part 2)’.