Sommerfeld effect concerns the non-linear jump phenomena induced due to the influence of the unbalance response on a non-ideal drive around the critical speed of the excited structure. In this work, we study the influence of external and internal dampings and gyroscopic forces on the Sommerfeld effect in rotationally symmetric planar dynamical systems. The rotational symmetry assumption allows ...

The dynamic response of an axially translating continuum subjected to the combined effects of a pair of spring supported frictional guides and axial acceleration is investigated; such systems are both non-conservative and gyroscopic. The continuum is modeled as a tensioned string translating between two rigid supports with a time dependent velocity profile. The equations of motion are derived w...

In this article, a model of rotor with an asymmetric disk is presented in order to represent Campbell’s diagrams and instability maps as function the rotations support which can significantly change dynamic behavior rotor. Critical rotating speeds also lead unacceptable levels vibration. Indeed, critical are rigidity systems presence gyroscopic forces creates dependence between speed rotation n...

Topological mechanical metamaterials are artificial structures whose unusual properties are protected very much like their electronic and optical counterparts. Here, we present an experimental and theoretical study of an active metamaterial--composed of coupled gyroscopes on a lattice--that breaks time-reversal symmetry. The vibrational spectrum displays a sonic gap populated by topologically p...