Yuri Trakht

Yuri Trakht, MSc

The present research uses analytical and numerical tools to study the vibrations of an elastic ring under parametric excitation. Parametric excitation can create large amplitude vibration and traveling waves. It is shown that periodic and uniform elongation of the neutral axis, tuned to a frequency which is the sum of bending and torsion natural frequencies, gives rise to parametric resonance and to large amplitude traveling transverse vibration waves.

 

Circular ring section

Analytical Modal Analysis

Strutt diagrams- axis is linear and y axis is logarithmic, the red zones are unstable zones where one of the eigenvalue is outside the unit circle

Steady State solution of the PDE in Time and Space