Parametric Resonance in Mechanics: Classical Problems and New Results

Abstract

We formulate and solve parametric resonance problems for one-and multiple degrees of freedom systems in three-dimensional space of physical parameters: excitation frequency, amplitude, and viscous damping coefficient assuming that the last two parameters are small. The main result obtained here is that we find the instability domains (simple and combination parametric resonances) as half-cones in three-parameter space with the use of eigenfrequencies and eigenmodes of the corresponding conservative system.

Vibrational Stabilization by Reshaping Arnold Tongues: A Numerical Approach

“…Some classical references are: [1] [7]- [9], while more recently there are [10]- [13], and some others. Less attention has been dedicated to the Arnold Tongues computation [10], maybe because the most common method of study would be numerical integration.…”