Multi-parametric analysis of the lowest natural frequencies of strongly inhomogeneous elastic rods

The results of a multi-parametric analysis of the near-rigid body motions of a three-component strongly inhomogeneous elastic rod are presented. It is demonstrated that the values of the associated lowest natural frequencies tend to zero at large/small ratios of material and geometric parameters. The low-frequency behaviour is classified into global and local regimes and the general conditions supporting global low-frequency regimes are derived. As an example, a rod with piecewise uniform properties is considered. A perturbation procedure oriented to a more general setup is developed.