Identifying, evaluating, and controlling dynamical integrity measures in non-linear mechanical oscillators

The erosion curves for the Helmholtz, the Duffing and rigid block oscillators are constructed to investigate the loss of integrity in different mechanical systems. Various definitions of safe basin and integrity measures are reviewed, compared with each other and applied to the considered cases. A control method aimed at shifting the erosion profiles towards larger excitation amplitudes is considered, too, and its main features are discussed in depth.